Question

Consider two masses that hang from an overhead beam. The first mass of 50.5 kg is attached to the beam using an ideal rope. The second mass of 16.9 kg is attached to the first mass with an ideal rope and hangs directly under the first mass.

(a) Find the tension in the lower rope.


(b) Find the tension in the upper rope.

Answer 1

a) 165.79 N

b) 661.19 N

Step-by-step explanation:

Given

First mass of mass, m1 = 50.5 kg

Second mass of mass, m2 = 16.9 kg

The tension in the lower rope balances the weight of the second mass, so that we have

T(lower) = 16.9 kg * 9.81 N/kg = 165.79 N

The tension in the upper rope would then balance the weight of the both the upper and lower masses together (if we assume the ropes to be ideal, then we can neglect their own masses), so that

T(upper) = (50.5 kg + 16.9 kg) * 9.81 N/kg

T(upper) = 67.4 kg * 9.81 N/kg

T(upper) = 661.19 N

Therefore, the tension in the lower rope is 165.79 N and that in the upper rope is 661.19 N