Question

A 200 kg set used in a play is stored in the loft above the stage. The rope holding the set passes up and over a pulley, then is tied backstage. The director tells a 100 kg stagehand to lower the set. When he unties the rope, the set falls and the unfortunate man is hoisted into the loft. What is the stagehand' acceleration? < Disregard this question and is an information for the question belowHow does the magnitude of the tension acting on the set change from when the rope was tied backstage to when the stagehand is being hoisted into the loft?A. The magnitude of the tension decreased B. The magnitude of the tension increased C. The magnitude of the tension is the same for both cases

Answer 1

a) a = 3.27 m/s²

b) The magnitude of the tension decreased

Step-by-step explanation:

Part A.

Given:

Mass of the Set: m = 200 Kg

Mass of the stagehand: M = 100 Kg

asystem = a = ?

We can assume masless rope and masless frictionless pulley. Since the rope is masless and the pulley is ideal, the tension Ts and Tm have the same magnitude, T.

In order to understand the question, we can see the pic shown.

We do the free body diagram for m and M, then we can apply Newton's Second Law:

Stagehand:

∑Fy = M*a (+↑)

T - M*g = M*a (I)

Set:

∑Fy = m*a (+↓)

- T + m*g = m*a (II)

Then, we solve the system of equations for a:

T - M*g = M*a

- T + m*g = m*a

⇒ a = g*(m - M)/(M+m)

⇒ a = (9.81 m/s²)*(200 - 100) Kg / (200+100) Kg

⇒ a = 3.27 m/s²

Part B.

The magnitude of the tension decreased due to the system is in motion. On the other hand, the inertia acts on the system (no motion, in this case).