How to do this Physics problem?
A crane raises a container weighing 1600 kg from the dock side to the level of the ship's deck, 10m above the dock. It takes 1 minute to raise the container this high and, in so doing the crane uses 240,000 J of energy.
a. Calculate the the rate at which the energy is used by the crane.
b. Calculate the rate at which work is done by the crane.
c. Calculate the efficiency of the crane
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I am assuming acceleration due to gravity g = 9.8m/s^2
a) It takes 1 minute to raise the container, and uses 240,000 Joules or energy for that. which means it consumes or uses energy at the rate
240000J/1 minute = 240000J/60 secs = 4000J/s
since 1 J/s is known as 1 Watt, it uses energy at 4000 W or 4 kW (kiloWatt)
b) The work done by the crane in lifting the crane will be measured by the changes it make to the gravitational potential energy of the container.
It lifts the container 10m above its initial level. So,
Change in P.E. of Container = mgh = 1600 kg * 9.8m/s^2 * 10m = 156800 Joules
so, Work Done by the Crane = 156800 Joules
This shows the Crane is inefficient, coz it uses 240000J of energy and outputs it by doing only 156800J of work.
The work is done in one minute. So, rate of crane doing work
156800J/60secs = 7840J/3secs = 2613J/s (approximately) = 2613W
C) efficiency = (Work done/energy consumed) * 100 = (156800/160000) * 100 = 0.98 * 100 = 98%
Hence the crane is 98% efficient.
And please, Select my answer as best. I typed a lot for you. :)