Question

A crane is lifting a body to a height 'h' in time 't'. Find the relation between the power of crane to the speed at which it is lifting the object.

Explain with complete calculations & justifications.

Points : 15 ☺

Answer 1

potential energy of body = -mgh
where m is the mass of body , g is acceleration due to gravity and h is height of body from ground level.

now,
potential energy of crane = -(potential energy of body ).

so ,
potential energy of crane = mgh

we also know,
power = energy/time

so, power of crane = energy of crane /time taken to consume energy
= mgh/t
=mg(h/t)

h/t is height of object per unit time e.g

speed of object lifting upward =h/t (let V)

so ,
power = mgV

Answer 2

Let the crane lifts a body of mass 'm' to height 'h' in time 't' .
Then Work Done by Crane = mgh
where g is acceleration due to gravity .
Further ;
Power(P) = (Work Done) / (time taken)
P= mgh/t
=> P = mg ×(h/t)
here( h/t) is the speed ( say 'v')by which the crane is lifting the body .
=> P = mgv
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hope it helps!