Answer to Question #88716 in Mechanics | Relativity for Samuel

Question

A 3 kg block is moved up a 37 degrees incline under the action of a constant horizontal force of 40 N. The coefficient of kinetic friction is 0.1, and the block is displaced 2 meters up the inclined. Calculate (a) the work done by the 40 N force,(b) the work done by the gravity, (c) the work done by the friction, and (d) the changed in kinetic energy of the block

Answer 1

(a) The work done by the 40 N force:

$$W_1=Fd=(40)(2)=80 \ J$$

(b) The work done by the gravity:

$$W_2=mgh=mgd \sin{37}=(3)(9.8)(2) \sin{37}=35.4\ J$$

(c) The work done by the friction:

$$W_3=F_fd=\mu mgd \cos{37}=0.1(3)(9.8)(2) \cos{37}=4.7\ J$$

(d) ) The change in kinetic energy of the block:

$$\Delta K=W_1-W_2-W_3=80-35.4-4.7=40\ J$$