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Chapter 7: Q30P (page 173)

In Fig. 7-10a, a block of mass lies on a horizontal frictionless surface and is attached to one end of a horizontal spring (spring constant ) whose other end is fixed. The block is initially at rest at the position where the spring is unstretched (x=0) when a constant horizontal force F→ in the positive direction of the x axis is applied to it. A plot of the resulting kinetic energy of the block versus its position x is shown in Fig.7-36. The scale of the figure’s vertical axis is set by Ks=4.0 J . (a) What is the magnitude of F→? (b) What is the value of k?

Short Answer

Expert verified
  1. The magnitude of F→ is, 8.0 N.
  2. The value of k is, 8.0 N/m.

Step by step solution

01

Given

The vertical axis is set by kinetic energy as Ks=4.0J.

02

Understanding the concept

The block is connected to the spring; hence, we can use the concept of the work by the spring on the block. We can use the work-kinetic energy theorem.

Formula:

F=-kxWs=12kxi2-12kxf2

03

Calculate the magnitude of  k

The work by the spring on the block:

From the graph, for vertical axis of1m,ΔK=4.0J

For vertical axis ofxi=2 m,ΔKs=0Jxi=2 m," width="9">

The work by the spring is,

According to the work-kinetic energy theorem,

Ws=ΔKs

Hence,

ΔKs=12kxi2-xf2k=2×ΔKsxi2-xf2

Substitute all the value in the above equation.

k=2×4.0 J02-1.0 m2k=8.0 N/m

Hence the value of k is, 8.0 N/m.

04

Calculate the magnitude of  F→

According to Hooke’s law,

F=-kx

Substitute all the value in the above equation.

F=-8.0 N/m×1.0 mF=8.0 N

Hence the value of F is, 8.0 N.

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Most popular questions from this chapter

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