How much work is needed to push a 147- kg packing crate a distance of 2.5 m up a frictionless inclined plane?

Question

that makes an angle of 31 degrees with the horizontal?

Answer 1

1854.91 Joules.

W=Fx

Fy=mgsin31
mgsin31=741.964
Fx=0 (no friction)

741.964*2.5=1854.91

Answer 2

The work done on the box to move it up the ramp will be equal to the change in the gravitational Potential Energy of the box.
The box initially has no Potential Energy when it located at the bottom of the ramp on the ground. As you exert the force on the box and do work by moving it up the ramp (against the force of gravity), you are increasing its Potential Energy.

PE = mass * gravity * height
Where “gravity” is the gravitational acceleration the box experiences (9.81 m/s^2) and “height” is the distance the box moves in the vertical direction as it travels up the ramp (its final height above the ground at the top of the ramp).

Work done on box = change in PE

We are given a value for the mass of the box and we are assumed to know the gravitational acceleration constant. All we need now is the change in the box’s height when it is at the top of the ramp.

To find the change in height we imagine the ramp as a triangle.
The incline plane the box slides on is the hypotenuse (length 2.5 meters). The side of the triangle opposite the angle is the vertical height of the ramp at the top.
|..\
|…\
|…..\
|__a_\_
Where a is the angle of incline.

To find the length of the opposite side of the triangle we multiply the length of the hypotenuse by the sine of the angle of incline.
Height = 2.5 meters * sin (31 degrees)
Height = 1.29 meters

Now we have all the information we need.

Work done on box = change in PE
Initially the box had zero PE, so the change in PE would be equal to the value of its final PE.
The PE of the box at the top equals,
PE = (147 kg)(9.81 m/s^2)(1.29 meters)
PE = 1860 Joules

The change in PE equals the work done to move the box to the top.
Work = 1860 Joules.

Answer 3

147 Kg