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Question · Revise, Reflect, Refine, Q15, page 114
A tractor pulls a harrow of mass m₁ with a net force F, giving acceleration a₁. The same tractor pulls a trolley of mass m₂ with force F, giving acceleration a₂. If the tractor now pulls the trolley with the harrow placed on it (same force F), find the resulting acceleration in terms of a₁ and a₂. Ignore friction.
![Question 15 — A tractor pulls a - How Forces Affect Moti - [Teachoo] - Questions at the end of the chapter](https://cdn.teachoo.com/9807de1f-ede4-432c-a592-ed03cd3b7068/animation-for-a-tractor-pulls-a-harrow-of-mass-m-with-a-net-force-f-giving-acceleration-a.-the-same-tractor-pulls-a.gif)
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Answer
- For the harrow alone: F = m₁a₁, so m₁ = F/a₁
- For the trolley alone: F = m₂a₂, so m₂ = F/a₂
- Now both move together, so the mass of the system is m₁ + m₂.
- a = F / (m₁ + m₂) = F / (F/a₁ + F/a₂)
- a = a₁a₂ / (a₁ + a₂)
