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Two persons manage to push a motorcar of mass 1200 kg at a uni... - Science
Two persons manage to push a motorcar of mass 1200 kg at a uniform velocity along a level road. The same motorcar can be pushed by three persons to produce an acceleration of 0.2 m s⁻². With what force does each person push the motorcar? (Assume that all persons push the motorcar with the same muscular effort.)
Given:
Mass of the motorcar (
m) =1200 \text{ kg}Acceleration produced by 3 persons (
a) =0.2 \text{ m s}^{-2}Let the force exerted by one person be
F.
Step 1: Analyze the situation with 2 persons
When 2 persons push, the car moves with uniform velocity (acceleration = 0). This means the force applied by them exactly balances the frictional force.
\text{Frictional Force} = 2 \times F = 2F
Step 2: Analyze the situation with 3 persons
When 3 persons push, the total force is 3F. The net force causing acceleration is the total force minus the frictional force.\text{Net Force} = \text{Total Force} - \text{Frictional Force}\text{Net Force} = 3F - 2F\text{Net Force} = F
Step 3: Calculate the force using Newton's Second Law
\text{Net Force} = m \times aF = 1200 \times 0.2F = 240 \text{ N}
Answer: The force exerted by each person is 240 \text{ N}.