Question 230: Laws of Motion

Question

A system consists of three masses m
1
, m
2
and m
3
connected by a string passing over a pulley P. The mass m
1
hangs freely and m
2
and m
3
are on a rough horizontal table (the coefficient of friction = $$\mu $$). The pulley is frictionless and of negligible mass. The downward acceleration of mass m
1
is (Assume m
1
= m
2
= m
3
= m)

Accepted Answer

Force of friction on mass m
2
= $$\mu $$m
2
g
Force of friction on mass m
3
= $$\mu $$m
3
g
Let a be common
acceleration of the
system.
$$ 	herefore $$ $$a = {{{m_1}g - \mu {m_2}g - \mu {m_3}g} \over {{m_1} + {m_2} + {m_3}}}$$
Here, m
1
= m
2
= m
3
= m
$$ 	herefore $$ $$a = {{mg - \mu mg - \mu mg} \over {m + m + m}} = {{mg - 2\mu mg} \over {3m}} = {{g\left( {1 - 2\mu } ight)} \over 3}$$
Hence, the downward acceleration of mass m
1
is $${{g\left( {1 - 2\mu } ight)} \over 3}$$

Answer

$${{g\left( {1 - g\mu } \right)} \over 9}$$

Answer

$${{2g\mu } \over 3}$$

Answer

$${{g\left( {1 - 2\mu } \right)} \over 3}$$

Answer

$${{g\left( {1 - 2\mu } \right)} \over 2}$$

Laws of Motion

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