Question

A 400-kg piano is being unloaded from a truck by rolling it down a ramp inclined at 23 ∘. There is negligible friction and the ramp is 15.0 m long. Two workers slow the rate at which the piano moves by pushing with a combined force of 1200 N parallel to the ramp.

If the piano starts from rest, how fast is it moving at the bottom?

V= ? m/s

Answer 1

Workdone by workers, W_workers = F*d*cos(180)

= 1200*d*(-1)

= 1200*15*(-1)

= -18000 J

Workdone by gravity, W_gravity = +m*g*sin(23)*d

= 400*9.8*sin(23)*15

= 22975 J

Net workdone = 22975 - 18000

= 4975 J

Net workdone, Wnet = gain in kineti energy

Wnet = 0.5*m*v^2

==> v = sqrt(2*Wnet/m)

= sqrt(2*4975/400)

= 4.99 m/s <<<<<<---------Answer