Question

How much work does it take to push an object with a mass of `2 kg` up a `3 m` ramp, if the ramp has an incline of `(5pi)/12` and a kinetic friction coefficient of `2`?

Answer 1

W = 87.21 J

Explanation:

The ramp is at an angle of 75 degrees, so to find the force of gravity pulling it down, we find:

`F_"g" = mg*sin(theta) rArr F_"g" = 19.6 *sin(75) = 18.93 N`

Now, to find the for of the opposing friction force, we find:

`F_"F" = mu * F_"N"`

In the case of a ramp, normal force is only the component of gravity perpendicular to the ramp, so:

`F_"N" = mg * cos(theta) = 5.07 N`

`F_"F" = 2 * 5.07 = 10.14 N`

Now we can use F_"net" = ma to find set up total force. And assuming the minimum work is wanted, a (an subsequently m) will be set to 0.

`F_"net" = ma`
`F_"net" = cancel(m)(0)`
`F_"net" = 0`
`F_"a" - 18.93 - 10.14 = 0`
`F_"a" = 29.07 N`

Now to find work, use W= f*d cos(theta), where theta will be set to 0 as we assume the force is applied in the same direction of the ramp.

`W = 29.07 * 3 cos(0)`
`W = 29.07 * 3`
`W = 87.21 J`