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Q. 49

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 258

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Short Answer

A horizontal spring with a spring constant is compressed and used to launch a box across a frictionless, horizontal surface. After the box travels some distance, the surface becomes rough. The coefficient of kinetic friction of the box on the surface is . Use work and energy to find how far the box slides across the rough surface before stopping.

The distance the box slides on the rough surface before stopping is

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Step by Step Solution

Step 1: Given information

A horizontal spring with spring constant is compressed and is used to launch box across a frictionless, horizontal surface. After the box travels some distance, the surface becomes rough. The coefficient of kinetic friction between the box and the rough surface is

Step 2: Explanation

The frictional force acting on a sliding mass m on a surface with a coefficient of kinetic friction . Energy is stored in the spring with a spring constant k when it is compressed by a distance .

This energy is stored in the spring when it is compressed. That is

This energy is transferred to the mass and used in doing work against the friction force. Work done by friction is

The energy is conserved. This energy stored in the spring is transferred to the mass and used in doing work against the friction force.

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