A 4.2x10^3-N piano is to be slid up a 3.5-m frictionless plank at a constant speed. The plank makes an angle of 30 deg. with the horizontalcalcwI...

Given:

Force exerted by the
piano = f = 4.2x10^3 N

Angle of the plank = A = 30
degrees

Distance to be moved = d = 3.5
m

The weight of piano, and their the force exerted by it is
acting in vertically downward direction.

The component of
gravitational force of piano acting along the plank (f1) is given by
formula:

f1 = fx(Sign A)

=
(4.2x10^3)x(Sin 30) = (4.2x10^3)x0.5 = 2.1x10^3

Since the
the plank is frictionless there is no frictional force to be overcome to move the piano
up the plank.

Also the plank is moved up at constant speed.
Therefor, there is no work done to accelerate the piano when it is
moved.

Therefor, the only force required to move the piano
up the plank is the force requires to exactly over come the force f1 pulling the piano
down the plank. Magnitude of this force is also equal to
f1.

And the work done to move the piano is given
by:

Work done = (Force)x(Distance moved) =
(f1)x(d)

= 2.1x10^3x3.5 = 7.35x10^3
N-m