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Chapter 15: Q. 20 (page 416)

FIGURE EX15.20 is a kinetic-energy graph of a mass oscillating on a very long horizontal spring. What is the spring constant?

Short Answer

Expert verified

The spring constant isk=4.0N/m

Step by step solution

01

Given data.

From the graph:

xmax=A=2mKmax=8.0J

Required: spring constant k

02

Conservation law.

To get a spring constant we will use conservation law which tells that:

1. At max position the potential energy is maxed and kinetic energy is 0.

2. At equilibrium position the kinetic energy is max and potential energy is 0.

3. The max kinetic energy = The max potential energy.

According to these notes get that

Umax=Kmax⇒12kA2=Kmax ⇒(1)

From (1)we get that

k=2KmaxA2 ⇒(2) ⇒(2)

Substitution in (2)to get that

k=2×8(2)2=4.0N/m

Umax=Kmax⇒12kA2=Kmax

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