A force produces acceleration of 16m/s2 in a body of mass 0.5 kg,and an acceleration of 4 m/s2 in another body.If the bodies are fastened together,then by how much acceleration will be produced by this force?

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Solution

in the first case
a₁ = 16 m/s²
m₁ = 0.5 kg
so, force
F₁ = m₁.a₁
or
F₁ = 0.5 x 16
so, F₁ = F = 8N
this same force is applied to the second body of mass m₂
so,
F = m₂a₂ = 8N
or
m₂ = 8N / a₂
or
m₂ = 8 / 4 = 2 kg
now,
the combined mass will be M = m₁ + m₂ = 0.5kg + 2kg = 2.5kg
the force applied is the same as before, F = 8 N
now, acceleration
a = F/M = 8N / 2.5kg
thus,
a = 3.2 m/s²

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