A spring has stiffness of 100Nmm, the initial compression of the spring is 15mm, and it is then compressed to 65mm.

•1Nmm = 0.001Nm
•100Nmm = 100 X 0.001 = 0.1Nm
•Comp.1 = 15 mm = 0.015m
•Comp.2 = 65 mm = 0.065m

a) i-Find potential energy at 15mm.
ii- Find potential energy at 65mm.
b) Find the work done during compression.

To find the potential energy at each compression length, you can use the formula for potential energy stored in a spring:

Potential energy = (1/2) * stiffness * (compression)^2

To find the potential energy at 15mm compression:
i) Convert the stiffness from Nmm to Nm:
stiffness = 100 Nmm * 0.001 Nmm/Nm = 0.1 Nm

ii) Convert 15mm to meters:
compression = 15 mm * 0.001 m/mm = 0.015 m

Now, substitute the values into the formula:
Potential energy = (1/2) * 0.1 Nm * (0.015 m)^2 = 0.0001125 Nm

Therefore, the potential energy at 15mm compression is 0.0001125 Nm.

To find the potential energy at 65mm compression:
i) Convert 65mm to meters:
compression = 65 mm * 0.001 m/mm = 0.065 m

Now, substitute the values into the formula:
Potential energy = (1/2) * 0.1 Nm * (0.065 m)^2 = 0.00021025 Nm

Therefore, the potential energy at 65mm compression is 0.00021025 Nm.

To find the work done during compression, you can use the difference in potential energy:

Work done = Potential energy at final compression - Potential energy at initial compression

Substitute the values into the formula:
Work done = 0.00021025 Nm - 0.0001125 Nm = 0.00009775 Nm

Therefore, the work done during compression is 0.00009775 Nm.