USING A TORQUE TO STOP A MOTION: Darrin pulls on a rod mounted on a  frictionless pivot with a force of 78.2 N at a distance of 49 cm from the pivot. Samantha...

USING A TORQUE TO STOP A MOTION: Darrin pulls on a rod mounted on a 

frictionless pivot with a force of 78.2 N at a distance of 49 cm from the pivot. Samantha

 is trying to stop the rod from undergoing an angular acceleration by exerting

 a force in the opposite direction to the one Darrin exerts.

Sam’ s force is applied 85 cm from the pivot and is

 perpendicular to the rod. What is the magnitude of the “balancing” force?

Asked on by nurhan

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You need to remember the torque equation, such that:

`T = F*d`

F represents the magnitude of force

d represents the perpendicular distance to pivot axis

Since the Sam's force needs to stop the rod from moving yields the following equilibrium equation, such that:

`F_1*d_1 - F_2*d_2 = ` 0

`F_1` represents the Darrin's force

`F_2` represents Sam's force

`d_1 = 49 cm`

`d_2= 85 cm`

Replacing the provided values in equation yields:

`78.2*49 - F_2*85 = 0=>F_2 = 78.2*49/85 N`

`F_2 = 45.08N`

Hence, evaluating the requested balancing force yields `F_2 = 45.08N.`

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