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?
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.`