Question

a uniform rod of length 30 cm having a mass of 3.0 kg. The strings are pulled by constant forces of 20 N and 32 N. Find the force exerted by 20 cm part of the rod on the 10 cm part. All the surfaces are smooth and the strings and pulleys are light. Force of 20 N acts on 10 cm part and 32 N on 20 cm

Answer 1

Answer on Question #44134-Physics-Mechanics-Kinematics-Dynamics

A uniform rod of length $30~\mathrm{cm}$ having a mass of $3.0~\mathrm{kg}$ . The strings are pulled by constant forces of $20~\mathrm{N}$ and $32~\mathrm{N}$ . Find the force exerted by $20~\mathrm{cm}$ part of the rod on the $10~\mathrm{cm}$ part. All the surfaces are smooth and the strings and pulleys are light. Force of $20~\mathrm{N}$ acts on $10~\mathrm{cm}$ part and $32~\mathrm{N}$ on $20~\mathrm{cm}$

Solution

Figure 5-E8

Clearly the $10~\mathrm{cm}$ part of the rod has mass $1~kg$ and the $20~\mathrm{cm}$ part $2~kg$ . Since both parts move together, let their acceleration due to the two force be $a$ . If $F$ be the force exerted by the $20~\mathrm{cm}$ part on $10~\mathrm{cm}$ part then from the motions of $10~\mathrm{cm}$ and $20~\mathrm{cm}$ parts we get

$F - 20 = a$

$- F + 32 = 2a.$

So

$F = \frac{72}{3} = 24N.$

Answer: $24N$ .

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