Question

To hoist himself into a tree, a 72.0-kg man ties one end of a nylon rope around his waist and throws the other end over a branch of the tree. he then pulls downward on the free end of the rope with a force of 371 n. neglect any friction between the rope and the branch, and determine the manâs upward acceleration. use g =9.80 m/sec2.

Answer 1

0.506 m/s^2 Given the arrangement of rope and the man, he's effectively suspended by a rope from a frictionless pulley. So he's pulling the rope with a force of 371 n causing him to be pulled upwards by his arms. Additionally, the rope goes up to the pulley and back down to the man causing an additional 371 n of force pulling him upwards. So the total force being used to lift the man is 742 n. Additionally, the man is being pulled downwards by gravity at 9.80 m/s^2. And since he masses 72.0 kg, the downward force in newtons is 72.0 kg * 9.80 m/s^2 = 705.6 n downward. So the total force being exerted on the man is 742 n - 705.6 n = 36.4 n To calculate his acceleration, simply divide the number of newtons applied by his mass. 36.4 kg m/s^2 / 72.0 kg = 0.505556 m/s^2 And round to 3 significant figures. 0.505556 m/s^2 = 0.506 m/s^2