To determine

To find:

i) The work done during the compression

ii) The work required to compress the spring to a length of 25 cm

Answer

i) 3 J

ii) 6.75 J

Explanation

1) Concept:

Use Hook’s law and formula of work done

2) Law and Formula:

Hook’s law:

The force required to stretch a spring x units beyond its natural length is proportional to x, and it is given by fx=kx where k is a positive constant called the spring constant

Work done:

W=∫abf(x)dx

Where f(x) is the force function.

3) Calculation:

i) According to Hook’s law, the force required to hold the spring stretched x meters beyond its natural length is fx=kx

From the given information the amount compressed is 40-30=10 cm=0.1 m

The given force is 60 N

Therefore,

60=k(0.1)

⇒k=600 N/m

Thus, fx=600x

Now, the work required to compress the spring by 0.1 m is

W=∫00.1600xdx

Simplify,

=600x2200.1

=300x200.1

=3000.12-02

=3000.01-0

=3 N.m

=3 J

Therefore,

W=3 J

ii) The work required to compress the spring to a length of 25 cm=0.15 m is

W=∫00.15600xdx

Simplify,

=600x2200.15

=300x200.15

=3000.152-02

=3000.0225-0

=6.75 N·m

=6.75 J

Therefore,

W=6.75 J

Conclusion:

i) The work done during the compression is 3 J

ii) The work required to compress the spring to a length of 25 cm 6.75 J