Question bank: Momentum and Impulse: Coefficient of Restitution

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Question 1:

Medium

When two particles collide, the result is influenced by the kinetic energy involved in the process. Which of the following alternatives correctly describes the concept of coefficient of restitution?

Momentum and Impulse: Coefficient of Restitution

Question 2:

Medium

Imagine two skaters practicing on a skate track. The first skater, with a mass of 60 kg, is moving at a speed of 5 m/s towards the second skater, who has a mass of 75 kg and is at rest. They collide and, after the collision, the first skater moves with a speed of 2 m/s. Assuming the coefficient of restitution for this collision is 0.6. From this information, answer: (a) Calculate the velocity of the second skater after the collision. (b) Determine the relative velocity between the two skaters before and after the collision. (c) Using the relative velocity and the coefficient of restitution, verify if the values are consistent with the proposed situation.

Momentum and Impulse: Coefficient of Restitution

Question 3:

Medium

When a ball of mass m and velocity v collides with a fixed wall, it returns with velocity -v. Explain what happens to the kinetic energy of the ball before and after the collision and what is the coefficient of restitution in this case. Also, explain how the coefficient of restitution can be used to calculate the final velocity after the collision of two objects.

Momentum and Impulse: Coefficient of Restitution

Question 4:

Very Hard

Two blocks A and B, of equal masses, are placed on a frictionless horizontal floor. Block A is initially at rest and block B, moving with a constant velocity of 4 m/s, collides head-on with block A, sticking to it after the collision. After the collision, the blocks move together with a velocity of 2 m/s. Determine the coefficient of restitution between blocks A and B, considering the one-dimensional collision and that the system is isolated from the external environment.

Momentum and Impulse: Coefficient of Restitution

Contextualized Question

Calculus Question

Question 5:

Medium

In a billiards game, it is common for the balls to collide with each other and with the edges of the table. Two billiard balls, ball A with a mass of 200g and ball B with a mass of 150g, are moving towards each other: A with a velocity of 2m/s and B with a velocity of -1m/s on the same x-axis. The coefficient of restitution, usually used to describe the effectiveness of kinetic energy conservation in collisions, has a value of 0.8 between the two balls. Considering this situation, answer the following items: a) What type of collision occurs between these billiard balls? b) Calculate the final velocity of each ball after the collision. c) Taking into account the risks involved in the activity, how can the velocity of the balls influence the safety of the players and the physical integrity of the balls and the billiard table?

Momentum and Impulse: Coefficient of Restitution

IARA TIP

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