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
assistance needed
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I agree with your numbers.
Thanks drwls... could you check the next one please
To find the potential energy at 15mm, we can use the formula Ep = (1/2) * K * c^2, where Ep is the potential energy, K is the stiffness of the spring, and c is the compression of the spring.
In this case, we are given that K = 100 Nmm, which is equivalent to 100 N * 0.001 m = 100 Nm. And c is 15mm, which is equal to 0.015m. Plugging these values into the formula:
Ep = (1/2) * 100 Nm * (0.015m)^2 = 11.25 Joules.
So the potential energy at 15mm is 11.25 Joules.
To find the potential energy at 65mm, we can use the same formula with the new value of c, which is 65mm or 0.065m:
Ep = (1/2) * 100 Nm * (0.065m)^2 = 211.25 Joules.
So the potential energy at 65mm is 211.25 Joules.
Lastly, to find the work done during compression, we can subtract the initial potential energy from the final potential energy:
Work Done = Ep2 - Ep1 = 211.25 J - 11.25 J = 200 Joules.
Therefore, the work done during compression is 200 Joules.