Here is the Problem: As shown in the diagram, a barrel of mass m slides down a p

Question

Here is the Problem:

As shown in the diagram, a barrel of mass mslides down a plank of length s from a height hdown to the ground. The coefficient of kinetic frictionbetween the plank and the barrel is K. Derive anexpression for the total work done by the force of friction on thekeg.

An algebraic formula, as opposed to a numerical answer, is onewhich contains symbols (such as m1 or g) instead ofnumbers with units (such as 9.8 m/s2).  Dimensionless numbers such as p or ½ are perfectly OK in analgebraic formula, but numbers with dimensions are not allowed.

Explanation / Answer

Wf= f S f= k N; since N=mgcos()  where = arcSin( h/S) [or   we can express N/F = (S2 -h2) / S ; N = F(S2 - h2) /S were F=mg] we have Wf= k N S = kmgcos() Wf= kmgcos() where = arcSin( h/S) or Wf= k [F(S2- h2) / S] S ;   Finallty Wf=k mg(S2 -h2)

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