help on physics?

Question

a hydraulic motor rotates 28000 revolutions to do 9000000 joules of work. what is the average torque produced by the motor?

Answer 1

As we know the work W is related to force F moving a body in a distance s by equation:

W = F*s

Assuming that this force results in a circular motion we have

s=R*theta

where R is the radius of the circular movement and theta the angle of rotation.

So W=F*R*theta

But F*R = T, where T is the torque of F.

So W = T * theta ->
T = W / theta

Substituting we get
T = 9000000 / 28000 N*m ->
T = 9000 / 28 N*m->
T = 321.4 N*m (approximate value)

Answer 2

Torque is essentially energy per revolution.

Thus, we can multiply torque by the number of revolutions to find out how much work was done.

Torque*(28000 revolutions)=9000000 Joules

Torque = (9000000 Joules)/(28000 revolutions)
Torque = 321.429 Newton-meters

Note that Newton-meters are essentially the same unit as Joules. However, torque is not exactly the same thing as energy, so we use a different name.