Question

While at a construction site, you see a crane lift a 1000kg steel beam up to a height of 10m in a time period of 5.0 seconds. A few minutes later, you see a 1000kg car go from rest to 10m/s in a time period of 2.0 seconds? Calculate the power output of the car engine and the crane motor. Which has a higher power output?

Answer 1

Car has more power output than crane

Step-by-step explanation:

We have given that mass of the crane m = 1000 kg

Height through which crane lift the steel beam h = 10 m

Acceleration due to gravity
`g=9.8m/sec^2`

So work done by crane
`W=mgh=1000* 9.8* 10=98000j`

Time period is given as t = 5 sec

We know that power
`P=(W)/(t)=(98000)/(5)=19600watt`

Now mass of the car = 1000 kg

Initial velocity u = 0 m /sec

Final velocity v = 10 m/sec

We know that work done is equal to the change in kinetic energy

So work done
`=(1)/(2)mv^2-(1)/(2)mu^2`

`=(1)/(2)* 1000* 10^2-(1)/(2)* 1000* 0^2=50000j`

Time ids given as t = 2 sec

So power
`P=(W)/(t)=(50000)/(2)=25000watt`

So car has more power output than crane