## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

(a) $W_T = 570~J$ $W_g = -200~J$ The normal force does zero work on the crate. (b) The increase in thermal energy is 85 J
(a) We can find the work done by tension; $W_T = T\cdot d$ $W_T = T~d~cos(\theta)$ $W_T = (120~N)(5.0~m)~cos(18^{\circ})$ $W_T = 570~J$ We can find the work done by gravity. $W_g = F_g \cdot d$ $W_g = (mg)~d~cos(\theta)$ $W_g = (8.0~kg)(9.80~m/s^2)(5.0~m)~cos(120^{\circ})$ $W_g = -200~J$ The normal force acts at a $90^{\circ}$ angle to the direction of motion. Therefore, the normal force does zero work on the crate. (b) The increase in thermal energy is equal in magnitude to the work done by friction; $W_f = F_f\cdot d$ $W_f = (mg)~cos(\theta)~\mu_k~d~cos(180^{\circ})$ $W_f = (8.0~kg)(9.80~m/s^2)~cos(30^{\circ})(0.25)(5.0~m)(-1)$ $W_f = -85~J$ The increase in thermal energy is 85 J