   Chapter 5, Problem 35P

Chapter
Section
Textbook Problem

A 0.250-kg block along a horizontal track has a speed of 1.50 m/s immediately before colliding with a light spring of force constant 4.60 N/m located at the end of the track. (a) What is the spring’s maximum compression if the track is frictionless? (b) If the track is not frictionless, would the spring’s maximum compression be greater than, less than, or equal to the value obtained in part (a)?

(a)

To determine
The maximum compression of the spring, if the track is frictionless.

Explanation

Given Info:

The mass of the block is 0.250kg .

The speed of the block immediately before colliding with the light spring is 1.50m/s .

The force constant of the spring is 4.60N/m .

Since, the track is frictionless; no external forces do work on the system. So, the total mechanical energy of the system is a constant.

Thus,

KEf+(PEg)f+(PEs)f=KEi+(PEg)i+(PEs)i       (I)

• (PEg)f is the final gravitational potential energy
• (PEg)i is the initial gravitational potential energy
• KEf is the final kinetic energy of the block
• KEi is the initial kinetic energy of the block
• (PEs)f is the final potential energy of the spring

The gravitational potential energy of the mass just before it made contact with the spring and at the rest are same because the track is horizontal

(b)

To determine
The spring’s maximum compression when the track is not frictionless

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