Question

A cart for hauling ore out of a gold mine has a mass of 413 kg, including its load. the cart runs along a straight stretch of track that is sloped 4.69° from the horizontal. a donkey, trudging along and to the side of the track, has the unenviable job of pulling the cart up the slope with a 4.10 × 102-n force for a distance of 175 m by means of a rope that is parallel to the ground and makes an angle of 14.3° with the track. the coefficient of friction for the cart\'s wheels on the track is 0.0163. use g = 9.81 m/s2. find the work that the donkey performs on the cart during this process.

Answer 1

Given from the problem :mass m = 413 kg;coefficient of friction u = 0.0163;acceleration due to gravity g = 9.8 m/s2;inclined angle @1 = 14.3;inclined angle  @2 = 4.69;distance travelled d = 175 m;applied fore F = 410 N;  the component of the force from the donkey in the direction of motion isF2 = F1 [email protected]= 397.2964498768165 N
Fy = N - mg [email protected] = 0N = mg [email protected] = 4037.964151113007 NFx = F2 - mg [email protected] - f = mahere f = u N=65.8188156631420141

F2 - mg [email protected] - f = maa = F2 - mg [email protected] - f/ m=0.31923412183075155 m/s^2
work done by donkeyW = F2 d=69526.8787284428875 J