Need help with calculating work done by friction and work done by weight of a block, as well as max weight for a system to be in equilibrium?

1) One might argue that the formula is the same in each case --

work = force * distance.

a) friction Ff = µmgcosΘ, so friction Work = µmgdcosΘ

The distance d = h / sinΘ, so Work = µmgh / tanΘ

Plug in µ, m, g, h and Θ to solve for Work.

b) gravity Work = mgh

Plug in m, g and h to solve for Work.

c) The increase in KE = gravity Work - friction Work. Then solve

KE = ½mv² where v² is the only unknown.

To find the acceleration, use Torricelli's equation:

v² = u² + 2as = 0 + 2as = 2as

where distance s = h / sinΘ. Therefore

a = v²sinΘ / 2h

2. That 45º angle tells you that the vertical and horizontal forces at that point are equal; therefore the maximum weight of A is equal to the maximum friction force under B.

max A = max static friction = µ*Wb = 0.25 * 710N = 180 N

Note: if the angle was 26º, then max A = ½ * 0.25 * Wb

and if the angle was 63º, then max A = 2 * 0.25 * Wb.

(In other words, take the tangent of the angle to find the ratio of A / friction.)