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.