A block of weight w sits on a plane inclined at an angle theta as shown.(Figure

Question

A block of weight w sits on a plane inclined at an angle theta as shown.(Figure 1)The coefficient of kinetic friction between the plane and the block is mu. Part A What is the work Wf done on the block by the force of friction as the block moves a distance L up the incline? Express your answer in terms of some or all of the following: mu, w, theta, L. Part B What is the work W done by the applied force of magnitude F? Express your answer in terms of some or all of the following: mu, w, theta, L. Part C What is the change in the potential energy of the block, Delta U, after it has been pushed a distance L up the incline? Express your answer in terms of some or all of the following: mu, w, theta, L.

Explanation / Answer

the forces acting on the block (e.g. gravity and friction).

The gravitation force Fe= sin(theta)*w.

The friction force Ff=cos(theta)*w*mu.

add these forces together to get the total force required to push the block. Tot=Fw+Ff.

Now work is just force times distance or in your case W=Ftot*L
Hence,
Work=[(sin(theta)*w)+(cos(theta)*w*mu)…

Now for Potential Energy (DeltaU).

Identify the two energies

1. the energy of the height gained by the block.

2. The energy the block must overcome as it slides down the slide.

1. The potential energy gained is PE=w*h, where h is height. I your case h=sin(theta)*L. Hence PE=w*sin(theta)*L.

2. Pfric=cos(theta)*w*mu*L

DeltaU=PE-Pfric= w*sin(theta)*L-cos(theta)*w*mu*L

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