Question

if a torque of 55.0 N/m is required and the largest force that can be exerted by you is 135 N what is th e length of the lever arm that must be used?

Answer 1

`r=0.41m`

Step-by-step explanation:

Torque is defined as the cross product between the position vector ( the lever arm vector connecting the origin to the point of force application) and the force vector.

`\tau=r* F`

Due to the definition of cross product, the magnitude of the torque is given by:

`\tau=rFsin\theta`

Where
`\theta` is the angle between the force and lever arm vectors. So, the length of the lever arm (r) is minimun when
`sin\theta` is equal to one, solving for r:

`r=(\tau)/(F)\\r=(55(N)/(m))/(135N)\\r=0.41m`