A block of mass 1.00 kg sits on an inclined plane as shown. A force of magnitude

Question

A block of mass 1.00 kg sits on an inclined plane as shown. A force of magnitude 50.0N is pulling the block up the incline. The coefficient of kinetic friction between the plane and the block is 0.500. The inclined plane makes an angle 50.0 degrees with the horizontal.

Part A
What is the total work W_fric done on the block by the force of friction as the block moves a distance 9.00m up the incline?
Part B
What is the total work W_F done on the block by the applied force F_vec as the block moves a distance 9.00m up the incline?
Part C
What is the total work W_fric done on the block by the force of friction as the block moves a distance 9.00 m down the incline?
Part D
What is the total work W_F done on the box by the applied force 50.0N in this case?

Explanation / Answer

1) N=mg cos 50= 1 x 9.8 x Cos50 = 9.8Cos50 N u*N= 0.5 x N = 0.5 x 9.8 Cos50 = 4.9Cos50 N Work Done by the Frictional Force = F(fric) . S = u*N x S = 4.9Cos50*9 = 38.1917 J This work is negative as it’s done against the motion( f(fric) acts in a direction opposite to the motion of the body). Work Done is actually F (dot product )S =F s Cos(theta). So work done by friction is -38.1917J 2) Work done by 50 N = 50 x 9 = 450 J ( positive; in direction of motion or theta =0) 3) Direction doesn't matter. The friction does work given by the magnitude of its force and the distance. The magnitude of its force doesn't change. is the same as 1 as the displacement is the same and it is still negative. 4) First lets make a triangle of hypotenuse 9m, then the vertical height is 9Sin50 = 6.89m Now place the block on the lower edge of the hypotenuse. Now as you move the block along 10m. really you are just raising the weight through a height of 6.89m ( an analogy would be like climbing stairs). Hence the total IDEAL work done is IDEAL WORK = mgh = 1 x 9.8 x 6.89 = 67.568 J But in our system we have friction, so if we count the work done to overcome friction we would get the work required to move the block 9m Frictional Work = 38.1917 J Net, Real Work = 67.568 + 38.1917 = 105.75 J

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