First slide

Connected bodies

Question

A particle of a small mass m is joined to a very heavy body by a light string passing over a light pulley. Both bodies are free to move. The total downward force on the pulley is

Moderate

A

mg
B

2mg
C

4mg
D

>> mg

Solution

$F = \frac{{4mMg}}{{(m + M)}}(M > > m)$
$= \frac{{4mMg}}{{M\left( {m/M + 1} \right)}} \simeq \frac{{4Mmg}}{M} \Rightarrow F \simeq 4mg$

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