1. Your boss tells you to load a VERY heavy box onto a truck. You and three of y

Question

1. Your boss tells you to load a VERY heavy box onto a truck. You and three of your friends try to lift it, but it doesn't budge. Remembering from physics class how pulleys can help in this situation, you rig up the following system (shown on left). Assume the pulleys are massless and frictionless.

a. If the mass of the box is 1900 kg, what are the tensions T1 through T5 and force F needed to hold the box in place?

b. What are the tensions T1 through T5 and force F needed to lift the box with an acceleration of 0.13 m/s2?

See below. Please show all steps. Draw any diagrams as needed

Explanation / Answer

We need to keep following points into consideration while solving the given problem

a.) As the strings are massless, the tension applied on one end of it will be same as that at the other end. As in the tension will be transmitted completely.

b.) As the pulleys are massless, the net force acting on it upwards will be same as that acting downwards. Hence in the diagram as shown, T1 = T2 + T3; T4 = T2 + T3 + T5

Also, T3 = T2 and T2 = T5 [Point a above]

Hence, T1 = 2T2 and T4 = 3T2 and T2 = T3 = T5

Now we will use the above reasoning to solve the given problems as follows:

a.) For a mass of 1900Kg at rest, we have:

1900(9.81) = T1

or T1 = 18639 N

Using the relations above, T2 = T3 = T5 = 18639/2 = 9319.5

Hence, T4 = 3(9319.5) = 27958.5 N

b.) For an acceleration of 0.13 m/s^2 upwards, we will have:

T1 - Mg = Ma

or T1 = M(g + a) = 2423.07

Hence, T2 = T3 = T5 = T1/2 = 1211.535 N

And T4 = 3T2 = 3634.605 N

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