Question

Determine the force P required to maintain equilibrium of the friction less pulley system shown and the reaction at the ceiling. W = 7.50 kip. Write the final answer here and upload the file with step by step calculations. W

Answer 1

Rule 1: Two ropes on both sides of the same pulley must have equal amount off tension.

Free body diagram 1:

th W

both tension are equal and that means

W = t + t

7.50 = 2 t

t = 7.50/2 = 3.75 kip

Rule 2: Tension on the same string is also same

Now look at the tension in green:

tal t, t t P W

t1 (green )= t (red) from rule 2

=> t1 = 3.75 kip

t2 = t1 from rule 1

t2 = 3.75 kip

Hence, P = t2 from rule 2

P = 3.75 kip

Now let us calculate reactions.

Ri R2 t, t P W

R2 = t from rule 2

hence R2 = 3.75 kip

R1 is pulled down by both t1 and t2, hence

R1 = t1 +t2

R1 = 3.75 + 3.75 = 7.5 kip

Total reaction at the ceiling = R1 + R2 = 7.5 + 3.75 = 11.25 kip

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