Question

A 3858 N piano is to be pushed up a(n) 3.49 m frictionless plank that makes an angle of 31.6 ◦ with the horizontal. Calculate the work done in sliding the piano up the plank at a slow constant rate. Answer in units of J.

Answer 1

The work done will be equal to the potential energy of the piano at the final position

P.E=m.g.h

.consider the plank the hypotenuse of the right triangle formed with the ground
.let x be the angle with the ground=31.6°
.h be the side opposite to the angle x (h is the final height of the piano)
.let L be the length of the plank

sinx=opposite side / hypotenuse
= h/L

then h=L.sinx=3.49×sin31.6°=0.638m

weight w=m.g
m=w/g=3858/10=385.8kg

Consider Gravity g=10m/s2

then P.E.=m.g.h=385.8kg×10×0.638=2461.404J

then Work W=P.E.=2451.404J

Answer 2

Answer:

7055.13 J

Explanation:

Step 1: identify the given parameters

• Applied force on the piano = 3858N
• Length of plank = 3.49m
• angle between the plank and horizontal surface = 31.6⁰

Note: frictional force between the piano and horizontal surface is zero since the plank is frictionless.

Step 2: work done in sliding the piano up the plank = applied force X distance moved by the piano.

The distance moved by the piano is equal to the height above ground when the piano reach top of the plank.

• make a sketch of right angle triangle
• length of the plank is the hypotenuse side
• angle between the hypotenuse and the horizontal is 31.6⁰
• height of the triangle is the height above ground , let it be the unknown  

Height of the triangle = 3.49m X sine31.6⁰

Height of the triangle = 1.8287m

Recall, height of the triangle is the height above ground which is equal to the distance moved by the piano

work done in sliding the piano up the plank = applied force X distance moved by the piano.

work done in sliding the piano up the plank = 3858N X 1.8287M

                                                                           = 7055.13 J