How Do Torque and Work Relate in Physical Systems?

[MLoren]

1. Four horses together pull an old-fashioned drill of the type used to make big guns. It has four levers mounted horizontally on a revolving central axes. Assuming each horse pulls at the same angle of 45 degress to the radial lever of the drill, and pulls with a given force, T, how much work do the horses perform together over one full revolution of the drill?

I got as far as drawing out the picture of this problem and starting the work: First of all the Work of one revolution is equal to 2*pi*torque right? Then in trying to find the torque... this is where I get confused.

Also...
2. How much work do the biceps perform when lifting a 2 kg mass from the lower arm positioned 45 degrees downward to horizontal?

This problem I don't even know where to start.

Both of these problems involve torque and work but i am not sure how to relate them.

Any help would be appreciated!

 

[Doc Al]

Welcome to PF!

I got as far as drawing out the picture of this problem and starting the work: First of all the Work of one revolution is equal to 2*pi*torque right?

Right.

Then in trying to find the torque... this is where I get confused.

The torque exerted by a force about an axis is \tau = \vec{r}\times\vec{F} = r F sin\theta, where r is the distance from the axis to the point where the force is applied and \theta is the angle the force makes with the radial vector.

Also...
2. How much work do the biceps perform when lifting a 2 kg mass from the lower arm positioned 45 degrees downward to horizontal?

Since the work is done against gravity, start by finding the vertical distance the mass is lifted.

 

[Tide]

Minor point, Al, but you have equated a vector to scalars. Obviously it's not what you meant.

 

[Doc Al]

Minor point, Al, but you have equated a vector to scalars. Obviously it's not what you meant.

You caught me being lazy, Tide!
Yes, the torque is a vector. r F sin\theta is just the magnitude of the torque.