Question #160922
A 50.0 g object connected to a spring with a force constant of 35.0N/m oscillates with amplitude of 4.00cm on a frictionless, horizontal surface. Find
(a) the kinetic and potential energy when its position is 3.00cm
1
Expert's answer
2021-02-12T18:38:16-0500

U=kx22,U=\frac{kx^2}{2},

U=350.0322=15.75 mJ,U=\frac{35\cdot 0.03^2}{2}=15.75~\text{mJ},

ω=km,\omega=\sqrt{\frac km},

cosωt=xA,sinωt=1x2A2,cos \omega t=\frac xA,\\sin\omega t=1-\frac{x^2}{A^2},

K=mω2A2sin2ωt2=k(A2x2)2,K=\frac{m\omega^2A^2sin^2\omega t}{2}=\frac{k(A^2-x^2)}{2},

K=35(0.0420.032)2=12.25 mJ.K=\frac{35\cdot(0.04^2-0.03^2)}{2}=12.25~\text{mJ}.


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!
LATEST TUTORIALS
APPROVED BY CLIENTS