Vertical Circular Motion Problems
1. A ball with a mass of 130 g is swung at the end of a string 93.0 cm in length. The ball is whirled in a vertical circle at 4.00 revolutions per second.
a. What is the tension on the string at the bottom of the loop?
b. What is the tension on the string at the top of the loop?
2. A jet fighter pilot knows he is able to withstand an acceleration of 9g before blacking out. The pilot points his plane vertically down while traveling at Mach 3 speed and intends to pull up in a circular maneuver before crashing to the ground.
a) Where does the maximum acceleration occur in the maneuver?
b) What is the minimum radius the pilot can take?
3. A roller coaster at an amusement park has a dip that bottoms out in a vertical circle of radius r. A passenger feels the seat of the car pushing upward on her with a force equal to 3.0 times her weight as she goes through the dip. If r = 25.0 m, how fast is the roller coaster traveling at the bottom of the dip?
4. What is the apparent weight of a 75-kg person driving a car with a constant speed of 12 m/s over a bump with a circular cross-section and radius of curvature of of 35 m?
5. What is the minimum speed of a roller coaster at the top of a 39.0 m vertical loop if the passengers are "weightless" at that point.
6. A ball of a mass 4.0 kg is attached to the end of a 1.2 cm long string and whirled around in a circle that describes a vertical plane.
a. What is the minimum speed that the ball can be moving at and still maintain a circular path? Provide a free body diagram.
b. At this speed, what is the maximum tension in the string? Provide a free body diagram.
c. If the ball was swung in a horizontal circle at this speed, what angle would the string make with the vertical?
7. How do you find the tension in the string of a ball traveling in a vertical circle at the 45 degree angle?
8. A hill is in the shape of an arch having the radius of curvature of 41. m. What is the maximum speed that a car can travel across the hill without 'getting some air'?
Banked Curves
1. Determine the minimum angle at which a road should be banked so that a car traveling at 20.0 m/s can safely negotiate the curve if the radius of the curve is 200.0 m.
2. If a curve with a radius of 65 m is properly banked for a car traveling 75 km/h, what must be the coefficient of static friction for a car not to skid when traveling at 90 km/h?
3. A Car is driven around a circle with a radius of 200m, bank angle 10 degrees. The static frictional coefficient is 0.60. Calculate the maximum velocity the car can travel.
4. An airplane is flying in a horizontal circle at a speed of 460 km/h. If its wings are tilted 40° to the horizontal, and force is provided by lift that is perpendicular to the wing surface. What is the radius of the circle?
Showing posts with label [A2 Phy-4] Further Mechanics. Show all posts
Showing posts with label [A2 Phy-4] Further Mechanics. Show all posts
Saturday, November 20, 2010
Circular Motion-1
A. Speed and Acceleration
1. A 2.0 kg mass swinging at the end of a 0.50 m string is traveling 3.0 m/s. What is the
a. centripetal acceleration of the mass?
b. centripetal force on the mass?
2. A person standing at the Earth's equator has what rotational speed? (R = 6.38 x 106 m)
3. A building is located 28º north of Earth's Equator. What distance does it travel as a result of the Earths rotation?
4. A planet has a radius of 6.04*106 m and free fall acceleration of 9.9 m/s2. What would be the tangential speed of a person standing at the equator, if its rotation increased to the point that the centripetal acceleration was equal to the gravitational acceleration?
B. Horizontal Circular Motion Problems
1. A stopper tied to the end of a string is swung in a horizontal circle. If the mass of the stopper is 13.0 g, and the string is 93.0 cm, and the stopper revolves at a constant speed 10 times in 11.8 s,
a. what is the tension on the string?
b. what would happen to the tension on the string if the mass was doubled and all other quantities stayed the same?
c. what would happen to the tension on the string if the period was doubled and all other quantities stayed the same?
2. A rock is whirled on the end of a string in a horizontal circle of radius R and period T. If the radius is halved while keeping the period constant, what happens to the centripetal acceleration of the rock?
3. A boy is whirling a yo yo on a string in a horizontal circle. What happens to the tension on the string when he whirls it twice as fast?
4. A 0.19 m cord passes through a hole in a table.. The cord attaches a mass m = 2.8 kg on the frictionless surface to a hanging mass M = 7.9 kg. Find the speed with which m must move in a circle in order for M to stay at rest?
5. A clock rests horizontally on a table with a pebble balanced at the end of its 1.0 cm long second hand.. What is the minimum coefficient of static friction which would allow the pebble to stay there without slipping?
6. What is the smallest radius of an unbanked (flat) track around which a motorcyclist can travel if her speed is 25 km/h and the coefficient of static friction between the tires and the road is 0.28?
7. A rock of mass 4.0*102 g is tied to one end of a string that is 2.0 m in length and swung around in a circle whose plane is parallel to the ground.
a. If the string can withstand a maximum tension of 4.5 N before breaking, what angle to the vertical does the string reach just before breaking?
b. At what speed is the rock traveling just as the string breaks?
8. A 1050 kg car travels around a turn of radius 70 m on a flat road. If the coefficient of friction between tires and road is 0.80 what is the maximum speed the car can travel without slipping? Does this result dependent on the mass of the car?
9. Two ice skaters of equal mass grab hands and spin in a circle once every four seconds. Their arms are 0.76 m long, and they each have a mass of 55.0 kg. How hard are they pulling on one another?
10. A hollow vertical cylinder with radius R spins about its vertical axis of symmetry. A stone is held to the inner cylinder wall by static friction. Express the period of rotation in terms of the radius and the coefficient of friction, μs.
11. A coin slides around a horizontal circle at height y inside a frictionless hemisphere bowl of radius R. Derive the coin’s velocity in terms of R, y and g.
12. A train travels at a constant speed around a curve of radius 225 m. A ceiling lamp at the end of a light cord swings out to an angle of 20.0º throughout the turn. What is the speed of the train?
1. A 2.0 kg mass swinging at the end of a 0.50 m string is traveling 3.0 m/s. What is the
a. centripetal acceleration of the mass?
b. centripetal force on the mass?
2. A person standing at the Earth's equator has what rotational speed? (R = 6.38 x 106 m)
3. A building is located 28º north of Earth's Equator. What distance does it travel as a result of the Earths rotation?
4. A planet has a radius of 6.04*106 m and free fall acceleration of 9.9 m/s2. What would be the tangential speed of a person standing at the equator, if its rotation increased to the point that the centripetal acceleration was equal to the gravitational acceleration?
B. Horizontal Circular Motion Problems
1. A stopper tied to the end of a string is swung in a horizontal circle. If the mass of the stopper is 13.0 g, and the string is 93.0 cm, and the stopper revolves at a constant speed 10 times in 11.8 s,
a. what is the tension on the string?
b. what would happen to the tension on the string if the mass was doubled and all other quantities stayed the same?
c. what would happen to the tension on the string if the period was doubled and all other quantities stayed the same?
2. A rock is whirled on the end of a string in a horizontal circle of radius R and period T. If the radius is halved while keeping the period constant, what happens to the centripetal acceleration of the rock?
3. A boy is whirling a yo yo on a string in a horizontal circle. What happens to the tension on the string when he whirls it twice as fast?
4. A 0.19 m cord passes through a hole in a table.. The cord attaches a mass m = 2.8 kg on the frictionless surface to a hanging mass M = 7.9 kg. Find the speed with which m must move in a circle in order for M to stay at rest?
5. A clock rests horizontally on a table with a pebble balanced at the end of its 1.0 cm long second hand.. What is the minimum coefficient of static friction which would allow the pebble to stay there without slipping?
6. What is the smallest radius of an unbanked (flat) track around which a motorcyclist can travel if her speed is 25 km/h and the coefficient of static friction between the tires and the road is 0.28?
7. A rock of mass 4.0*102 g is tied to one end of a string that is 2.0 m in length and swung around in a circle whose plane is parallel to the ground.
a. If the string can withstand a maximum tension of 4.5 N before breaking, what angle to the vertical does the string reach just before breaking?
b. At what speed is the rock traveling just as the string breaks?
8. A 1050 kg car travels around a turn of radius 70 m on a flat road. If the coefficient of friction between tires and road is 0.80 what is the maximum speed the car can travel without slipping? Does this result dependent on the mass of the car?
9. Two ice skaters of equal mass grab hands and spin in a circle once every four seconds. Their arms are 0.76 m long, and they each have a mass of 55.0 kg. How hard are they pulling on one another?
10. A hollow vertical cylinder with radius R spins about its vertical axis of symmetry. A stone is held to the inner cylinder wall by static friction. Express the period of rotation in terms of the radius and the coefficient of friction, μs.
11. A coin slides around a horizontal circle at height y inside a frictionless hemisphere bowl of radius R. Derive the coin’s velocity in terms of R, y and g.
12. A train travels at a constant speed around a curve of radius 225 m. A ceiling lamp at the end of a light cord swings out to an angle of 20.0º throughout the turn. What is the speed of the train?
Monday, September 27, 2010
Momentum, momentum conservation and impulse
Questions
1).A boy hits a 0.05-kg golf ball, giving it a speed of 75 m/sec.What impulse did he deliver to the ball? If the duration of impact is 0.01 seconds, what was the average force of impact?
2)During an automobile crash test, a 1000 kg car is sent towards a cement wall at a speed of 14 m/sec and is brought to a stop in 0.08 seconds. What was the average force of the car on the wall?
3)Two children, totaling 200 kg, are traveling at 10 m/sec in a 100-kg bumper car during an amusement park ride. They deliberately collide with an empty second car, mass 100 kg, which is at rest. Afterwords, the car with the two children moves off at a speed of 4.0 m/sec. What is the final velocity of the empty car?
4)James, a 65-kg skin diver, shoots a 2.0-kg spear with a speed of 15 m/sec at a fish which is darting past him. How fast does James recoil when the spear is initially released?
5)Running at 2 m/sec, Jack, the 45-kg quarterback, collides with Leon, the 90-kg tackle, who is traveling towards him at 7.0 m/sec. Upon colliding, Leon continues to travel forward towards Jack, at 1.0 m/sec. How fast is Jack knocked backwards?
6)A 620-kg moose stands in the middle of the railroad tracks in Sweden, frozen by the lights of an oncoming 10,000-kg locomotive traveling at 10 m/sec. Even though the engineer attempted in vain to slow the train down in time to avoid hitting the moose, the moose rides down the remaining track sitting on the locomotive's cowcatcher. What is the final velocity of the locomotive and moose after the collision?
7)On a hot summer day, Jack and Leon are fishing in their boat, when they decide to jump into the water to cool off. Jack, 45-kg, jumps off the front of the boat with a speed of 2 m/sec. While at the exact same moment, Leon, 90-kg, jumps out of the back of the boat at a speed of 4 m/sec. If the boat has a mass of 100 kg and was at rest prior to the two boys jumping off, what will be its velocity just after both boys have abandoned ship?
8)A 5.0 kg boy runs at a speed of 10.0m/s and jumps onto a cart. The cart is initially at rest. If the speed, with the boy on the cart, is 2.50 m/s, what is the mass of the cart?
9)Assuming no water resistance, a big fish is gliding through the water with momentum 2.0kg m/s. It swallowed a small fish of mass 200g, moving in the opposite direction at a very fast speed of 17m/s relative to the big fish. As a result of that, the big fish felt a punch in his stomach and regretted his move. The mass of the big fish is 1kg .What was the final velocity of the big fish after the meal?
10)A wooden block of 1 kg is at rest. A metal bullet of speed 500m/s and mass 10g was embedded in the wooden block upon impact. A second bullet, having the same mass and speed as the first one , but made of rubber, bounced back with speed of 200m/s upon impact with the same wooden block.
i) Which bullet has undergone a greater change in momentum? Please show your workings.
ii) What is the final kinetic energy of the bullet-block system in each case?
11) A 2.5 kg ball and a 5.0 kg ball have an elastic collision. The 2.5 kg ball was at rest and the other ball had a speed of 3.5 m/s. What is the kinetic energy of the 2.5 kg ball after the collision?
1).A boy hits a 0.05-kg golf ball, giving it a speed of 75 m/sec.What impulse did he deliver to the ball? If the duration of impact is 0.01 seconds, what was the average force of impact?
2)During an automobile crash test, a 1000 kg car is sent towards a cement wall at a speed of 14 m/sec and is brought to a stop in 0.08 seconds. What was the average force of the car on the wall?
3)Two children, totaling 200 kg, are traveling at 10 m/sec in a 100-kg bumper car during an amusement park ride. They deliberately collide with an empty second car, mass 100 kg, which is at rest. Afterwords, the car with the two children moves off at a speed of 4.0 m/sec. What is the final velocity of the empty car?
4)James, a 65-kg skin diver, shoots a 2.0-kg spear with a speed of 15 m/sec at a fish which is darting past him. How fast does James recoil when the spear is initially released?
5)Running at 2 m/sec, Jack, the 45-kg quarterback, collides with Leon, the 90-kg tackle, who is traveling towards him at 7.0 m/sec. Upon colliding, Leon continues to travel forward towards Jack, at 1.0 m/sec. How fast is Jack knocked backwards?
6)A 620-kg moose stands in the middle of the railroad tracks in Sweden, frozen by the lights of an oncoming 10,000-kg locomotive traveling at 10 m/sec. Even though the engineer attempted in vain to slow the train down in time to avoid hitting the moose, the moose rides down the remaining track sitting on the locomotive's cowcatcher. What is the final velocity of the locomotive and moose after the collision?
7)On a hot summer day, Jack and Leon are fishing in their boat, when they decide to jump into the water to cool off. Jack, 45-kg, jumps off the front of the boat with a speed of 2 m/sec. While at the exact same moment, Leon, 90-kg, jumps out of the back of the boat at a speed of 4 m/sec. If the boat has a mass of 100 kg and was at rest prior to the two boys jumping off, what will be its velocity just after both boys have abandoned ship?
8)A 5.0 kg boy runs at a speed of 10.0m/s and jumps onto a cart. The cart is initially at rest. If the speed, with the boy on the cart, is 2.50 m/s, what is the mass of the cart?
9)Assuming no water resistance, a big fish is gliding through the water with momentum 2.0kg m/s. It swallowed a small fish of mass 200g, moving in the opposite direction at a very fast speed of 17m/s relative to the big fish. As a result of that, the big fish felt a punch in his stomach and regretted his move. The mass of the big fish is 1kg .What was the final velocity of the big fish after the meal?
10)A wooden block of 1 kg is at rest. A metal bullet of speed 500m/s and mass 10g was embedded in the wooden block upon impact. A second bullet, having the same mass and speed as the first one , but made of rubber, bounced back with speed of 200m/s upon impact with the same wooden block.
i) Which bullet has undergone a greater change in momentum? Please show your workings.
ii) What is the final kinetic energy of the bullet-block system in each case?
11) A 2.5 kg ball and a 5.0 kg ball have an elastic collision. The 2.5 kg ball was at rest and the other ball had a speed of 3.5 m/s. What is the kinetic energy of the 2.5 kg ball after the collision?
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