Answer:
- 30 kW
Explanation:
IDEA:
Power of an object that does work(source) is given by:
[tex] \boxed{ \mathsf{power = \frac{work \: done}{time} }}[/tex]
where work done is mostly shown as the Force applied on an object to Displace it through some distance in the same direction as the Force.
[tex] \boxed{ \mathsf{ work = force \times displacement}}[/tex]
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INFORMATION:
In the question,
The source of power is the crane, while the object is a load of 36000N.
Note, what's given is the force, not the mass. Since, the SI unit of mass is kg and that of Force is Newton(N).
[The weight of the load is represented in Newton, since weight of an object is the amount of Force with which the Earth attracts that object]
I) work done
So,
- Force = 36000N
- Displacement = 50 m
=> Work = 36000 × 50
= 1,800,000 J
(The SI unit of work is Joules(J)).
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II) power
After getting the amount of work done, now we have to place it in the formula for power.
That is:
[tex] \boxed{ \mathsf{power = \frac{work \: done}{time} }}[/tex]
Note, During calculations, all quantities must be in their SI units.
SI unit for time is Seconds (s)
But the time we have is in minutes.
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Converting time from minutes to Seconds:
1 minute = 60 Seconds.
Hence,
[tex] \implies \mathsf{power = \frac{1800000}{60} } \: [/tex]
=> power = 30,000 W
(SI unit of power is Watts(W))
To write four zeroes with a 3 and W is a lot of effort. So, we can look for simple expressions like kilowatts(kW) that can express bigger quantities in lesser terms.
1000 W = 1 kW
•°• 30,000 W = 30 kW.
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Direction and sign:
The crane displaces the load in an upward direction (from the term "lifts")
But, the Force is acting downwards, as the weight of the body is always towards the Earth.
Since, the directions of Force and displacement are opposite, a minus takes its place in front of both Work and power.
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Therefore, the final answer will be:
Power of the crane = - 30 kW
