Ch 08: Momentum, Impulse, and Collisions

Young & Freedman Calc - University Physics 14th Edition

Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook

Young & Freedman Calc 14th Edition

Ch 08: Momentum, Impulse, and Collisions

Problem 21b

Chapter 8, Problem 21b

On a frictionless, horizontal air table, puck A (with mass 0.250 kg) is moving toward puck B (with mass 0.350 kg), which is initially at rest. After the collision, puck A has a velocity of 0.120 m/s to the left, and puck B has a velocity of 0.650 m/s to the right. Calculate the change in the total kinetic energy of the system that occurs during the collision.

Verified step by step guidance

Step 1: Identify the type of collision and apply the principle of conservation of momentum. Since the air table is frictionless, momentum is conserved. Write the equation for the conservation of momentum:

m_{A} v_{A1} + m_{B} v_{B1} = m_{A} v_{A2} + m_{B} v_{B2}

, where

v_{A1}

is the initial velocity of puck A,

v_{B1}

is the initial velocity of puck B (0 m/s),

v_{A2}

is the final velocity of puck A (-0.120 m/s, to the left), and

v_{B2}

is the final velocity of puck B (0.650 m/s, to the right).

Step 2: Substitute the given values into the momentum conservation equation. Use

= 0.250 \, kg

= 0.350 \, kg

= 0 \, m/s

= -0.120 \, m/s

, and

= 0.650 \, m/s

. Solve for

v_{A1}

, the initial velocity of puck A.

Step 3: To calculate the change in total kinetic energy, use the formula for kinetic energy:

K = \frac{1}{2} m v^{2}

. Compute the initial kinetic energy of the system using the initial velocities of both pucks (

v_{A1}

and

v_{B1}

Step 4: Compute the final kinetic energy of the system using the final velocities of both pucks (

v_{A2}

and

v_{B2}

Step 5: Find the change in kinetic energy by subtracting the initial kinetic energy from the final kinetic energy:

ΔK = K

_final - K_initial. Interpret the result to determine whether the collision was elastic or inelastic.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Conservation of Momentum

The principle of conservation of momentum states that in a closed system with no external forces, the total momentum before a collision is equal to the total momentum after the collision. This is crucial for solving problems involving collisions, as it allows us to relate the velocities and masses of the colliding objects to find unknown quantities, such as the initial speed of puck A in this scenario.

Kinetic Energy

Kinetic energy is the energy an object possesses due to its motion, calculated using the formula KE = 0.5 * m * v^2, where m is mass and v is velocity. Understanding kinetic energy is essential for analyzing the energy changes that occur during collisions, as it helps determine how much energy is conserved or transformed into other forms during the interaction between the pucks.

Elastic vs. Inelastic Collisions

Collisions can be classified as elastic or inelastic based on whether kinetic energy is conserved. In elastic collisions, both momentum and kinetic energy are conserved, while in inelastic collisions, momentum is conserved but kinetic energy is not. This distinction is important for calculating changes in kinetic energy and understanding the nature of the collision between pucks A and B.

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Intro To Elastic Collisions

Related Practice

Textbook Question

On a frictionless, horizontal air table, puck A (with mass 0.250 kg) is moving toward puck B (with mass 0.350 kg), which is initially at rest. After the collision, puck A has a velocity of 0.120 m/s to the left, and puck B has a velocity of 0.650 m/s to the right. What was the speed of puck A before the collision?

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Textbook Question

When cars are equipped with flexible bumpers, they will bounce off each other during low-speed collisions, thus causing less damage. In one such accident, a 1750-kg car traveling to the right at 1.50 m/s collides with a 1450-kg car going to the left at 1.10 m/s. Measurements show that the heavier car's speed just after the collision was 0.250 m/s in its original direction. Ignore any road friction during the collision. Calculate the change in the combined kinetic energy of the two-car system during this collision.

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Textbook Question

Two ice skaters, Daniel (mass 65.0 kg) and Rebecca (mass 45.0 kg), are practicing. Daniel stops to tie his shoelace and, while at rest, is struck by Rebecca, who is moving at 13.0 m/s before she collides with him. After the collision, Rebecca has a velocity of magnitude 8.00 m/s at an angle of 53.1° from her initial direction. Both skaters move on the frictionless, horizontal surface of the rink. What are the magnitude and direction of Daniel's velocity after the collision?

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Textbook Question

You are standing on a sheet of ice that covers the football stadium parking lot in Buffalo; there is negligible friction between your feet and the ice. A friend throws you a 0.600-kg ball that is traveling horizontally at 10.0 m/s. Your mass is 70.0 kg. If the ball hits you and bounces off your chest, so afterward it is moving horizontally at 8.0 m/s in the opposite direction, what is your speed after the collision?

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Textbook Question

When cars are equipped with flexible bumpers, they will bounce off each other during low-speed collisions, thus causing less damage. In one such accident, a 1750-kg car traveling to the right at 1.50 m/s collides with a 1450-kg car going to the left at 1.10 m/s. Measurements show that the heavier car's speed just after the collision was 0.250 m/s in its original direction. Ignore any road friction during the collision. What was the speed of the lighter car just after the collision?

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Textbook Question

You are standing on a sheet of ice that covers the football stadium parking lot in Buffalo; there is negligible friction between your feet and the ice. A friend throws you a 0.600-kg ball that is traveling horizontally at 10.0 m/s. Your mass is 70.0 kg. If you catch the ball, with what speed do you and the ball move afterward?

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