Unit 3 - Energy and Momentum Problem Set
*Make sure your calculator is in DEGREE mode!
Part A - Energy Problems
1. A 75 kg sled slides down a 20° slope covering a distance of 150 m, starting at a velocity of 4.5 m/s.
a) If friction is negligible, find the final velocity.
b) If a friction force of 150 N opposes the motion of the sled, find the final velocity.
c) If the final velocity is 12.3 m/s, find the work done by the frictional force.
d) If the final velocity is 13.7 m/s, find the average frictional force.
2. A rollercoaster of mass 230 kg (including the riders) passes over a rise at a height
of 23 m and at a velocity of 12.2 m/s. Assuming frictional forces are negligible,
a) find the velocity at the bottom of the next hill (height of 11 m)
b) find the height of the next hill if the velocity at the top is 13.7 m/s
3. Batman (mass 85 kg) swings on the 17 m long bat-rope, pushing off with an initial velocity of 7.6 m/s. The bat-rope initially makes an angle of 30° with the vertical.
a) Neglecting frictional forces, find Batman’s velocity at the lowest point in his swing.
b) Neglecting frictional forces, find the maximum height to which Batman could swing.
c) If Batman’s velocity at his lowest point is 9.3 m/s, find the work done by frictional forces.
d) Find the average force of air friction (for part c) assuming batman follows a circular path.
4. A 300 kg rocket takes off from ground level and gains 300 m of elevation in 33 seconds, reaching a velocity of 87 m/s.
a) Find the work done by the rocket engine.
b) Find the power output of the engine.
c) If the rocket is 23% efficient at converting chemical energy to mechanical energy, find the total amount of energy used.
5. A 900 kg car accelerates from 20 m/s to 30 m/s in 9.5 seconds, gaining 50 m of elevation in the process.
a) Find the minimum power output required.
b) If the car is only 17% efficient, what is the minimum horsepower of the engine?
6.A force is exerted on an object of mass
25 kg. The force varies according to the graph.
a) Find the total work done over the 23 meters
b) Find the final velocity of the mass assuming
all of the work is converted into kinetic energy,
and the mass starts at rest.
c) If the process is only 57% efficient
at converting work into mechanical
energy, what is the final velocity?
8.A 170 kg cart and rider start from rest on a 20.0 m high incline.
a) How much energy is transformed to heat?
b) What is the average force of friction acting on the cart?
c) What was the average coefficient of friction?
9.A 70.0kg base runner begins his slide into second base when moving at a speed of 4.0m/s. The coefficient of friction between his clothes and the ground is 0.70. He slides so that his speed is zero just as he reaches the base. a) How much mechanical energy is lost due to friction acting on the runner?
b) How far does he slide?
10.A 5.00g bullet moving at 600m/s penetrates a tree trunk to a depth of 4.00cm. a) Use work and energy considerations to find the average frictional force that stops the bullet. b) Assuming that the frictional force is constant, determine how much time elapses between the moment the bullet enters the tree and the moment it stops moving.
11.A softball pitcher hurls a 0.250kg ball around a vertical circular path of radius 0.6m before releasing it. The pitcher maintains a 30.0N force component of force in the direction of the motion around the complete circular path. The speed of the ball at the top of the circle is 15.0m/s. If the ball is released at the bottom of the circle, what is its speed upon release?
12. A 50-kg pole-vaulter running at 10m/s jumps over the bar. Assuming that the horizontal component of velocity over the bar is 1.0m/s, and neglecting air resistance, how high did she jump?
13. Tarzan swings on a 30.0m vine initially inclined at an angle of 37 with the vertical. What is his speed at the bottom of the swing a) if he starts from rest, and b) if he pushes off with a speed of 4.0m/s?
14. A child starts from rest at the top of a 4.00m-high slide. a) What is her speed at the bottom if the slide is frictionless? b) If she reaches the bottom with a speed of 6.00m/s, what percentage of her total energy at the top is lost as a result of friction?
15.A 2.10x103kg car starts from rest from at the top of a 5.0m-long driveway that is sloped at 20 with the horizontal. If an average friction force of 4.0x103N impedes the motion, find the speed of the car at the bottom of the driveway.
16.An airplane of mass 1.5x104kg is moving at 60m/s. The pilot then revs up the engine so that the forward thrust of the propeller becomes 7.5x104N. If the force of air resistance has a magnitude of 4.0x104N, find the speed of the airplane after it has travelled 500m. Assume that the airplane is in level flight throughout this motion.
17. A 70-kg diver steps off a 10m tower and drops straight down into the water. If he comes to rest 5 m beneath the surface, determine the average force exerted on him by the water.
18.A 25.0kg child on a 2.00m-long swing is released from rest when the rope makes an angle of 30.0 with vertical. a) Neglecting friction, find the child’s speed at the lowest position. b)If the speed of the child at the lowest point is 2.00m/s, what is the mechanical energy lost due to friction?
19.A 5.00g feather is held 40.0cmabove a table. It is dropped from rest and subjected to a non-conservative, constant force of air friction f. When the feather reaches the table, it is falling at a speed of 10.0cm/s. Calculate a) the magnitude of the force of air resistance, f, and b) the mechanical energy lost by the feather due to air resistance.
20.In a circus performance, a monkey on a sled is given an initial speed of 4.0m/s up a 20 incline. The combined mass of monkey and sled is 20kg, and the coefficient of friction between sled and incline is 0.20. How far up the incline does the sled move?
Answers
1. 32 m/s,20.6 m/s, -32800 J, 210 N
2. 19.6 m/s, 21 m
3. 10.1 m/s, 5.23 m, 676 J, 76 N
4. 2.0x106 J, 6.11x104 W, 8.77x106J
5. 70100 W, 553 HP
6. 730 J, 7.6 m/s,5.8 m/s
8. 11600 J, 193 N, 0.12
9. a) -560J b)1.2m
10. a)2.3x104Nb)1.3s
11. 26.5m/s
12. 5.1 m
13. a)10.9m/s b)11.6m/s
14.a)8.85m/s b)54.1%
15. 3.7m/s
16. 77m/s
17. 2.1N
18.a) 2.29m/sb)-15.6J
19.a) 0.049N b)1.96J
20. 1.5m
Part B - Momentum Problems
1. An 850 kg car traveling at 12 m/s due east collides with a 620 kg car traveling at 24 m/s due north. As a result of the collision, the two cars lock together. What is the velocity immediately after the collision?
2. A 0.31 kg baseball moving horizontally at 41 m/s is hit back in the direction of the pitcher at an upward angle of 30 degrees at a speed of 53 m/s. Find the impulse given to the ball.
4.A 9.0 kg object moving at 12 m/s to the east explodes into two unequal fragments. The
larger 5.0 kg fragment moves at 15 m/s south.
What is the velocity (speed and direction) of the smaller fragment?
5. A defective 8.5 kg landmine explodes into 3 pieces. A 2.5 kg piece goes Northeast at 190 m/s and a 2.9 kg piece goes 30o N of W at 280 m/s. Find the velocity of the third piece.
6. A 140 g tennis ball traveling 30O east of north at 15 m/s is struck by a tennis racquet, giving it a velocity of 25 m/s west. What are the magnitude and direction of the impulse given to the ball?
7. A 12.0 kg shopping cart rolls due south at 1.70 m/s. After striking the bumper of a car, it travels at 0.80 m/s, 30°E of S. What is the magnitude of the change in momentum sustained by the shopping cart?
8. An 1100 kg vehicle traveling westward at 17 m/s is subjected to a 1.0x104 N·s impulse northward. What is the magnitude of the final momentum of the vehicle?
9. A 310 000 kg meteor is heading directly towards a space shuttle at 35 m/s. It is pushed for a period of 45 seconds after which its velocity is 27 m/s and it has veered 22o from its original course.
a) Find the impulse given to the meteor (magnitude and direction).
b) Find the magnitude of the force applied.
Answers
1. 12.3 m/s, 55.6° N of E
2. 28.1 N·s, 17° upwards
4. 33 m/s, 35° N of E
5. 267 m/s, 64° S of E
6. 4.9 N·s 22° S of W
7. 13 kg·m/s
8. 21200 kg·m/s
9. a) 4.4x106 N·s, 45° from original direction
b) 98000 N