A spring with a spring constant of 3200 N/m is initially stretched until the elastic potential energy of the spring is 1.44 J. (U =0 for the relaxed spring.)

What is Uif the initial stretch is changed to

(a) a stretch of 2.0 cm,

(b) a compression of 2.0 cm, and

(c) a compression of 4.0 cm?

Short Answer

Expert verified

(a) Th change in potential energy of the spring if initial stretch is changed to x=2.0 cm is U=-0.8J.

(b) The change in potential energy of the spring if initial compression is changed to x=2.0 cm is ΔU=-0.8J.

(c) The change in potential energy of the spring if initial compression is changed to x =4.0 cm is ΔU=1.12J.

Step by step solution

01

Given data:

The spring constant, k=3200 n/m

The initial potential energy, Ui=1.44J

02

To understand the concept:

Use the concept of elastic potential energy of the spring. Find the potential energies at given displacements and then find the change in potential energies.

Formula:

The potential energy is,

U=12kx2

Here, U is the potential energy, k is the kinetic energy, and x is the distance.

03

(a) Calculate ∆U if the initial stretch is changed to a stretch of 2.0 cm:

The potential energy of the spring if the initial stretch changed to x=2.0 cm :

You can find the potential energy at

x=2.0cm=0.02m

The potential energy is,

U1=123200N/m0.02m2=0.64J

The change in potential energy you get,

U=U1-Ui=0.64J-1.44J=-0.8J

04

(b) Calculate ∆U if the initial stretch is changed to a compression of 2.0 cm:

Potential energy of the spring if initial compression changed to

x =2.0 cm

The answer will be same as part (a) because the spring is elongated at 2.0 cm . It doesn’t matter whether it is stretched or compressed. Potential energy will be the same.

05

(c) Calculate ∆U if the initial stretch is changed to a compression of 4.0 cm :

Potential energy of the spring if initial compression changed to

x=4.0cm=0.04m

Therefore, the potential energy is define as below.

U2=123200N/m0.04m2=2.56J

Determine the change in potential energy as follow.

U=U2-Ui=2.56J-1.44J=1.12J

Hence, the required change in potential energy is U=1.12J.

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