   Chapter 13, Problem 66AP

Chapter
Section
Textbook Problem

A 0.500-kg block is released from rest and slides down a frictionless track that begins 2.00 m above the horizontal, as shown in Figure P13.66. At the bottom of the track, where the surface is horizontal, the block strikes and sticks to a light spring with a spring constant of 20.0 N/m. Find the maximum distance the spring is compressed. Figure P13.66

To determine
The maximum distance the spring is compressed.

Explanation

Given info: The mass of the block is 0.500kg . The height of the track is 2.00m above horizontal. The spring constant of the spring is 20.0Nm-1 .

The conservation of mechanical energy,

(KE+PEg+PEs)f=(KE+PEg+PEs)i (1)

• KE is the kinetic energy
• PEg is the gravitational potential energy
• PEs is the elastic potential energy

Consider the initial state to be when the block is on the top of the track, where gravitational potential energy is the only form of energy. Gravitational potential energy of the initial state is,

(PEg)i=mgh (2)

• m is the mass of the block
• g is the free fall acceleration
• h is the height of the track

Consider the final state to be when the block comes to rest along with the spring, where elastic potential energy is the only form of energy

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