# What is the lenght of the lever arm? (when torque and force are given)

• DeeAussie
In summary, the problem is finding the length of the lever arm that must be used to exert a torque of 55N.m with a maximum force of 135N. The equations lever arm=(r)(sin) and torque=(force)(r)(sin) can be used to solve for the lever arm, but the problem statement is not clear on the angle theta, so it must be assumed that the force is applied perpendicular to the arm. This means that the lever arm is the perpendicular distance from the line of action of the force to the axis of rotation.

## Homework Statement

If a torque of 55N.m is required and the largest force that can be exerted by you is 135N, what is the length of the lever arm that must be used?

## Homework Equations

Lever Arm=(r)(sin)
Torque=(Force)(r)(sin)

## The Attempt at a Solution

To be honest, I'm stumped

The answers are in the formulas you've posted. If lever arm = r sin theta, and torque = force * r sin theta, then torque = force * lever arm. Since you know torque and force, you can solve for lever arm.

kelly_kelly said:
The answers are in the formulas you've posted. If lever arm = r sin theta, and torque = force * r sin theta, then torque = force * lever arm. Since you know torque and force, you can solve for lever arm.
That's not quite right, and neither is the problem statement very clear. if T=rFsintheta, then you need to know theta in order to solve for r, where r is the length of the lever arm, unless one assumes that the force is applied perendicular to the arm. Is theta given in the problem?

PhanthomJay said:
That's not quite right, and neither is the problem statement very clear. if T=rFsintheta, then you need to know theta in order to solve for r, where r is the length of the lever arm, unless one assumes that the force is applied perendicular to the arm. Is theta given in the problem?

Everything I listed was what was given so I guess you do have to assume perpendicular?

DeeAussie said:
Everything I listed was what was given so I guess you do have to assume perpendicular?
I looked up the definition of 'lever arm' on several web sites, and discovered that some call it the length of the position vector between the point of application of the load and the axis of rotation (Wiki) while others call it the perpendicular distance from the line of action of the force to the axis of rotation. I tend not to trust Wiki most of the time (they take a simple topic and make it as complex as is humanly possible), so let's go with the latter. In which case the lever arm is __________(fill in the blank).