In an experimental test conducted on hoisting machine, it was found that an effort of 40 kN was applied to lift a load of 180 kN. An effort of 32 kN was required to lift a load of 140 kN. As per law of machine, effort required to lift 15kN load is

Explanation:

Concept:

Hoisting machine:

• A hoist is a device used for lifting or lowering a load by means of a drum or lifts wheel around which a rope or chain wraps.
• It may be manually operated, electrically, or pneumatically driven and may use chain, fiber, or wire rope as its lifting medium.
• The hoist works on the same principle of level or hydraulic jack to take load advantage.

• In the above figure higher weight M₁ is raised using lower weight M₂ because of lever advantage.

          M₁ × a = M₂ × b  

• In the case of the hoist, one more thing is to be considered while making calculations. It is the dead weight of hoist cables and trolleys.

          M1 × a + c = M2 × b   .......  (1)

• Here, the term "c" indicates that some of the torque is used for lifting the dead weight of the hoist which will be the same irrespective of the load raised.

​Calculation:

Data given, M₁ = 180 kN, M₂ = 40 kN

                   L₁ = 140 kN, L₂ = 32kN

                   N₁ = 15 kN

Putting the values in equation (1),

180 × a + c = 40 × b

140 × a + c = 35 × b

Now, assuming \(\frac{a}{b}\) as m and \(\frac{c}{b}\) as n, we get

180 × m + n = 40   ...... (2)

140 × m + n = 32   ...... (3)

After solving the above 2 equations, we get m = 0.2, n = 4

∴ 15 × m + n = N₂

∴ 15 × 0.2 + 4 = N₂

 ∴ N₂ = 7 kN