A monkey is sitting on a wood plate attached to a rope whose other end is passed
ID: 2184155 • Letter: A
Question
A monkey is sitting on a wood plate attached to a rope whose other end is passed over a tree branch, as shown in the figure. The monkey holds the rope and tries to pull it down. The combined mass of the monkey and the wood plate is 144 kg.(a) What is the minimum force the monkey has to apply to lift off the ground?
(b) What applied force is needed to move the monkey with an upward acceleration of 1.40 m/s2?
(c) Explain how the answers would change if a second monkey on the ground pulled on the rope instead.
Explanation / Answer
a, Consider the situation with the monkey just off the ground. You have the weight force mg downwards in equilibrium with the tension force in TWO lengths of rope upwards. {One rope tied to the wood plate and the other being pulled by the monkey.} It's the same rope over the branch, so assuming no friction, the tension force (T) in both parts of the rope will be equal, and equal to the force provided by the monkey. So, 2T = mg = 144 * 9.81 = 1412.64 N T =1412.64/ 2 = 706.32 N b. The net force required to result in an upward acceleration of 2.69 m/s² can be found using Newton's Second Law Force = mass * acceleration Force = 144 kg * 1.4m/s² = 201.6 N upwards. That net force is made up of the weight force mg = 1412.64 N downwards {from part (a)} and the upward force 2T due to the rope. 2T - 1412.64 = 201.6 2T = 1637.5 N T = 1637.5 / 2 = 807.12N c. The monkey on the ground does not benefit from the 'pulley effect' and so has to provide a force = mg = 1412.64 N