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A runaway railroad car, with mass 3.0 × 10 5 kg, coasts across a level track at 2.0 m/s when it collides elastically with a spring-loaded bumper at the end of the track. If the spring constant of the bumper is 2.0 × 10 6 N/m, what is the maximum compression of the spring during the collision? (a) 0.77 m (b) 0.58 m (c) 0.34 m (d) 1.07 m (e) 1.24 m

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Physics for Scientists and Enginee...

9th Edition
Raymond A. Serway + 1 other
Publisher: Cengage Learning
ISBN: 9781305116399

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Chapter
Section
BuyFindarrow_forward

Physics for Scientists and Enginee...

9th Edition
Raymond A. Serway + 1 other
Publisher: Cengage Learning
ISBN: 9781305116399
Chapter 15, Problem 15.6OQ
Textbook Problem
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A runaway railroad car, with mass 3.0 × 105 kg, coasts across a level track at 2.0 m/s when it collides elastically with a spring-loaded bumper at the end of the track. If the spring constant of the bumper is 2.0 × 106 N/m, what is the maximum compression of the spring during the collision? (a) 0.77 m (b) 0.58 m (c) 0.34 m (d) 1.07 m (e) 1.24 m

To determine

The maximum compression of the spring during the collision.

Explanation of Solution

Given info: The mass of the car is 3.0×105kg , the velocity of the car is 2.0m/s and the spring constant is 2.0×106m/s .

Write the expression for the kinetic energy of the car.

K=12mv2 (1)

Here,

m is the mass of the car.

v is the velocity of the car.

Write the expression for the elastic potential energy in the spring.

U=12kx2 (2)

Here,

k is the spring constant.

x is the length of the stretched spring.

The kinetic energy of the car is stored as elastic potential energy in the spring.

Equate equation (1) and equation (2).

12mv2=12kx2mv2=kx2

Substitute 3.0×105kg for m , 2.0m/s for v and 2

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Chapter 15 Solutions

Physics for Scientists and Engineers, Technology Update (No access codes included)
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