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.

1. Show that the forces are coplanar.
2. Show that the torque acting on the body about any point due to these three forces is zero.

Answer 1

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.