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

Answer:

Car has more power output than crane      

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 $W=mgh=1000\times 9.8\times 10=98000j$

Time period is given as t = 5 sec

We know that power $P=\frac{W}{t}=\frac{98000}{5}=19600watt$

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 $=\frac{1}{2}mv^2-\frac{1}{2}mu^2$

$=\frac{1}{2}\times 1000\times 10^2-\frac{1}{2}\times 1000\times 0^2=50000j$

Time ids given as t = 2 sec

So power $P=\frac{W}{t}=\frac{50000}{2}=25000watt$

So car has more power output than crane