A spring has stiffness of 100Nmm, the initial compression of the spring is 15mm, and it is then compressed to 65mm.
a)Find potential energy at 15mm:
K=100Nmm*1000=100000Nm
Ep=Kc^2/2
Ep=(100000*0.015^2)/2
Ep=11.25 joule (ans.)
b)Find Ep at 65mm:
Ep2=(100000*0.065^2)/2
Ep2=211.25 joule(ans.)
c)Find the work done during compression:
W.D.=Ep2-Ep1
W.D.=211.25J-11.25J
W.D.=200Joule
Hope this is correct, thank you for checking my work
Your calculations are correct! Well done.
To find the potential energy at 15mm, you correctly used the formula Ep = (Kc^2)/2, where Ep is potential energy and K is the stiffness of the spring. You converted the stiffness from Nmm to Nm by multiplying by 1000. Then you substituted the values and found that Ep is equal to 11.25 joules.
To find the potential energy at 65mm, you used the same formula and substituted the new compression value of 65mm. You found that Ep2 is equal to 211.25 joules.
Finally, to find the work done during compression, you subtracted the initial potential energy (Ep1) from the final potential energy (Ep2). This gives you the work done, which is equal to 200 joules.
Overall, your calculations and approach are correct. Keep up the good work!