Question

A 6.7-kg box is being lifted by means of a light rope that is threaded through a single, light, frictionless pulley that is attached to the ceiling. (a) If the box is being lifted at a constant speed of 2.0 m/s, what is the power delivered by the person pulling on the rope? kW (b) If the box is lifted, at constant acceleration, from rest on the floor to a height of 1.2 m above the floor in 0.42 s, what average power is delivered by the person pulling on the rope?

Answer 1

a.
`P=131.32 W`

b.
`P=447.95W`

Step-by-step explanation:

a).

`v=2.0 m/s`

`P=m*g*v`

`P=6.7kg*9.8m/s^2*2.0m/s=131.32 (kg*m^2)/(s^3)`

`P=131.32 W`

b).

`h=(1)/(2)*a*t^2`

`a=(2*h)/(t^2)=(2*1.2m)/((0.42s)^2)`

`a=13.6 m/s^2`

`F=m*g+m*a`

`F=6.7kg*9.8m/s^2+6.7*13.6m/s^2`

`P=(F*d)/(t)`

`P=(188.136kg*m^2/s^2)/(0.42s)`

`P=447.95W`