Question 190: Laws of Motion

Question

A constant force acts on two different masses independently and produces accelerations $\mathrm{A}_1$ and $A_2$. When the same force acts on their combined mass, the acceleration produced is

Accepted Answer

From Newton's second Law
$$ \mathrm{F}=\mathrm{ma} \Rightarrow \mathrm{a}=\frac{\mathrm{F}}{\mathrm{~m}} $$
Acceleration $\mathrm{A}_1$ in mass $\mathrm{m}_1$,
$$ A_1=\frac{F}{m_1} \Rightarrow m_1=\frac{F}{A_1} $$
Acceleration $A_2$ in mass $m_2$,
$$ A_2=\frac{F}{m_2} \Rightarrow m_2=\frac{F}{A_2} $$
Acceleration ' a ' of combined Mass.
$$ 	herefore \quad a=\frac{F}{m_1+m_2}=\frac{F}{\frac{F}{A_1}+\frac{F}{A_2}}=\frac{1}{\frac{1}{A_1}+\frac{1}{A_2}}=\frac{A_1 A_2}{A_1+A_2} $$

Answer

$\quad A_1-A_2$

Answer

$\mathrm{A}_1+\mathrm{A}_2$

Answer

$\frac{A_1 A_2}{A_1+A_2}$

Answer

$\sqrt{A_1^2+A_2^2}$

Laws of Motion

A constant force acts on two different masses independently and produces accelerations \mathrm{A}_1 and A_2. When the same force acts on their combined mass, the acceleration produced is

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