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Friction and Vertical Circular Motion Problems

Three blocks ...

Question

Three blocks are placed at rest on a smooth inclined plane with force acting on $m_{1}$ parallel to the inclined plane. Find the contact force between $m_{2}$ and $m_{3}$ .

\frac{(m_{1} + m_{2} + m_{3}) F}{m_{3}}

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\frac{m_{3} F}{m_{1} + m_{2} + m_{3}}

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F - (m_{1} + m_{2}) g

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None of the above

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Solution

The correct option is B $\frac{m_{3} F}{m_{1} + m_{2} + m_{3}}$
Acceleration, $a = \frac{F}{m_{1} + m_{2} + m_{3}}$
Forces acting on the combination of $m_{1}$ and $m_{2}$
$F - T = (m_{1} + m_{2}) a$
$T = F - (m_{1} + m_{2}) a$
$T = F - (m_{1} + m_{2}) (\frac{F}{m_{1} + m_{2} + m_{3}})$
$T = F (\frac{m_{1} + m_{2} + m_{3} - m_{1} - m_{2}}{m_{1} + m_{2} + m_{3}})$
$T = \frac{m_{3} F}{m_{1} + m_{2} + m_{3}}$

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Three blocks are placed at rest on a smooth inclined plane with force acting on m1 parallel to the inclined plane. Find the contact force between m2 and m3.

The correct option is B m3Fm1+m2+m3Acceleration, a=Fm1+m2+m3Forces acting on the combination of m1 and m2F−T=(m1+m2)aT=F−(m1+m2)aT=F−(m1+m2)(Fm1+m2+m3)T=F(m1+m2+m3−m1−m2m1+m2+m3)T=m3Fm1+m2+m3

Three blocks are placed at rest on a smooth inclined plane with force acting on $m_{1}$ parallel to the inclined plane. Find the contact force between $m_{2}$ and $m_{3}$ .