Question

4. A block that has a mass of 750 kg is suspended by a rope from the end of a construction crane. Thecrane is moving the block upward with an acceleration of 2.5 m/s?a) Draw the free-body diagram of this situation. Label all of the forces with the appropriatesymbol. Be sure that the lengths of your arrows accurately represent the magnitudes of the forces.b) What is the weight (F) of the block? Show your work. Label the weight in part a with themagnitude you calculated here.c) What is the net force acting on the block? Show your work.d) What is the tension force acting on the block? Show your work. Label the tension force in parta with the magnitude you calculated here.no

Answer 1

a) The free-body diagram of the given situation is shown below:

where you can notice that the vector for the tension is larger than the vector for the weight of the block, due to the block is going up. That is, the force T, in magnitude is greater than F.

b) The weight of the block is:

F = m·g = (750 kg)(9.8 m/s²)

F = 7,350 N

c) The net force is:

Fn = m·a

Fn = (750 kg)(2.5 m/s²)

Fn = 1,875 N

d) The tension force is:

T - F = m·a

T = m·a + F

T = 1,875N + 7,350N

T = 9,225N