Three different pulley systems are shown to the right. Each system supports a cy

Question

Three different pulley systems are shown to the right. Each system supports a cylinder with a mass specified in the table below. Take the following value: Loads m_cylinder = 30.06 kg Complete the following: Determine the force P_a required for system (a) to be in equilibrium. Assume the pulleys and cable are massless. Determine the force P_b required for system (b) to be in equilibrium. Assume the smaller diameter pulley has a mass of m_1 = 10 kg, the larger diameter pulley has a mass of m_1 = 20 kg, and all other elements (other than the cylinder) are massless. Determine the force P_c required for system (c) to be in equilibrium. Assume the pulleys and cable are massless.

Explanation / Answer

(a) Let T be the tension in the string, as the pulley and the rope is mass less, the tenstion T in all parts of string is same.

On the left most part

T = Pa

Now the weight is supported by total 4 strings and tension in each part of the string is T

hence 4T = 30.06*9.8 = 294.59 N

Pa  = T = 73.65 N

b) The weight is supported 3 strings, hence

3T = 30.6*9.8 = 294.59 N

Pb = T = 98.20 N

c) T = Pc

The string connecting the weight ends at the left free pulley.

Let the tension in the string be T'

Now this pulley is carried by two string in which the tension is T

hence T' = 2T

Now the weight is carried by three string in which the tension is T'

3T' = 30.6*9.8 = 294.59 N

6T = 294.59

Pc = T = 294.59/6 = 49.1 N

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