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  • There are three forces F_1, F_2, and 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

There are three forces F_1, F_2, and 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

Answers (1)

(a) The acceleration of the body is zero since it is moving with uniform speed due to the action of the forces F_1, F_2, and F_{3} on a point on the body. It has no circular motion.

 Since, F = ma, resultant force will be

\overrightarrow{F_{1}}+\overrightarrow{F_{2}}+\overrightarrow{F_{3}}=0

\overrightarrow{F_{1}}+\overrightarrow{F_{2}}=-\overrightarrow{F_{3}} or \overrightarrow{F_{3}} = -(\overrightarrow{F_{1}}+\overrightarrow{F_{2}})

Let us consider that the forces \overrightarrow{F_1} and \overrightarrow{F_2} as well as the resultant of these forces, are in the same plane of the paper, but in [-(\overrightarrow{F_{ 1}} + \overrightarrow{F_{ 2}})] it is in the same plane except for the direction which is rephrased.

\overrightarrow{F_{3}} will be in the same plane since \overrightarrow{F _{3}} = -(\overrightarrow{F_{ 1}} +\overrightarrow{ F_{ 2}}), hence \overrightarrow{F_{ 1}} ,\overrightarrow{ F_{ 2}} and \overrightarrow{F _{3}} are coplanar.

 (b) The resultant of \overrightarrow{F_{ 1}} ,\overrightarrow{ F_{ 2}} and \overrightarrow{F _{3}} is zero, therefore, its torque= r \times \overrightarrow{F} = 0

F=\overrightarrow{F_{ 1}} +\overrightarrow{ F_{ 2}} + \overrightarrow{F _{3}} =0

Hence, the torque acting on the body at any point will be zero.    

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infoexpert24

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