Question

The system is in equilibrium and the pulleys are frictionless and massless. 5 kg 8 kg 9 kg T Find the force T. The acceleration of gravity is 9.8 m/s 2 . Answer in units of N.

Answer 1

Explanation:

It is given that mass at the right side of the pulley weighs 9 kg, mass at the center weighs 8 kg and mass at the left side weighs 5 kg.

Hence, starting from the right side

              $T_{1}$ = 9 kg

Now,  $T_{2} = 2 \times 9 kg$

                      = 18 g

Hence, the force balance on 8 kg mass is as follows.

            $T_{2} + mg = T_{3}$

     $T_{3}$ = $(18 + 8) \times g$

                 = 26 g

Now, force balance on 5 kg mass is as follows.

              5 g + T = $2 \times 26 g$

                 T = 47 g

                   = $47 \times 9.8$

                   = 460.6 N

Therefore, we can conclude that value of force T is 460.6 N.

Answer 2

The value of force T is 460.6N

Tension

Tension is a force developed by a rope, string, or cable when stretched under an applied force.

Given:

Mass (m₁) = 9 kg, m₂ = 8 kg, m₃ = 5kg, g = acceleration due to gravity = 9.8 m/s².

T₁ = 9 kg * 9.8 m/s² = 88.2N

T₂ = 2 * m₁ * g = 2 * 9 kg * 9.8 = 176.4N

T₂ + m₂g = T₃

176.4 + 8*9.8 = T₃

T₃ = 254.8N

Force balance on 5 kg mass:

T + 5(9.8) = 2 * T₃

T + 5(9.8) = 2 * 254.8

T = 460.6N

The value of force T is 460.6N

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