Question

There are three forces $\overrightarrow{F_1},\overrightarrow{F_2}$ and $\overrightarrow{F_3}$ acting on a body, all acting on a point $P$ on the body. The body is found to move with uniform speed.

A Show that the forces are coplanar.

B Show that the torque acting on the body about any point due to these three forces is zero.

Answer 1

A) Since the body is moving with no acceleration, the sum of the forces is zero

$\overrightarrow{F_1}+\overrightarrow{F_2}+\overrightarrow{F_3}=0$

Let $\overrightarrow{F_1},\overrightarrow{F_2},\overrightarrow{F_3}$ be the three forces passing through a point. Let $\overrightarrow{F_1}$ and $\overrightarrow{F_2}$ be in the plane $A$.

Then $\overrightarrow{F_1}+\overrightarrow{F_2}=$ exists in plane $A$

$\because \overrightarrow{F_3}=-(\overrightarrow{F_1}+\overrightarrow{F_2}),\overrightarrow{F_3}$ is also in the plane $A$.



B) Consider the torque of the forces about $P$. Since all the forces pass through $P$, the torque is zero. Now consider torque about another point $O$. Then,

Torque about $O=\overrightarrow{OP}\times (\overrightarrow{F_1}+\overrightarrow{F_2}+\overrightarrow{F_3})+$ Torque about $P$

Since $\overrightarrow{F_1}+\overrightarrow{F_2}+\overrightarrow{F_3}=0$, Torque about $P=0$.

Torque about $O=0$