help making physics formulas?

Question

A block of weight w sits on a plane inclined at an angle theta as shown. View Figure The coefficient of kinetic friction between the plane and the block is mu. Theresa Carlson
A force F_vec is applied to push the block up the incline at constant speed.

What is the work W_f 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. and i got W_f,L.

L*cos theta *mu *-w.

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.

and

What is the change in the potential energy of the block, DeltaU, 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.

Answer 1

To solve this problem first understand all the forces acting on the block (e.g. gravity and friction).



The gravitation force as I will call Fe= sin(theta)*w. Draw a free body diagram and think about why this is true.



The friction force as I will call Ff=cos(theta)*w*mu. Do the same thing here.



Then add these forces together to get the total force required to push the block. In other words what I will cal 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)]*L



Now for Potential Energy (DeltaU).



First Identify the two energies to handle. 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. We already calculated this Pfric=cos(theta)*w*mu*L



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

Answer 2

Work done by force of kinetic friction:



W_f=(mu)(wcostheta)L



mu=coefficient of kinetic friction

wcostheta=component of weight normal to the incline

L=the displacement



Assuming F is applied parallel to the incline:



W=FL



Assuming F is applied parallel to the ground.



W=(Fcostheta)L



Change in Potential Energy, DeltaU:



DeltaU=wLsintheta



Who is Theresa Carlson? Anyway, I suggest you draw the diagram showing the block and the inclined plane and the angle.



Just remember the basic formula for work which is force*distance; the basic formula for force of friction which is coefficient of friction*weight normal to the plane: basic formula for potential energy=weight*vertical displacement. It doesn't matter whether you are given symbols like x,y,z . As long as you know your basic formulas you can still do the problems. Also try to remember how to compute the components of the weight or force if you are given the angle of the incline. These things are repeated over and over again in problems in Physics.

Answer 3

The work done on the block is (F_r) * L + w*∆h, F_r is the friction force, L is the distance moved along the incline, and ∆h is the change in elevation of the block. F_vec will be F_r + w*sin(theta), it has to push against friction as well a lift the block. F_r will be µ*F_n where F_n is the normal force on the plane, which will be w*cos(theta). ∆h will be L/sin(theta).



The change in potential energy is w*∆h

Answer 4

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Answer 5

Sorry but there is no figure.