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A tractor pulls a harrow of mass m
1
with net force F, giving acceleration a
1
. The same tractor pulls a trolley of mass m
2
with force F, giving a
2
. If it now pulls the trolley with the harrow on it (same force F), find the resulting acceleration in terms of a
1
and a
2
. (Ignore friction.)
View Answer
From F = ma: \( m_1 = \dfrac{F}{a_1} \) and \( m_2 = \dfrac{F}{a_2} \).
Together the mass is \( m_1 + m_2 = \dfrac{F}{a_1} + \dfrac{F}{a_2} \). The new acceleration is
\( a = \dfrac{F}{m_1 + m_2} = \dfrac{F}{\frac{F}{a_1} + \frac{F}{a_2}} = \dfrac{1}{\frac{1}{a_1} + \frac{1}{a_2}} = \mathbf{\dfrac{a_1 a_2}{a_1 + a_2}} \).
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