1. How much work is done by a crane lifting a 200.0 kg crate from the ground to a floor 21.0 m above the ground. What is the change in gravitational potential energy of the crate?
2. A 25-kg box slides, from rest, down a 9.0-m-long incline that makes an angle of 15° with the horizontal. The speed of the box when it reaches the bottom of the incline is 2.4 m/s.
a. What is the coefficient of kinetic friction between the box and the surface of the incline?
b. How much work is done on the box by the force of friction and
c. What is the change in the potential energy of the box?
3. A 40.0-kg wagon is towed up a hill inclined at 18.5º with respect to the horizontal. the tow rope is parallel to the incline and has a tension of 140N in it. Assume that the wagon starts from rest at the bottom of the hill, and neglect friction. How fast is the wagon going after moving 80 m up the hill?
4. A 25.6kg child pulls a 4.81kg toboggan up a hill inclined at 25.7° to the horizontal. The vertical height of the hill is 27.3 m. Friction is negligible. Determine how much work the child must do on the toboggan to pull it at a constant velocity up the hill.
5. An 81.0-kg in-line skater does +3500 J of nonconservative work by pushing against the ground with his skates. In addition, friction does -710 J of nonconservative work on the skater. The skater's initial and final speeds are 2.50 m/s and 1.60 m/s, respectively. (a) Has the skater gone uphill, downhill, or remained at the same level? (b) Calculate the change in height of the skater.
6. A solid object with mass (m) is initially at rest. An applied constant vertical force (F) causes the object to reach an upward speed (V), and total displacement (h). Use newton's second law to derive an expression (in terms of m,g,h, & V) for the work.
1. A cart moving along a track 1.00 m above the floor at 3 m/s eventually reaches a higher plateau What is the maximum height of the plateau above the floor?
2. A 10.5 g bullet strikes a pendulum that consists of a block of wood of mass 3.00 kg suspended by a cord. The bullet gets embedded in the block. How fast was the bullet traveling just before impact to raise the block by 0.220 m?
3. Sheila, running 5.3m/s, grabs a vine hanging vertically from a tall tree.
a. How high can she swing upward?
b. Does the length of vine affect the answer?
4. A roller coaster at the top of a 39.0 m high vertical loop is traveling 13.8 m/s. Find the maximum speed of the cars as they move through the bottom of the loop.
5. Analyze the motion of a simple swinging pendulum in terms of energy, (a) ignoring friction; and (b) taking friction into account. Explain why a grandfather clock has to be wound up.
6. A ball is attached to a horizontal cord of length L whose other end is fixed.
a. If the ball is released, what will be its speed at the lowest point of its path?
b. A peg is located a distance h directly below the point of attachment of the cord. If h= 0.080L, what will be the speed of the ball when it reaches the top of the circular path about the peg?
7. A projectile is fired at an upward angle of 45.0 degree from the top of a 265 m cliff with a speed of 185 m/s. What will be its maximum speed of impact with the ground below?
8. If a projectile is launched from Earth with a speed equal to the escape speed, how high above the Earth's surface is it when its speed is one third the escape speed?
9. Two pieces of space debris, each with a mass of 0.116 kg, are separated by a distance of 380 m. If re released from rest, what speed do they have when their separation has decreased to 171 m? Ignore the gravitational effects from any other objects.
10. A baseball is thrown first with an initial upward velocity of + 4.0 m/s. Later, it is thrown from the same height but with and initial downward velocity of -3.0m/s. How do the impact velocities of the baseball with the ground differ? What is its acceleration in each case?
11. A 200 g ball is thrown upwards with an initial kinetic energy of 10 Joules. What maximum height will the ball attain?
12. Bruce grasps the end of a 20.0 m long rope attached to a tree and swings. If the rope starts at an angle 35 degrees with the vertical, what is Bruce's speed at the bottom of the swing?
13. Jack and Jill, whose total mass is 120 kg, sit on a swing at the end of a 5m long rope. Initially the rope attached to their swing makes an angle of 36 degrees with the horizontal. At the bottom of the arc, Jill, whose mass is 52 kg, steps off. What is the maximum height Jack can reach as the swing continues?
14.
a. A 1.9-kg block slides down a curved, frictionless ramp. The top of the ramp is 1.5 m above ground; the bottom of the ramp is 0.25 m above the ground. The block leaves the bottom of the ramp moving horizontally. What horizontal distance away from the base of the ramp does it land?
b. Suppose friction on the ramp does -9.7 J of work on the block. What horizontal distance away from the base of the ramp does it land?
15. A ball bounces upward from the ground with a speed of 16 m/s and hits a wall with a speed of 12 m/s How high above the ground does the ball hit the wall? Ignore air resistance.
16. From what height would a car have to be dropped to have the same kinetic energy that it has when being driven at 100 km/h?
17. A 135 m long ramp is to be built for a ski jump. If a skier starting from rest at the top is to have a speed no faster than 19m/s at the bottom, what should be the maximum angle of inclination?
18. Show that the escape speed from the surface of a planet of uniform density is directly proportional to the radius of the planet.
19. Two objects, m1 = 4.50kg and m2 = 3.00kg, are connected by a light string passing over a light frictionless pulley. The object of the mass 4.50kg is released from rest 4.50m above the ground. Using the principle of conservation of energy, determine the speed of the 3.00kg object just as the 4.50kg object hits the ground.
20.
(a) What is the escape speed on a spherical asteroid whose radius is 525km and whose gravitational acceleration at the surface is 2.7m/s2?
(b.)How far from the surface will a particle go if it leaves the asteroid's surface with a vertical speed of 1000m/s?
21. In a looping the loop setup, an object of mass m is released from rest from A with the initial height h and loops the loop in the circular track of radius R.
a) Write an expression for the initial mechanical energy at A in terms of m, g, h
b) Write an expression for energy at point B at the top of the vertical circle in terms of mass m, velocity v, radius R and g
c) If in the absence of friction the object just manages to loop the loop without losing contact with the track, what is the minimum height h from which you will need to release the object? Write the expression in terms of R .
22. A 75 kg parcel falls out of a window to a sidewalk 1 m below.
a. With what speed does it impact the pavement?
b. If the packaging provides 0.50 cm of cushioning, calculate the average force exerted on the parcel by the ground in this situation.
23. Roy was transporting balls in the trunk of a car to a clubhouse. Two boxes on the floor of the trunk each contained an equal number of balls. The balls were identical except that all the balls in one box were dimpled, while all the balls in the other box were smooth. Upon arriving, Roy realized there were no lids on the boxes, and found balls all over the trunk of the car. He observed that more dimpled balls escaped than smooth balls. Why would more dimpled balls escape than smooth balls? There was nothing else in the trunk.
Showing posts with label [AS Phy-1] Mechanics. Show all posts
Showing posts with label [AS Phy-1] Mechanics. Show all posts
Saturday, November 20, 2010
Work and Kinetic Energy
1. A boy pushes a 5.00 kg cart in a circle, starting at 0.500 m/s and accelerating to 3.00 m/s. How much work was done on the cart?
2. A 30.0 kg box initially sliding at 5.00 m/s on a rough surface is brought to rest by 20.0 N of friction. What distance does the box slide?
3. A 1000.0 kg truck accelerates from 20.0 m/s to 25.0 m/s over a distance of 300.0 m. What is the average net force on the truck?
4. A space ship of mass 5.00 ×104 kg is traveling at a speed 1.15 × 104 m/s in outer space. Except for the force generated by its own engine, no other force acts on the ship. As the engine exerts a constant force of 4.00 × 105 N, the ship moves a distance of 2.50 × 106 m in the direction of the force of the engine.
a. Determine the final speed of the ship using the work-energy theorem.
b. Determine the final speed of the ship using the kinematics equations.
5. A force of 6.0 N is used to accelerate a mass of 1.0 kg from rest for a distance of 12m. The force is applied along the direction of travel. The coefficient of kinetic friction is 0.30. What is the
a. work done by the applied force?
b. work done by friction?
c. kinetic energy at the 12-m mark?
6. A 0.600-kg particle has speed of 2.00 m/s at point A and kinetic energy of 7.50 J at point B. What is
a. its kinetic energy at A?
b. its speed at B?
c. the total work done on the particle as it moves from A to B?
7. Two carts, one twice the mass of the other, experience the same force for the same time. What is their difference in momentum? What is their difference in kinetic energy?
8. A weapon fired a 25.8-kg shell with a muzzle speed of 880 m/s. What average force acted on the shell?
9. A catcher stops a 91 mi/h pitch in his glove, bringing it to rest in 0.00179 m. If force exerted by the catcher is 785 N, what is the mass of the ball?
10. A 7.80 kg package was dropped onto a flatbed moving horizontally at 1.60 m/s. The coefficients of friction are as follows: µs= 0.470 and µk = 0.150 . How far does the package slide on the flatbed?
11. A 12.4 g bullet is fired horizontally into a 96 g wooden block initially at rest on a horizontal surface. After impact, the block slides 7.5 m before coming to rest. If the coefficient of kinetic friction between block and surface is 0.650, what was the speed of the bullet immediately before impact?
12. A toy cart moves with a kinetic energy of 30 J. If its speed is doubled, what is its kinetic energy?
13. A car traveling 59 miles/hour locks its brakes until the car reaches 42 miles/hour. The mass of the car is 79.2 slugs. Calculate the energy lost to friction.
14. A 70 kg diver steps off a 10 m tower and drops from rest straight down into the water. If he comes to rest 5 m beneath the surface, determine the average force exerted by the water.
15. A 1300-kg car slows from 18 m/s to 15 m/s through a distance of 30 m. (a) Was the net work done on the car positive, negative, or zero? Explain. (b) Find the magnitude of the average net force on the car in the sandy section.
2. A 30.0 kg box initially sliding at 5.00 m/s on a rough surface is brought to rest by 20.0 N of friction. What distance does the box slide?
3. A 1000.0 kg truck accelerates from 20.0 m/s to 25.0 m/s over a distance of 300.0 m. What is the average net force on the truck?
4. A space ship of mass 5.00 ×104 kg is traveling at a speed 1.15 × 104 m/s in outer space. Except for the force generated by its own engine, no other force acts on the ship. As the engine exerts a constant force of 4.00 × 105 N, the ship moves a distance of 2.50 × 106 m in the direction of the force of the engine.
a. Determine the final speed of the ship using the work-energy theorem.
b. Determine the final speed of the ship using the kinematics equations.
5. A force of 6.0 N is used to accelerate a mass of 1.0 kg from rest for a distance of 12m. The force is applied along the direction of travel. The coefficient of kinetic friction is 0.30. What is the
a. work done by the applied force?
b. work done by friction?
c. kinetic energy at the 12-m mark?
6. A 0.600-kg particle has speed of 2.00 m/s at point A and kinetic energy of 7.50 J at point B. What is
a. its kinetic energy at A?
b. its speed at B?
c. the total work done on the particle as it moves from A to B?
7. Two carts, one twice the mass of the other, experience the same force for the same time. What is their difference in momentum? What is their difference in kinetic energy?
8. A weapon fired a 25.8-kg shell with a muzzle speed of 880 m/s. What average force acted on the shell?
9. A catcher stops a 91 mi/h pitch in his glove, bringing it to rest in 0.00179 m. If force exerted by the catcher is 785 N, what is the mass of the ball?
10. A 7.80 kg package was dropped onto a flatbed moving horizontally at 1.60 m/s. The coefficients of friction are as follows: µs= 0.470 and µk = 0.150 . How far does the package slide on the flatbed?
11. A 12.4 g bullet is fired horizontally into a 96 g wooden block initially at rest on a horizontal surface. After impact, the block slides 7.5 m before coming to rest. If the coefficient of kinetic friction between block and surface is 0.650, what was the speed of the bullet immediately before impact?
12. A toy cart moves with a kinetic energy of 30 J. If its speed is doubled, what is its kinetic energy?
13. A car traveling 59 miles/hour locks its brakes until the car reaches 42 miles/hour. The mass of the car is 79.2 slugs. Calculate the energy lost to friction.
14. A 70 kg diver steps off a 10 m tower and drops from rest straight down into the water. If he comes to rest 5 m beneath the surface, determine the average force exerted by the water.
15. A 1300-kg car slows from 18 m/s to 15 m/s through a distance of 30 m. (a) Was the net work done on the car positive, negative, or zero? Explain. (b) Find the magnitude of the average net force on the car in the sandy section.
Work done, Energy and Power
1. A man pushes against a car stuck in a snow bank while his date sits nervously behind the steering wheel trying not to make the tires spin. [Other distracting details are usually given, often including numeric information regarding force, weight and so on.] However, the car does not move. How much work did he do on the car?
Answer: The man did no work on the car since d=0. He may have burned calories, converting chemical energy into heat, but still, the car did not move.
2. Sally carries a text book under her arm along a horizontal path. [Distracting information is often also given such as the weight or mass of the text book, the distance or more perversely the path taken implying some distance must be calculated and so on.] How much work was done on the text book?
Answer: None, since both gravity and the force Sally exerted against gravity are perpendicular to the distance the book moved. (cosø = 0 so W = 0).
3. An asteroid traveling at constant velocity out of reach of gravitational fields [etc.]... How much work is done on the satellite?
Answer: None, since F = 0, W = 0.
Another type of question gives the wrong angle.
4. A 200.0 kg load on frictionless coasters is pushed 5 m along a ramp that makes an angle of 20º to the ground. How much work was done on the cart?
Answer: Drawing a diagram is a must for any problem involving 2 dimensions or 2 or more forces.
When you do this, the glitch becomes obvious: the angle is not between the force and the distance. The angle between the force and the distance is 70º.
The force applied against gravity is F = mg = (200.0 kg)(9.8 N/kg) = 1960 N
Therefore, W = Fdcosø = 1960(5)(cos70º) = 3352 J
5. A 70 kg cart is pushed for 50 m with a constant velocity upon a 45º frictionless incline. Find the work done on the cart.
6. A 100 kg object is pulled vertically upward 5.0 m by a rope with an acceleration of 1.0 m/s2. Find the work done by the tension force in the rope.
7. A 0.40 kg ball is thrown vertically upward with a speed of 30 m/s. The ball reaches a height of 40 m. What is the energy dissipated due to air friction?
8. If 4 kW of power is dissipated for 30 min, how much energy was involved?
9. A tug pulls on a barge with a constant force of 2.50*106 N, 19° west of north. Another tug pulls on the same barge with the same force but 19° east of north. . What is the total work they done on the barge it is pulled 0.74 km toward the north?
10. A conveyor belt moves for 2.0 m horizontally, then for 2.0 m down an incline angled 10° from the horizontal. A 2.0 kg box is moved by the belt at 0.50 m/s without slipping. At what rate is work being done on the box
a. as the box moves up the 10° incline
b. as the box moves horizontally
11. A 40 kg case is pushed across a floor at a steady speed of 1.5 m/s. When the pushing stops, the case slides a further distance of 1.2 m before coming to rest. Calculate:
a. The frictional force acting on the case when it slides.
b. The work done per second to push the case at a steady speed of 1.5 m/s.
12. A generator harnesses water flowing through a tube 12.5 feet in diameter. About 50% of the kinetic energy of the water is converted to electricity. How fast must the water flow to produce 52 MW of electrical power?
13. A 130 N suitcase is dragged a distance of 250m at a constant speed. A force of 60 N is exerted at an angle 40 degrees above the horizontal.
a. How much work is being done?
b. How much work is done by friction?
14. How many kilocalories of food energy does a person with a metabolic rate of 97.0 W burn per day?
15. A 1000 kg rocket generating 80 kW of power gains altitude at 3.0 m/s. What percentage of the engine power is being used to make the rocket climb?
16. How does a person burn calories by just breathing?
17. Calculate the work done by a force acting through a distance, d, if the force changes over the distance according to
F = kx4.
18. Can the normal force on an object ever do work?
19. If 6 million J of energy is consumed in a day, what is this rate of energy consumption in watts?
20. A force of 109 N is applied along along a lawnmower's handle, which is 14.7 degrees above the horizontal. If 61.9 W of power was developed for 39 s, what distance is the roller pushed?
21. Suggest a method to mesure the power in your legs. Outline the calculations involved.
22. A 1900 kg car experiences a combined force of air resistance and friction that has the same magnitude whether the car goes up or down a hill at 27 m/s. Going up a hill, the car's engine needs to produce 47 hp more power to sustain the constant velocity than it does going down the same hill. At what angle is the hill inclined above the horizontal?
23. Find the work done by pushing a mass of 700 kg through a distance of 4.5m along a surface if the coefficient of friction is 0.2. Assume the force is applied horizontally.
24. At a speed of 70 km/h, the average frictional force on a light car is 1050 N. What power must the motor generate to maintain this speed?
25. A winch is used to slide a 350 kg load at constant speed 3.50 m down a 27.0° incline. The rope between the winch and the load is parallel to the incline. The coefficient of kinetic friction between the ramp and the load is 0.40. Calculate the force exerted by the winch, the work done by the winch on the load, the work done by the friction force, the work done by the force of gravity, and the net work done on the load.
26. A 60 kg person developed 70 W of power during a race, dissipating about 0.60 J of mechanical energy per step per kilogram of body mass. If each stride was about 1.5 m, how fast was the person running?
Answer: The man did no work on the car since d=0. He may have burned calories, converting chemical energy into heat, but still, the car did not move.
2. Sally carries a text book under her arm along a horizontal path. [Distracting information is often also given such as the weight or mass of the text book, the distance or more perversely the path taken implying some distance must be calculated and so on.] How much work was done on the text book?
Answer: None, since both gravity and the force Sally exerted against gravity are perpendicular to the distance the book moved. (cosø = 0 so W = 0).
3. An asteroid traveling at constant velocity out of reach of gravitational fields [etc.]... How much work is done on the satellite?
Answer: None, since F = 0, W = 0.
Another type of question gives the wrong angle.
4. A 200.0 kg load on frictionless coasters is pushed 5 m along a ramp that makes an angle of 20º to the ground. How much work was done on the cart?
Answer: Drawing a diagram is a must for any problem involving 2 dimensions or 2 or more forces.
When you do this, the glitch becomes obvious: the angle is not between the force and the distance. The angle between the force and the distance is 70º.
The force applied against gravity is F = mg = (200.0 kg)(9.8 N/kg) = 1960 N
Therefore, W = Fdcosø = 1960(5)(cos70º) = 3352 J
5. A 70 kg cart is pushed for 50 m with a constant velocity upon a 45º frictionless incline. Find the work done on the cart.
6. A 100 kg object is pulled vertically upward 5.0 m by a rope with an acceleration of 1.0 m/s2. Find the work done by the tension force in the rope.
7. A 0.40 kg ball is thrown vertically upward with a speed of 30 m/s. The ball reaches a height of 40 m. What is the energy dissipated due to air friction?
8. If 4 kW of power is dissipated for 30 min, how much energy was involved?
9. A tug pulls on a barge with a constant force of 2.50*106 N, 19° west of north. Another tug pulls on the same barge with the same force but 19° east of north. . What is the total work they done on the barge it is pulled 0.74 km toward the north?
10. A conveyor belt moves for 2.0 m horizontally, then for 2.0 m down an incline angled 10° from the horizontal. A 2.0 kg box is moved by the belt at 0.50 m/s without slipping. At what rate is work being done on the box
a. as the box moves up the 10° incline
b. as the box moves horizontally
11. A 40 kg case is pushed across a floor at a steady speed of 1.5 m/s. When the pushing stops, the case slides a further distance of 1.2 m before coming to rest. Calculate:
a. The frictional force acting on the case when it slides.
b. The work done per second to push the case at a steady speed of 1.5 m/s.
12. A generator harnesses water flowing through a tube 12.5 feet in diameter. About 50% of the kinetic energy of the water is converted to electricity. How fast must the water flow to produce 52 MW of electrical power?
13. A 130 N suitcase is dragged a distance of 250m at a constant speed. A force of 60 N is exerted at an angle 40 degrees above the horizontal.
a. How much work is being done?
b. How much work is done by friction?
14. How many kilocalories of food energy does a person with a metabolic rate of 97.0 W burn per day?
15. A 1000 kg rocket generating 80 kW of power gains altitude at 3.0 m/s. What percentage of the engine power is being used to make the rocket climb?
16. How does a person burn calories by just breathing?
17. Calculate the work done by a force acting through a distance, d, if the force changes over the distance according to
F = kx4.
18. Can the normal force on an object ever do work?
19. If 6 million J of energy is consumed in a day, what is this rate of energy consumption in watts?
20. A force of 109 N is applied along along a lawnmower's handle, which is 14.7 degrees above the horizontal. If 61.9 W of power was developed for 39 s, what distance is the roller pushed?
21. Suggest a method to mesure the power in your legs. Outline the calculations involved.
22. A 1900 kg car experiences a combined force of air resistance and friction that has the same magnitude whether the car goes up or down a hill at 27 m/s. Going up a hill, the car's engine needs to produce 47 hp more power to sustain the constant velocity than it does going down the same hill. At what angle is the hill inclined above the horizontal?
23. Find the work done by pushing a mass of 700 kg through a distance of 4.5m along a surface if the coefficient of friction is 0.2. Assume the force is applied horizontally.
24. At a speed of 70 km/h, the average frictional force on a light car is 1050 N. What power must the motor generate to maintain this speed?
25. A winch is used to slide a 350 kg load at constant speed 3.50 m down a 27.0° incline. The rope between the winch and the load is parallel to the incline. The coefficient of kinetic friction between the ramp and the load is 0.40. Calculate the force exerted by the winch, the work done by the winch on the load, the work done by the friction force, the work done by the force of gravity, and the net work done on the load.
26. A 60 kg person developed 70 W of power during a race, dissipating about 0.60 J of mechanical energy per step per kilogram of body mass. If each stride was about 1.5 m, how fast was the person running?
Free fall
A. Drop /Throw Down Problems
1. A peso is dropped into a well and it falls for 3 seconds before hitting the water. What is the peso's average speed during its 3 second drop?
2. A rock is dropped from the top of an overhang and strikes the ground 6.5 seconds later. How high is the overhang in meters?
3. It takes 0.210s for a dropped wrench to travel past a poster that is 1.35 meters tall. How high above the top of the poster was the wrench released?
4. A falling paratrooper (100 kg with parachute) experiences air resistance equal to 25% of his weight. What is his acceleration?
5. Consider a transparent elevator accelerating upward with acceleration equal to that of the gravity. If a rock was dropped inside the elevator, what would an observer on the ground see the rock do?
B. Throw Up Problems
1. You throw a ball downward from a window at a speed of 2.0 m/s. The ball accelerates at 9.8 m/s2.
a. How fast is it moving when it hits the sidewalk 2.5 m below?
b. If you throw the same ball up instead of down, how fast is it moving when it hits the sidewalk?
2. A ball is thrown straight up with a speed of 4.6 m/s. How long does the ball take to reach its maximum height?
3. A round is launched straight up at 460 m/s. How long will it take it to reach its apex and how high will that be? (air resistance may be neglected.)
4. What height will a dart achieve 7 seconds after being blown straight up at 50 m/s?
5. An apple thrown straight upward rises to 24 m above its launch point. At what height has apple's speed decreased to one-half of its initial value?
6. A stone is flung straight up from a point 1.50 m above the ground and with an initial speed of 19.6 m/s.
a. What is the stone's maximum height above the ground?
b. How much time passes before the stone hits the ground?
7. A blimp is hovering above the ground. When the pilot drops a sandbag overboard, the blimp rises with a constant velocity of 2 m/s. At the moment the sandbag hits the ground, the blimp is 50 m above the ground.
a. How far above the ground was the blimp when the sandbag was dropped?
b. When the sandbag is halfway to the ground, what is its acceleration?
8. A helicopter is ascending vertically with a speed of 5.00 m/s. At a height of 105 m above the ground, a package is dropped from a window. How much time does it take for the package to reach the ground?
9. A rock is thrown up at an initial velocity of 9.8 m/s. What is the time it takes to hit the ground?
C. Catch Up Problems
1. An archer shoots an arrow with an initial velocity of 21 m/s straight up from his bow. He quickly reloads and shoots another arrow in the same way 3.0 s later. At what time and height do the arrows meet?
2. A hoist is lifting a naturalist to the top of a cliff at 2.03 m/s vertically. The naturalist suddenly realizes she has left her pet rock behind. A friend picks it up and tosses it straight upward. If the naturalist is 2.50 m above her friend, what is the minimum initial speed the pet rock must have to reach the naturalist?
3. A boy shoots a rock from his slingshot at a target just as the target drops from a tree branch. Should the boy aim a little above the target, a little below the target, or straight at the target?
1. A peso is dropped into a well and it falls for 3 seconds before hitting the water. What is the peso's average speed during its 3 second drop?
2. A rock is dropped from the top of an overhang and strikes the ground 6.5 seconds later. How high is the overhang in meters?
3. It takes 0.210s for a dropped wrench to travel past a poster that is 1.35 meters tall. How high above the top of the poster was the wrench released?
4. A falling paratrooper (100 kg with parachute) experiences air resistance equal to 25% of his weight. What is his acceleration?
5. Consider a transparent elevator accelerating upward with acceleration equal to that of the gravity. If a rock was dropped inside the elevator, what would an observer on the ground see the rock do?
B. Throw Up Problems
1. You throw a ball downward from a window at a speed of 2.0 m/s. The ball accelerates at 9.8 m/s2.
a. How fast is it moving when it hits the sidewalk 2.5 m below?
b. If you throw the same ball up instead of down, how fast is it moving when it hits the sidewalk?
2. A ball is thrown straight up with a speed of 4.6 m/s. How long does the ball take to reach its maximum height?
3. A round is launched straight up at 460 m/s. How long will it take it to reach its apex and how high will that be? (air resistance may be neglected.)
4. What height will a dart achieve 7 seconds after being blown straight up at 50 m/s?
5. An apple thrown straight upward rises to 24 m above its launch point. At what height has apple's speed decreased to one-half of its initial value?
6. A stone is flung straight up from a point 1.50 m above the ground and with an initial speed of 19.6 m/s.
a. What is the stone's maximum height above the ground?
b. How much time passes before the stone hits the ground?
7. A blimp is hovering above the ground. When the pilot drops a sandbag overboard, the blimp rises with a constant velocity of 2 m/s. At the moment the sandbag hits the ground, the blimp is 50 m above the ground.
a. How far above the ground was the blimp when the sandbag was dropped?
b. When the sandbag is halfway to the ground, what is its acceleration?
8. A helicopter is ascending vertically with a speed of 5.00 m/s. At a height of 105 m above the ground, a package is dropped from a window. How much time does it take for the package to reach the ground?
9. A rock is thrown up at an initial velocity of 9.8 m/s. What is the time it takes to hit the ground?
C. Catch Up Problems
1. An archer shoots an arrow with an initial velocity of 21 m/s straight up from his bow. He quickly reloads and shoots another arrow in the same way 3.0 s later. At what time and height do the arrows meet?
2. A hoist is lifting a naturalist to the top of a cliff at 2.03 m/s vertically. The naturalist suddenly realizes she has left her pet rock behind. A friend picks it up and tosses it straight upward. If the naturalist is 2.50 m above her friend, what is the minimum initial speed the pet rock must have to reach the naturalist?
3. A boy shoots a rock from his slingshot at a target just as the target drops from a tree branch. Should the boy aim a little above the target, a little below the target, or straight at the target?
Projectiles
1. A golf ball is projected with a horizontal velocity of 30 m/s and takes 4.0 seconds to reach the ground. (Assume g= 10 m/s² and the air resistance is negligible.) Calculate: the height from which the golf ball was projected. The magnitude of the golf balls' vertical velocity component just before hitting the ground. The horizontal velocity component. Resultant velocity just before the object strikes the ground. The horizontal component of the object's displacement.
2. Erica kicks a soccer ball 12 m/s at an angle of 40 degrees above the horizontal.
a. What is the ball's maximum height?
b. What is the ball's maximum range?
c. With what velocity does the ball strike the ground?
d. What are the ball's acceleration and velocity at the top of its rise?
A Horizontal Projectile Motion
1. Erica kicks a soccer ball 12 m/s at horizontally from the edge of the roof of a building which is 30.0 m high.
a. When does it strike the ground?
b. With what velocity does the ball strike the ground?
2. A car drives straight off the edge of a cliff that is 54 m high. The police at the scene of the accident note that the point of impact is 130 m from the base of the cliff. How fast was the car traveling when it went over the cliff?
3. A ball thrown horizontally at 22.2 m/s from the roof of a building lands 36 m from the base of the building. How tall is the building?
4. A boy kicked a can horizontally from a 6.5 m high rock with a speed of 4.0 m/s. How far from the base of the rock the can land?
5. A pilot flying a constant 215 km/h horizontally in a low-flying helicopter, wants to drop secret documents into his contact"s open car which is traveling 155 km/h in the same direction on a level highway 78.0 m below. At what angle (to the horizontal) should the car be in his sights when the packet is released?
6. A ski jumper travels down a slope and leaves the ski track moving in the horizontal direction with a speed of 25 m/s. The landing incline falls off with a slope of 33º.
a. How long is the ski jumper air borne?
b. Where does the ski jumper land on the incline?
7. Stones are thrown horizontally with the same velocity. One stone lands twice as far as the other stone. What is the ratio of the height of the taller building to the height of the shorter?
8. A fleck moving horizontally to the right at 2.5 m/s begins to accelerate downward at 0.75 m/s2 . Where is the fleck 4.0 s later?
B General Projectile Motion
1. In example 2, if Erica kicked the ball from the edge of the roof of a building which is 30.0 m high.
a. When does it strike the ground?
b. How far from the building does it land?
2 . A daredevil decides to jump a canyon of width 10 m. To do so, he drives a motorcycle up an incline sloped at an angle of 15 degrees. What minimum speed must he have in order to clear the canyon?
3. A ball is kicked from a point 38.9 m away from the goal. The crossbar is 3.05 m high. If the ball leaves the ground with a speed of 20.4 m/s at an angle of 52.2º to the horizontal
a. By how much does the ball clear or fall short of clearing the crossbar?
b. What is the vertical velocity of the ball at the time it reaches the crossbar?
4. A rocket is accelerating vertically upward at 30 m/s2 near Earth's surface. A bolt separates from the rocket. What is the acceleration of the bolt?
5. Water is leaving a hose at 6.8 m/s. If the target is 2 m away horizontally, What angle should the water have initially?
6. A 5.0 kg brick lands 10.1 m from the base of a building. If it was given an initial velocity of 8.6 m/s [61º above the horizontal], how tall is the building?
7. A spear is thrown upward from a cliff 48 m above the ground. Given an initial speed of 24 m/s at an angle of 30º to the horizontal,
a. how long is the spear in flight?
b. what is the magnitude and direction of the spear's velocity just before it hits the ground?
8. A projectile is shot from the edge of a cliff 125 m above ground level with an initial speed of 65.0 m/s at an angle of 37º above the horizontal. Determine the the magnitude and the direction of the velocity at the maximum height.
9. A projectile leaves a gun at the same instant that the target is dropped from rest. If the projectile is initially aimed straight at the target, will it hit the target?
10. A basketball is lobbed toward a hoop 3.05 m above the floor. If released 2 m above the floor 10 m from the basket and at a 45 degree angle, how fast must the basketball be thrown so that it goes through the hoop?
11. Dick is tossing chocolates up to Jane's window from 8.0 m below her window and 9.0 m from the base of the wall. If the chocolates are traveling horizontally through the open window, how fast are they going through her window?
12. A projectile has an initial velocity of 15.0 m/s at an angle of 30 degrees above the horizontal. What is the location of the projectile 2.0 seconds later?
13. If a ball is kicked with an initial velocity of 25 m/s at an angle of 60° above the ground, what is the "hang time"?
14. A water balloon hits a target 26 m away, at the same height as the release point. The horizontal component of the initial velocity was 5 m/s. What was the vertical component of the initial velocity? What was the launch angle?
15. A soccer ball leaves a cliff 20.2 m above the valley floor, at an angle of 10 degrees above the horizontal. The ball hits the valley floor 3.0 seconds later. What is the initial velocity of the ball? What maximum height above the cliff did the ball reach?
16. A flea stands 2.00 m from a dog's haunches .55m in height. Jumping at an angle of 32 degrees, what initial speed must the flea have to reach her new home?
17. A bullet hit a target 301.5m away. What maximum height above the muzzle did the bullet reach if it was shot at an angle of 25 degree to the ground?
18. A 3.00 kg parcel is dropped out of a window from a height of 176.4 m. Wind exerts an average 12.0 N force on the parcel away from the building. How long is the parcel in the air? Where does it land? What is its impact velocity?
19. A projectile is shot from the ground at an angle of 60 degrees with respect to the horizontal, and it lands on the ground 5 seconds later. Find:
a. the horizontal component of initial velocity
b. the vertical component of initial velocity
c. initial speed
20. An arrives 30m away horizontally and 5m above the point from which it was launched. It reaches this point 3 seconds after it was launched. Find:
a. the horizontal component of initial velocity
b. the vertical component of initial velocity
c. the vertical component of the impact velocity
d. the horizontal component of the impact velocity
21. Find the minimum initial speed of a champagne cork that travels a horizontal distance of 11 meters.
22. During practice, a soccer player kicks a ball, giving it a 32.5 m/s initial speed. It travels the maximum possible distance before landing down field.
(a) How much time does the ball spend in the air?
(b) How far did the ball travel?
23. A projectile was launched 64° above the horizontal, attaining a height of 10 m. What is the projectile's initial speed?
24. At what launch angle will the range of a projectile equal its maximum height?
25. A boy kicks a soccer ball directly at a wall 41.8 m away. The ball leaves the ground at 42.7 m/s with an angle of 33.0 degrees to the ground. What height will the ball strike the wall?
26. What is the relationship between the maximum height of the projectile, the projectile's range, and the launch angle?
27. A projectile is fired with an initial velocity of 120 m/s at an angle above the horizontal. If the projectile's initial horizontal speed is 55 m/s, then at what angle was it fired?
28. A boulder rolls 35 m down a hill, starting from rest and accelerating at 3.06 m/s2. The boulder then rolls off a 45 m high vertical cliff, launching at 19.0° below the horizontal. (a) How far from the cliff's base does the boulder land? (b) How much time does the boulder spend falling?
2. Erica kicks a soccer ball 12 m/s at an angle of 40 degrees above the horizontal.
a. What is the ball's maximum height?
b. What is the ball's maximum range?
c. With what velocity does the ball strike the ground?
d. What are the ball's acceleration and velocity at the top of its rise?
A Horizontal Projectile Motion
1. Erica kicks a soccer ball 12 m/s at horizontally from the edge of the roof of a building which is 30.0 m high.
a. When does it strike the ground?
b. With what velocity does the ball strike the ground?
2. A car drives straight off the edge of a cliff that is 54 m high. The police at the scene of the accident note that the point of impact is 130 m from the base of the cliff. How fast was the car traveling when it went over the cliff?
3. A ball thrown horizontally at 22.2 m/s from the roof of a building lands 36 m from the base of the building. How tall is the building?
4. A boy kicked a can horizontally from a 6.5 m high rock with a speed of 4.0 m/s. How far from the base of the rock the can land?
5. A pilot flying a constant 215 km/h horizontally in a low-flying helicopter, wants to drop secret documents into his contact"s open car which is traveling 155 km/h in the same direction on a level highway 78.0 m below. At what angle (to the horizontal) should the car be in his sights when the packet is released?
6. A ski jumper travels down a slope and leaves the ski track moving in the horizontal direction with a speed of 25 m/s. The landing incline falls off with a slope of 33º.
a. How long is the ski jumper air borne?
b. Where does the ski jumper land on the incline?
7. Stones are thrown horizontally with the same velocity. One stone lands twice as far as the other stone. What is the ratio of the height of the taller building to the height of the shorter?
8. A fleck moving horizontally to the right at 2.5 m/s begins to accelerate downward at 0.75 m/s2 . Where is the fleck 4.0 s later?
B General Projectile Motion
1. In example 2, if Erica kicked the ball from the edge of the roof of a building which is 30.0 m high.
a. When does it strike the ground?
b. How far from the building does it land?
2 . A daredevil decides to jump a canyon of width 10 m. To do so, he drives a motorcycle up an incline sloped at an angle of 15 degrees. What minimum speed must he have in order to clear the canyon?
3. A ball is kicked from a point 38.9 m away from the goal. The crossbar is 3.05 m high. If the ball leaves the ground with a speed of 20.4 m/s at an angle of 52.2º to the horizontal
a. By how much does the ball clear or fall short of clearing the crossbar?
b. What is the vertical velocity of the ball at the time it reaches the crossbar?
4. A rocket is accelerating vertically upward at 30 m/s2 near Earth's surface. A bolt separates from the rocket. What is the acceleration of the bolt?
5. Water is leaving a hose at 6.8 m/s. If the target is 2 m away horizontally, What angle should the water have initially?
6. A 5.0 kg brick lands 10.1 m from the base of a building. If it was given an initial velocity of 8.6 m/s [61º above the horizontal], how tall is the building?
7. A spear is thrown upward from a cliff 48 m above the ground. Given an initial speed of 24 m/s at an angle of 30º to the horizontal,
a. how long is the spear in flight?
b. what is the magnitude and direction of the spear's velocity just before it hits the ground?
8. A projectile is shot from the edge of a cliff 125 m above ground level with an initial speed of 65.0 m/s at an angle of 37º above the horizontal. Determine the the magnitude and the direction of the velocity at the maximum height.
9. A projectile leaves a gun at the same instant that the target is dropped from rest. If the projectile is initially aimed straight at the target, will it hit the target?
10. A basketball is lobbed toward a hoop 3.05 m above the floor. If released 2 m above the floor 10 m from the basket and at a 45 degree angle, how fast must the basketball be thrown so that it goes through the hoop?
11. Dick is tossing chocolates up to Jane's window from 8.0 m below her window and 9.0 m from the base of the wall. If the chocolates are traveling horizontally through the open window, how fast are they going through her window?
12. A projectile has an initial velocity of 15.0 m/s at an angle of 30 degrees above the horizontal. What is the location of the projectile 2.0 seconds later?
13. If a ball is kicked with an initial velocity of 25 m/s at an angle of 60° above the ground, what is the "hang time"?
14. A water balloon hits a target 26 m away, at the same height as the release point. The horizontal component of the initial velocity was 5 m/s. What was the vertical component of the initial velocity? What was the launch angle?
15. A soccer ball leaves a cliff 20.2 m above the valley floor, at an angle of 10 degrees above the horizontal. The ball hits the valley floor 3.0 seconds later. What is the initial velocity of the ball? What maximum height above the cliff did the ball reach?
16. A flea stands 2.00 m from a dog's haunches .55m in height. Jumping at an angle of 32 degrees, what initial speed must the flea have to reach her new home?
17. A bullet hit a target 301.5m away. What maximum height above the muzzle did the bullet reach if it was shot at an angle of 25 degree to the ground?
18. A 3.00 kg parcel is dropped out of a window from a height of 176.4 m. Wind exerts an average 12.0 N force on the parcel away from the building. How long is the parcel in the air? Where does it land? What is its impact velocity?
19. A projectile is shot from the ground at an angle of 60 degrees with respect to the horizontal, and it lands on the ground 5 seconds later. Find:
a. the horizontal component of initial velocity
b. the vertical component of initial velocity
c. initial speed
20. An arrives 30m away horizontally and 5m above the point from which it was launched. It reaches this point 3 seconds after it was launched. Find:
a. the horizontal component of initial velocity
b. the vertical component of initial velocity
c. the vertical component of the impact velocity
d. the horizontal component of the impact velocity
21. Find the minimum initial speed of a champagne cork that travels a horizontal distance of 11 meters.
22. During practice, a soccer player kicks a ball, giving it a 32.5 m/s initial speed. It travels the maximum possible distance before landing down field.
(a) How much time does the ball spend in the air?
(b) How far did the ball travel?
23. A projectile was launched 64° above the horizontal, attaining a height of 10 m. What is the projectile's initial speed?
24. At what launch angle will the range of a projectile equal its maximum height?
25. A boy kicks a soccer ball directly at a wall 41.8 m away. The ball leaves the ground at 42.7 m/s with an angle of 33.0 degrees to the ground. What height will the ball strike the wall?
26. What is the relationship between the maximum height of the projectile, the projectile's range, and the launch angle?
27. A projectile is fired with an initial velocity of 120 m/s at an angle above the horizontal. If the projectile's initial horizontal speed is 55 m/s, then at what angle was it fired?
28. A boulder rolls 35 m down a hill, starting from rest and accelerating at 3.06 m/s2. The boulder then rolls off a 45 m high vertical cliff, launching at 19.0° below the horizontal. (a) How far from the cliff's base does the boulder land? (b) How much time does the boulder spend falling?
Monday, October 4, 2010
Force
1. Three blocks are in contact with each other on a frictionless horizontal surface.The masses of the blocks are m1 = 1 kg , m2 = 2 kg, m3 = 3 kg. A horizontal force F = 24 N is applied on m1.
a. Find the net force on each block.
b. Find magnitude of the contact forces between the blocks.
2. Two blocks, joined by a string, have masses of 6.0 and 9.0 kg. They rest on a frictionless horizontal surface. A 2nd string, attached only to the 9-kg block, has horizontal force = 30 N applied to it. Both blocks accelerate. Find the tension in the string between the blocks.
3. A 1000-kg car moving north at 100km/h brakes to a stop in 50m. What are the magnitude and direction of the force?
4. A mass, m1, accelerates at 3 m/s/s when a force, F, is applied. A second mass, m2, accelerates at 1.0 m/s/s when F is applied to it.
a. Find the value of the ratio m1/m2.
b. Find the acceleration of the combined mass ( m1 + m2) under the action of the force, F.
5. A 5.0 kg missile is projected from rest to a speed of 4.5 x 103 m/s. How much time is required to do this by a net force of 5.3 x 105 N?
a. Find the net force on each block.
b. Find magnitude of the contact forces between the blocks.
2. Two blocks, joined by a string, have masses of 6.0 and 9.0 kg. They rest on a frictionless horizontal surface. A 2nd string, attached only to the 9-kg block, has horizontal force = 30 N applied to it. Both blocks accelerate. Find the tension in the string between the blocks.
3. A 1000-kg car moving north at 100km/h brakes to a stop in 50m. What are the magnitude and direction of the force?
4. A mass, m1, accelerates at 3 m/s/s when a force, F, is applied. A second mass, m2, accelerates at 1.0 m/s/s when F is applied to it.
a. Find the value of the ratio m1/m2.
b. Find the acceleration of the combined mass ( m1 + m2) under the action of the force, F.
5. A 5.0 kg missile is projected from rest to a speed of 4.5 x 103 m/s. How much time is required to do this by a net force of 5.3 x 105 N?
Subscribe to:
Posts (Atom)