Shaft speed of a motor at 80% efficiency

[NEGATIVE_40]

Homework Statement

A motor produces 1000kW of power, running at 1500rpm. What is the running speed if it runs at 80% power?

Homework Equations

None that I know of. You can find the torque by the below equation (but again, I don't know how to deal with the 80%)

$$P = \frac{Tn}{9549}$$
where P is power (kW), T is torque (N.m), n is rotational speed in rpm.

The Attempt at a Solution

Is it just a proportion type thing?

i.e

80% power means 0.8*1000 kW = 800 kW
so then
0.8*1500rpm = 1200 rpm ?

 

[KataKoniK]

Dear fellow scientist,

You are correct in your approach! Since power is directly proportional to rotational speed, we can use the equation P = Tn/9549 to solve for the new rotational speed at 80% power.

First, we can rearrange the equation to solve for rotational speed:
n = 9549P/T

Then, we can substitute in the given values:
n = 9549(800kW)/(1000kW)
n = 7639.2 rpm

Therefore, the running speed at 80% power would be approximately 7639 rpm.

I hope this helps! Keep up the good work in your scientific endeavors.