   Chapter 5, Problem 66AP

Chapter
Section
Textbook Problem

A block of mass 12.0 kg slides from rest down a frictionless 35.0° incline and is stopped by a strong spring with k = 3.00 × 104 N/m. The block slides 3.00 m from the point of release to the point where it comes to rest against the spring. When the block comes to rest, how far has the spring been compressed?

To determine
How far the spring be compressed because of the block.

Explanation

Given Info:

The mass of the block is 12.0kg .

The inclination of the incline is 35.0° .

The spring constant of the spring is 3.0×104N/m .

The length that the block slides before it come to rest is 3.0m .

Since the incline is frictionless and no other non-conservative forces are acting on the system, the conservation of the mechanical energy is given by

KEf+PEg,f+PEs,f=KEi+PEg,i+PEs,i

Consider that the level with which the spring come to rest against the spring is PEg equals to zero.

Thus,

0+0+12kxf2=0+mgLsinθ+0

• k is the spring constant
• L is the length that the block slide
• m is the mass of block
• g is acceleration due to gravity
• xf is the length that the spring is compressed
• θ is the angle of inclination of the incline

On re-arranging,

xf=2mgLsinθk

Substitute 12

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