How Far Does a Block Compress a Spring on a Frictionless Surface?

Thread starter ice2morrow
Start date Dec 9, 2009
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Kinematics Springs

AI Thread Summary

A 4.0 kg block moving at 5.0 m/s compresses a spring with a spring constant of 200 N/m on a frictionless surface. The problem involves calculating the distance the spring compresses before the block stops and reverses direction. Using the equations for potential energy (P.E.) and kinetic energy (K.E.), the correct formula to find the compression distance is x = sqrt(mv^2/k). The calculated compression distance is approximately 0.707 meters. This solution effectively demonstrates the energy transfer from kinetic to potential energy in the system.

Dec 9, 2009

ice2morrow

Homework Statement

A 4.0 kg block slides along a frictionless horizontal surface at 5.0 m/s. It runs into and compresses a spring with a spring constant of 200 N/m. How far does it compress the spring before it stops and changes direction?

Homework Equations

P.E. = 0.5 kx^2
K.E. = 0.5 mv^2

The Attempt at a Solution

x = sqrt (mv^2/k) = 0.707 m?

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Dec 9, 2009

Chewy0087

that's right.

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