Question

A tractor pulls a harrow (a ploughing tool) of mass m1 with a net force F resulting in an acceleration of a₁. The same tractor pulls a trolley of mass m₂ with a force F producing an acceleration of a₂. If the tractor now pulls the trolley with the harrow placed on it (with the same force F), then obtain an expression for the resulting acceleration in terms of a₁ and a₂. Ignore friction.

Answer 1

Using Newton’s second law of motion (F = ma) for the harrow,

F = m₁a₁

∴ m₁ = `F/(a_1)`

For the trolley,

F = m₂a₂

∴ m₂ = `F/(a_2)`

The total mass = m₁ + m₂ when the same force F pulls the trolley with the harrow on it.

Let the resulting acceleration be a. Then,

F = (m₁ + m₂) × a

or

`a = F/(m_1 + m_2)`

Substituting the values of m₁ and m₂,

`a = F/(F/a_1 + F/a_2)`

= `F/(F (1/a_1 + 1/a_2))`

= `1/(1/a_1 + 1/a_2)`

Hence, the resulting acceleration is

`a = (a_1a_2)/(a_1 + a_2)`