# Calculating power

1. Nov 5, 2007

### pooface

1. The problem statement, all variables and given/known data
An escalator in a department store is designed to carry 300 passengers per minute from the ground floor to the mezzanine, 10m vertically higher. The design assumes an average weight per person of 70 kg. Allowing 30 percent loss for friction, calculate the power output which the driving motor must have.

2. Relevant equations
KE = 0.5mv^2

3. The attempt at a solution
So calculating the velocity of the escalator
since it travels 10 meters in 60 seconds
10m/60 = 0.16667 m/s

mass is 300 passengers * 70kg = 21000 kg

work=0.5mv^2 = 291.167 J

power = 291.167J/60 s = 4.86 W

Is this good so far? 4.86 W is pretty low.

2. Nov 5, 2007

### anap40

You also need to account for the potential energy(massxgravityxheight) that each person gains from moving up 10m

3. Nov 5, 2007

### pooface

so in this case it would be

work=0.5mv^2 + mgh?

= 2.06 MJ

power = 34.34 KW

so i should add 30% to this for the motor to compensate for 30% frictional loss?

power the motor should output = 44.642 KW?

thanks.

Last edited: Nov 5, 2007
4. Nov 5, 2007

### anap40

That looks correct to me.