what is the power supplied by the force of friction?

Question

a block of mass, m = 353g is dragged with a string across a rough horizontal table. The string tension is T= 3.27 N, and it pulls upward at an angle of 45º with the horizontal. At one particular instant, the block is moving at a speed of 6.70 m/s. The coefficient of kinetic friction between the block and the table is 0.684.

1. what is the power supplied to the block by the string tension?
2. what is the power supplied by the force of friction?

Answer 1

Lily,

The power P supplied by a force component F acting in the direction of velocity v is P=Fv ; if F is opposite to the velocity , then P=-Fv

A force T applied to our block upward at an angle θ to the horizontal, would have a component Tcosθ that causes the block to move.

The role of the other (vertical) component Tsinθ would be to decrease the normal force pressing the block to the surface. W/o the rope, the block would press on the surface with a normal force (equal to it weight) N=mg. When being pulled by the rope, the block would now press on the ground with a reduced normal force N=mg-Tsinθ, causing the frictional force (acting against the velocity) to become

F_fr =- μ_k(mg-Tsinθ)

The power P supplied to the block by the rope T would be

P=(Tcosθ) v (1)

while the power of frictional force

P_fr=-μ_k(mg-Tsinθ) v. (2)

In our problem sinθ=cosθ=1/Sqrt(2) [θ=45^o]

By using the given data in (1) and (2) you'd get the result

Hope it was helpful

Dr.Ariel B.