Question

How much work would it take to push a `8 kg` weight up a `5 m` plane that is at an incline of `pi / 4`?

Answer 1

The work done against the force of gravity is 277 joules.

Explanation:

The reason work must be done in this situation is that an applied force must act against gravity.

Work done on against (or by) a force is defined by

`W=FDeltadcostheta`

where `theta` is the angle between the direction of travel of the object and the direction of the force being applied.

You need to notice that in a problem such as this, the angle of the incline (and therefore of `Deltad`) is stated with respect to the horizontal, but because gravity is a vertical force, the angle we use in the formula is not this angle, but rather, we use its compliment (`pi/2 - theta`), because `theta` must be measured with respect to `F_g`.

That said, this time, both angles would be `pi/4`, but in the future, if faced with this question, try to keep this in mind.

The work done is `W=F(Deltad)cos(pi/4) = (8)(9.8)(5)(sqrt2/2)=277 J`