(a) (15 pts) A net force is applied to a mass m that is initially at...

(a) (15 pts) A net force is applied to a mass m that is initially at rest on a level frictionless surface. The force varies with position and is given by F(x)=Ax3/2. The force is applied tothemassfrompositionsx=0tox=d. Aftertheforcestopsacting,the mass then slides throughalevelfrictionpatchwithcoefﬁcientoffriction µk.

How far does the mass travel through the friction patch before coming to rest? Put your answer in terms of m,g,d, µk,and A.

(b) (5 pts) Now, suppose that instead of the position-varying force acting on the mass, a time-varyingnetforceF(t)=At3/2 acted on the block from time st =0tot =t1. After the time-varying force stopped acting, then the block went through the same friction patch. For this new scenario, what would be your approach to solving this problem? Brieﬂy explains using equations and/or technical words. Be speciﬁc to earn full credit. Solving part (b) is not required for full credit.

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genius_generous answered 1 year ago

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