Question

The figure above shows an 80-kilogram person standing on a 20-kilogram platform suspended by a rope passing over a stationary pulley that is free to rotate. The other end of the rope is held by the person. The masses of the rope and pulley are negligible. You may use g = 10m/s². Assume that friction is negligible, and the parts of the rope shown remain vertical.

a. If the platform and the person are at rest, what is the tension in the rope?

The person now pulls on the rope so that the acceleration of the person and the platform is 2 m/s² upward.

b. What is the tension in the rope under these new conditions?

c. Under these conditions, what is the force exerted by the platform on the person?

Answer 1

a. Combining the person and the platform into one object, held up by two sides of the rope we have ΣF = ma; 

2T = (80kg + 20kg)g giving T = 500N 

b. Similarly, ΣF = ma; 2T – 1000N = (100kg)(2m/s²) giving T = 600N

c. For the person only: ΣF = ma; N + 600N – mg = ma gives N = 360N