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Q.19

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 256

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Short Answer

A 10 kg runaway grocery cart runs into a spring with spring constant 250 N/m and compresses it by 60 cm. What was the speed of the cart just before it hit the spring?

As a result, the cart's speed when it hits the spring is 3.0 m·s-1.

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Step by Step Solution

Step 1: Introduction

The ratio of an object's distance travelled (in any direction) to the time necessary to travel that distance.

Step 2: Explanation

The kinetic energy of a moving object is expressed as,

T=12mv2

we have T is kinetic energy, m is mass, v is velocity.

The phrase for spring's potential energy is as follows:

U=12kx2

we put k= spring constant, and x = compression in the spring.

The kinetic energy of the cart before it collides with the spring must equal the potential energy stored in the spring, according to the rule of conservation of energy.

12mv2=12kx2 we have, m= mass , v = velocity, k = spring constant, and x= compression in the spring.

Arranging them again for v as follows,

mv2=kx2

v2=kmx2

v=kmx

The cart's velocity when it hits the spring is computed as follows: Substitute 250 N·m-1 for k,10 kg for m, and 60 cm for x,

v=250 N·m-110 kg(60 cm)1.0 m100 cm

=3.0 m·s-1

As a result, the cart's speed when it hits the spring is 3.0 m·s-1.

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