The Physics
Hypertextbook
Opus in profectus

# Simple Machines

## Practice

### practice problem 1

Write something else.

### practice problem 2

A bucket grain elevator is powered by a 150 kW electric motor. Determine its efficiency if it can lift grain to a height of 60 m at a rate of 900 m3/h. Assume the elevator is lifting wheat with a density of 770 kg/m3.

#### solution

Start with the definition of power. Replace work with potential energy. We will ignore the kinetic energy of the wheat, since our real goal is to elevate the grain, not accelerate it. Replace mass with density times volume.

 P = W = mgh = ρVgh t t t

Rearrange it just a bit and substitute the numbers given to compute the power delivered as useful work.

 P = ρ V gh t
 P = (770 kg/m3) (900 m3) (9.8 m/s2)(60 m) (3600 s)
 P = 113 kW

Compare this to the rated power of the motor to get the efficiency of the grain elevator.

 η = Wout = Pout = 113 kW = 75% Win Pin 150 kW

### practice problem 3

Write something different.