Momentum and Collisions: Extra Problems

Problem Set A

Problem 1:

If an ostrich with a mass of 156 kg and is running northward with a velocity of 12.4 m/s, then with what velocity (in m/s) must a chicken run with a mass of 39 kg to have the same momentum as the ostrich?

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Problem 2:

Lee Mealone, a hermit, pushes a 11.9 kg boulder into the wall of his cave at a speed of 2.9 m/s, the boulder is brought to a stop in 1.28 seconds. What was the magnitude of the impulse (in N*s) imparted to the boulder? (No + or - signs.)

Problem 3:

A 1.6-kg object is thrown upward with an initial speed of 5.61 m/s. The ball is caught when it has a downward speed of 5.61 m/s. How much time (in s) was the ball in the air? (Hint: use the weight of the ball as the impulse force and use 9.8 m/s/s for acceleration due to gravity.)

Problem 4:

A 1.21-kg rubber ball moving with a speed of 5.36 m/s strikes a wall and rebounds with a speed of 2.01 m/s in the opposite direction. Determine the impulse (in N*s) encountered by the ball.

Problem 5:

A 71.5-kg football player moving with a speed of 6.68 m/s collides mid-air with another player and gets knocked backwards. If the player experiences a force of 928 N over a time period of 0.910 s, then determine the final speed (in m/s) of the player. Enter a positive number.

Problem 6:

A 74.2-kg football player moving with a speed of 4.72 m/s collides mid-air with another player. If the player experiences a force of 3287 N over a time period of 0.272 s, then determine the momentum change (in kg*m/s) of the player. (No + or - signs.)

Problem 7:

The momentum of a 731-kg car is equal to the momentum of a 1463-kg truck traveling with a speed of 11.6 m/s. What is the speed (in m/s) of the car?

Problem 8:

A 937-kg car moving with a speed of 13.4 m/s collides with a utility pole and is brought to rest in 0.203 seconds. Find the average force (in N) exerted on the car during the collision.

Problem 9:

A 1547-kg van is moving with a speed of 26.5 m/s. If Superman is to stop the van in 0.448 seconds, what average force (in N) must he exert on the van?

Problem 10:

A 0.484-kg football is thrown with a speed of 13.7 m/s. A stationary receiver catches the ball and brings it to rest in 0.016 seconds. What is the impulse (in N*s) delivered to the ball?

Problem 11:

(Referring to Problem #10 above.) What is the average force (in N) exerted on the receiver?

Problem 12:

An object at rest encounters an impulse of 72.1 N*s for 8.20 seconds. It then encounters a force of friction of 7.3 N for 2.31 seconds. For what time period (in s) must a final resistive force of 42.1 N be exerted in order to bring it to a final resting position? Enter your answer to the third decimal place.

Problem 13:

A 11.4-kg object is in motion with a velocity of 3.21 m/s. It encounters an impulse of 42.1 N*s for 6.31 seconds in the same direction as its motion. What force (in N) would be required to stop it in 3.31 seconds?

Problem 14:

An object with mass of 3.1 kg encounters a force of 4.31 N for 5.00 seconds to accelerate it from rest. It then encounters an impulse of 22.4 N*s in the direction of motion for 6.50 seconds. Finally, a resistive force of 3.58 N is applied for 6.21 seconds. Determine the final momentum (in kg*m/s) of the object.

Problem 15:

A 5.53-kg object is moving with a speed of 4.21 m/s. It encounters a force of 6.37 N in the directon of motion for 2.5 seconds. It then encounters another force of 5.4 N in the direction of motion for 7.4 seconds. What is the final velocity (in m/s) of the object?

Problem Set B

Problem 1:

A 37.2-kg child standing on a frozen pond throws a 0.565-kg stone to the east with a speed of 17.4 m/s. Neglecting friction between child and ice, find the recoil velocity (in m/s) of the child. Enter a positive value, accurate to the third decimal place.

Problem 2:

A rifle with a weight of 33.2 N fires a 6.45-g bullet with a speed of 330 m/s. Find the recoil speed (in m/s) of the rifle.

Problem 3:

A rifle with a weight of 33.2 N fires a 6.45-g bullet with a speed of 330 m/s. If a 807-N man holds the rifle firmly against his shoulder, find the recoil speed (in m/s) of the man and rifle. Enter a positive value, accurate to the fourth decimal place.

Problem 4:

A popcorn kernel initially at rest explodes into two pieces, one piece having 7 times the mass of the other. What is the ratio of the velocities of the fragments? 

Problem 5:

A 70.9-kg boy and a 43.2-kg girl, both wearing skates face each other at rest on a skating rink. The boy pushes the girl, sending her eastward with a speed of 4.64 m/s. Determine the subsequent speed (in m/s) of the boy. (Neglect friction.)

Problem 6:

A 867-N man stands in the middle of a frozen pond of radius 7.45 m. He is unable to reach the other side because of a lack of friction beween his shoes and the ice. To overcome his difficulty, he throws his 1.332-kg physics textbook horizontally at a speed of 6.49 m/s toward the north shore. How much time (in s) does it take him to reach the south shore?

Problem 7:

A 7.49-kg bowling ball collides head-on with a 2.32-kg bowling pin. The pin flies forward with a speed of 3.3 m/s. If the ball continues forward with a speed of 1.7 m/s, what was the initial speed (in m/s) of the ball?

Problem 8:

A person with a mass of 65.5 kg throws a 2.29-kg snowball forward with a ground speed of 23.3 m/s. A second person with a mass of 60.0-kg catches the snowball. Both persons are on skates. The first person is initially moving forward with a speed of 5.54 m/s, and the second person is initially at rest. What is the velocity (in m/s) of the first person after the snowball is thrown? Disregard the friction between the skates and the ice.

Problem 9:

A swimmer of mass 80.8-kg stands on the stern of a boat of mass 229 kg at rest on a lake. The swimmer dives off the boat with a velocity that has a horizontal component of 1.33 m/s in the westerly direction. Determine the magnitude of the resulting velocity (in m/s) of the boat. Enter your answer to the third decimal place.

Problem 10:

A 81.3-kg astronaut is working on the engines of his ship, which is drifting through space with a constant velocity. The astronaut, wishing, to get a better view of the universe, pushes against the ship and later finds himself 37.5 m behind the ship. Without a thruster, the only way to return to the ship is to throw his .572-kg wrench directly away from the ship. If he throws the wrench with a a speed of 23.3 m/s, how much time (in s) does it take the astronaut to reach the ship?

Problem 11:

The bird perched on the swing in figure 6.22 has a mass of 52.3 g and the base of the swing has a mass of 181 g . Assume that the swing and the bird are originally at rest and that the bird then takes off in a horizontal direction at 2.37 m/s. If the base can swing freely (i.e., without friction) around the pivot, how high (in cm) will the base of the swing rise above its original level? Enter your answer accurate to the fourth decimal place.

Problem 12:

A 2.65 kg cannon is at rest. When ignited, it fires a 58.2 g tennis ball forward with a speed of 89.5 m/s. Determine the post-explosion speed (in m/s) of the cannon

Problem 13:

A 1.5-kg cannon is mounted on top of a 2.0-kg cart and loaded with a 66.5 gram ball. The cannon, cart, and ball are moving forward with a speed of 2.65 m/s. The cannon is ignited and launches a 66.5 gram ball forward with a speed of 103 m/s. Determine the post-explosion velocity (in m/s) of the cannon and cart. Enter a + value for a forward velocity and a - value for a backward velocity.

Problem 14:

A 74.7 kg skater is carrying a 2.5 kg snowball and moving forward with a velocity of 10.7 m/s. The skater throws the snowball forward with a speed of 36.5 m/s. Determine the speed (in m/s) of the skater after hurling the snowball. Enter a negative value for a backward velocity and a positive value for a forward velocity.

Problem 15:

Anna Litical and Noah Formula are doing The Cart and the Brick Lab. They drop a brick on a 2.6 kg cart moving at 28.2 cm/s. After the collision, the dropped brick and cart are moving together with a velocity of 15.7 cm/s. Determine the mass (in kg) of the dropped brick.

Problem Set C

Problem 1:

A 828-kg car moving at a speed of 10.9 m/s crashes into an identical car stopped at a light. What is the velocity (in m/s) of the wreckage immediately after the collision, assuming the cars stick together?

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Problem 2:

A bumper car at an amusement park ride traveling at 2.24 m/s collides with an identical car at rest. This second car moves forward with a speed of 1.34 m/s. What is the velocity (in m/s) of the first car after the collision? 

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Problem 3:

A 1.14-kg skateboard is coasting along the pavement at a speed of 3.53 m/s, when a 1.1-kg cat drops from a tree vertically down on the skateboard. What is the speed (in m/s) of the skateboard-cat combination?

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Problem 4:

A railroad car of mass 16708 kg moving with a speed of 2.80 m/s collides and couples with two other already coupled railroad cars each of the same mass as the single car and moving in the same direction at a speed of 1.81 m/s. What is the speed (in m/s) of the three coupled cars after the collision?

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Problem 5:

A 3.01-kg sphere makes a perfectly inelastic collision with a second sphere initially at rest. The composite system moves with a speed equal to 1/3-th the original speed of the 3.01-kg sphere. What is the mass (in kg) of the second sphere?

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Problem 6:

A 4.53-g object moving to the right with a speed of 19.2 cm/s makes an elastic head-on collision with a 10.31-g object initially at rest. Find the velocity (in cm/s) of the 10.31-g object after the collision.

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Problem 7:

A 21.0-g object moving to the right with a speed of 20.0 cm/s overtakes and collides elastically with a 14.0-g object moving in the same direction with a speed of 12.0 cm/s. Find the velocity (in cm/s) of 14.0-g object after the collision.

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Problem 8:

A 7.61-g bullet is fired into a 1.38-kg ballistic pendulum (initially at rest) and becomes embedded in it. If the pendulum rises a vertical distance of 5.6 cm, calculate the initial speed (in m/s) of the bullet.

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Problem 9:

A 7.0-g marble has a head-on collision with a 3.0-g marble, initially at rest on a playing surface. The speed of the 7.0-g marble is reduced from 1.08 m/s to 0.75 m/s in the collision. What is the speed (in m/s) of 3.0-g marble after the collision? 

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Problem 10:

Two pieces of 'Silly Putty' are thrown in opposite directions toward one another and stick together after the collision. If one piece has a mass of 10.4-g and is traveling with a speed of 9.4 m/s, and the second piece has a mass of 4.7 g and a speed of 5.4 m/s, then what is the speed (in m/s) of the combination after the collision?

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Problem 11:

A 4.0-gram object moving to the right with a speed of 3.9 cm/s makes an elastic head-on collision with a 6.0-gram object moving in the opposite direction with a speed of 6.6 cm/s. Find the velocity (in cm/s) of the 6.0-gram object after the collision. Indicate the direction (left or right).

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Problem 12:

A pool ball (Ball A) rolling across a table at 2.14 m/s makes a head-on collision with an identical slower ball (Ball B) having a speed of 1.40 m/s in the same direction. Assume the collision is perfectly elastic and find the speed (in m/s) of the first ball (Ball A) after the collision.

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Problem 13:

A 46.3-kg baseball pitching machine is placed on a frozen pond. It fires a 0.143-kg baseball at an angle of 30 degrees with the vertical at a speed of 19.2 m/s. What is the recoil velocity (in cm/s) of the machine?

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Problem 14:

A 83.3-kg fullback moving east with a speed of 4.72 m/s is tackled by a 96.9-kg opponent running north with a speed of 3.34 m/s. If the collision is perfectly inelastic, calculate the speed (in m/s) of the 83.3-kg fullback just after the tackle.

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Problem 15:

An eastern kingbird and a bee are approaching each other at right angles. The bird has a mass of 0.121 kg and a speed of 1.6 m/s, and the bee has a mass of 4.67 grams and a speed of 13.8 m/s. If the bird catches the bee, what is the new speed (in cm/s) of the bird? (Be cautious of units!)

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Problem Set D

Problem 1:

A 2.68-g bullet is fired vertically at a speed of 177 m/s into a 0.138-kg ball initially at rest. How high (in cm) will the combination rise after the collision assuming the bullet embeds in the ball?

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Problem 2:

A 6.75-g bullet is fired horizontally into a 73.6-g wooden block initially at rest on a horizontal surface. After impact, the bullet remains embedded in the block and the combined system slides 7.12 m before coming to rest. If the coefficient of friction between the block and the surface is 0.635, what was the speed (in m/s) of the bullet immediately before impact?

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Problem 3:

A 0.402-kg bead slides on a curved frictionless wire, starting from rest 1.43 meters above the table top (point A in the diagram below). At point B, the bead collides elastically with a 0.586-kg bead at rest. Find the height (in m) that the 0.586-kg bead moves up the wire.

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Problem 4:

Tarzan, whose mass is 75.1-kg, swings from a 4.19-m vine which is horizontal when he starts. At the bottom of his arc, he picks up 53.6-kg Jane, in an inelastic collison. What maximum height (in m) tree limb can they reach on their upward swing?

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Problem 5:

A 1.1-kg mass moving with an initial speed of 5.3 m/s collides with and sticks to a 4.9-kg mass initially at rest. The combined mass then proceeds to collide with and stick to a 2.1-kg mass also at rest initially. If the collisions are head-on, find the final speed (in m/s) of the triple-mass system?

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Problem 6:

A baseball batter was able to impart to a 6.21 N-s impulse to a 0.143-kg baseball thrown at 60 mph, before receiving instruction. After improving his follow-through, the batter has been able to increase the impulse by 10.7%. What will be the new speed of the ball leaving the bat (in m/s) with this greater impulse? (Use 1.0 m/s = 2.24 mi/hr) 

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Problem 7:

A 1.8-kg block is sliding down a 8.0-kg frictionless incline. Both are initially moving to the right at 10.0 m/s. If the block ends up moving to the right at 26.7 m/s on the horizontal surface, determine the final velocity of the incline (in m/s). Indicate the direction as right or left.

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Problem 8:

A 0.553-kg bead slides on a curved frictionless wire, starting from rest at a point A, 1.34 meters above point B, the bead collides elastically with a 0.786-kg bead at rest. Find the height (in m) that the 0.786-kg bead moves up the wire.

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Problem 9:

A 26.8 gram bullet is shot vertically into a 0.753-kg block of wood. If the block rises to a height of 5.12 meters above its original position, find the original velocity of the bullet ( in m/s).

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Problem 10:

A 1206-kg car moving eastward at a speed of 14.2 m/s collides with a 1683-kg car moving northward. The cars stick together and move as a unit after the collision at an angle of 47.6 degrees north of east. Find the speed (in m/s) of the 1683-kg car before the collision.

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Problem 11:

A 2.0-kg mass is given an initial velocity by a spring-loaded mechanism on a frictionless surface. This mass impacts a 3.0-kg mass sitting on the edge of the table. The 2.0-kg mass ends up moving backwards at 1.34 m/s. How far from the base of the 1.22-meter high table does the 3.0-kg mass land (in m)? The spring constant is 344 Newtons/meter and the spring is initially compressed 0.15 meters. TIP: If necessary, you might want to review principles of horizontally-launched projectiles.

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