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Question
There are three forces F1, F2 and F3 acting on a body, all acting on a point P on the body. The body is found to move with uniform speed.
- Show that the forces are coplanar.
- Show that the torque acting on the body about any point due to these three forces is zero.
Solution
As the body is moving with uniform speed (velocity) its acceleration a = 0.
∴ The sum of the forces is zero, F1 + F2 + F3 = 0
a. Let F1, F2 and F3 be the three forces passing through a point. Let F1, and F2, be in plane A (one can always draw a plane having two intersecting lines such that the two lines lie on the plane). Then F1 + F2 must be in plane A. Since, F3 = – (F1 + F2), F3 is also in 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 is Torque = OP × (F1 + F2 + F3). Since, F1 + F2 + F3 = 0, torque = 0.
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