A constant force F acts on the mass m1and m2 to produce respective acceleration of a1 and a2 - If same force acts on the object of mass - m1-m2- then prove that the magnitude of acceleration produced is -a1a2-a1-a2

Acceleration #160;of #160;first #160;mass:a1=Fm1Then, #160;m1=Fa1Acceleration #160;of #160;second #160;mass:a2=Fm2Then, #160;m2=Fa2Acceleration ...

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Standard IX

Physics

Third Law of Motion

A constant fo...

Question

A constant force F acts on the mass m₁and m₂ to produce respective acceleration of a₁ and a₂ . If same force acts on the object of mass ( m₁+m₂), then prove that the magnitude of acceleration produced is (a₁a₂)/a₁+a₂

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Solution

$Acceleration of first mass : a_{1} = \frac{F}{m_{1}} Then, m_{1} = \frac{F}{a_{1}} Acceleration of second mass : a_{2} = \frac{F}{m_{2}} Then, m_{2} = \frac{F}{a_{2}} Acceleration of combined mass : a = \frac{F}{m_{1} + m_{2}} = \frac{F}{\frac{F}{a_{1}} + \frac{F}{a_{2}}} = \frac{F}{F [\frac{1}{a_{1}} + \frac{1}{a_{2}}]} = \frac{1}{[\frac{1}{a_{1}} + \frac{1}{a_{2}}]} = \frac{a_{1} a_{2}}{a_{1} + a_{2}}$

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A constant force F acts on the mass m1and m2 to produce respective acceleration of a1 and a2 . If same force acts on the object of mass ( m1+m2), then prove that the magnitude of acceleration produced is (a1a2)/a1+a2

Acceleration of first mass:a1=Fm1Then, m1=Fa1Acceleration of second mass:a2=Fm2Then, m2=Fa2Acceleration of combined mass:a=Fm1+m2 =FFa1+Fa2 =FF1a1+1a2 =11a1+1a2 =a1a2a1+a2

A constant force F acts on the mass m₁and m₂ to produce respective acceleration of a₁ and a₂ . If same force acts on the object of mass ( m₁+m₂), then prove that the magnitude of acceleration produced is (a₁a₂)/a₁+a₂