The motor of a crane uses power P to lift a steel beam. By what
factor must the motor's power increase to lift the beam twice as
high in half the time?
factor must the motor's power increase to lift the beam twice as
high in half the time?
Answer
P = mgh / t
P ' = mg 2h / [ t/2 ] = 4 mgh / t = 4 P
4 times
We know that
Power = workdone / time
= m g h /
t
Now
P ' = m g h' / t'
Given that h' = 2 h
t' = t / 2
Therefore
P ' = m g 2h / t/2
= 4
m g h / t
= 4
P
Therefore power increases by four times of intial power
general formula-->P = mgh / t
changed power P ' = mg 2h / [ t/2 ] = 4 mgh / t = 4 P
hence,factor must be increased by factor 4.