COLLEGE PHYSICS
COLLEGE PHYSICS
2nd Edition
ISBN: 9781711470832
Author: OpenStax
Publisher: XANEDU
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Chapter 8, Problem 50TP
To determine

(a)

The final velocity of mass B after the collision.

Expert Solution
Check Mark

Answer to Problem 50TP

The final velocity of mass B after collision is 5 m/s.

Explanation of Solution

Given:

The mass A is moving in +x direction with an initial velocity, v1=15 m/s.

The mass of B is, m2=2m1.

The mass B is moving in x direction with an initial velocity, v2=10 m/s.

The mass A is moving in x direction after collision with a final velocity, v1=15 m/s.

Formula used:

Write the expression for conservation of momentum.

  m1v1+m2v2=m1v1+m2v2

Here, m1 is the mass of A, m2 is the mass of B, v1 is the initial velocity of mass A, v2 is the initial velocity of mass B, v1 is the final velocity of the mass A and v2 the final velocity of mass B.

Calculation:

The final velocity of mass B is calculated as

  m1v1+m2v2=m1v1+m2v2m1(15m/s)+2m1(10m/s)=m1(15m/s)+2m1v22m1v2=10m1v2=5m/s

Conclusion:

The velocity of mass B after collision is 5 m/s.

To determine

(b)

The change in kinetic energy after the collision.

Expert Solution
Check Mark

Answer to Problem 50TP

The change in kinetic energy after collision is 375 J.

Explanation of Solution

Given:

The mass of A is, m1=5 kg.

Formula used:

The initial kinetic energy KEi of the system is given by

  KEi=12(m1v12+m2v22)

The final kinetic energy KEf of the system is given by

  KEf=12[m1( v 1)2+m2( v 2)2]

The formula for change in kinetic energy ΔKE is given by

  ΔKE=KEfKEi

Calculation:

The mass of B is calculated as

  m2=2m1=2(5 kg)=10 kg

The initial kinetic energy KEi of the system is calculated as

  KEi=12[(5 kg)( 15 m/s )2+(10 kg)( 10 m/s )2]=1062.5J

The final kinetic energy KEf of the system is calculated as,

  KEf=12[(5 kg)( 15 m/s )2+(10 kg)( 5 m/s )2]=687.5J

The change in kinetic energy is calculated as

  ΔKE=687.5J1062.5J=375J

Conclusion:

The change in kinetic energy after collision is 375J.

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Chapter 8 Solutions

COLLEGE PHYSICS

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