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Chapter 7: Q. 37 (page 179)

The $10.2 k g$ block in FIGURE $P 7.37$ is held in place by a force applied to a rope passing over two massless, frictionless pulleys. Find the tensions $T_{1} t o T_{5}$ and the magnitude of force $\overset{鈫�}{F}$ .

Short Answer

Expert verified

Tension in the rope, $T_{1} = 100 N, T_{2} = T_{3} = T_{5} = F = 50 N a n d T_{4} = 150 N$ .

Step by step solution

01

Given information

Mass of the block, $m = 10.2 k g$

Given the mass and pulleys system

02

Explanation

Consider the equilibrium block

$T_{1} = m g$

localid="1649647716658" $T_{1} = (10.2 k g) 脳 (9.81 m / s^{2}) = 100 N$

Consider the equilibrium of a small pulley

$T_{1} = T_{2} + T_{3}$

Since T₂ and T₃ are attached to the same pulley, therefore the tension $T_{2} = T_{3}$

localid="1649647731493" $100 N = 2 T_{2} T_{2} = T_{3} = 50 N$

Similarly, T₂ and T₅ are attached to the same pulley, therefore the tension $T_{2} = T_{5}$

$T_{5} = 50 N$

Since the tension in the ropeT₅would be equal to the forceF

$F = T_{5} = 50 N$

Consider the equilibrium of a large pulley

localid="1649647749005" $T_{4} = T_{2} + T_{3} + T_{5} T_{4} = 50 N + 50 N + 50 N = 150 N$

Tension in the rope, $T_{1} = 100 N, T_{2} = T_{3} = T_{5} = F = 50 N a n d T_{4} = 150 N$ .

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