Power
(Use g = 9.8 Nkg-1)
Examples
A Find the work done in lifting a mass of
6 kg through a height of 10 m.
W
= Fx W work done in J
F
force in N
x distance
moved in the direction of the force in m
W
= 6 x 9.8 x 10
= 588 J
B) An
escalator carries 100 people of average mass 70 kg to a height of 6 m in one
minute.
Find the
power necessary to do this.
Work done = F
x = 100 x (70 x 9.8) x 6 J
Power = rate of doing work = work done
per second
= (100 x 70 x 9.8 x 6) / 60 s = 6860
W or 6.86 kW
- Find the work done to lift a mass
of 10 kg through a height of 5 m. If this takes 15 s what is the power?
- A mass of 5 kg is pulled along a
surface at a constant speed. Frictional force between the mass and the
surface is 4N what work is done in moving the mass 2 m along the surface? Find
the power if this takes 2 s.
- A girl of mass
50 kg runs up a flight of steps 4.5 m high in 5 s. What power does she
develop?
- 2000000 kg of
water per second flow over a large waterfall of height 50 m. What power is
available?
- The
first-stage rocket motors of the Saturn 5 moon rocket burnt fuel at the
rate of 13600 kg per second. The work done by the pumps to drive the fuel
into the combustion chambers was the same as that necessary to lift the
fuel through 1680 m. What power is needed to do this? (Your answer is
about twice the engine power of the largest ocean liner.)
- A gas turbine
locomotive developing 6330 kW pulls a train at a steady velocity of 108 kmh-
1. What is the total force in
- A mechanical
loader driven by an engine developing 3 kW lifts a total load of 200000 kg
to a height of 3 m in one hour. What is the work done on the load? How
much power is developed lifting the load? How does this compare with the
work done by the motor in the same time?
