Question

How much work is required? A motor of what power is required?

Answer 1

See below

Explanation:

Work is essentially change in potential energy in this case, as the kinetic energy of the mass remains unchanged as the object travels at constant velocity.

`W=mgh`

Where `m` is mass of the skiir
Where `g` is the gravity
Where `h` is the height of the ramp

Another condition of work is that the force must be parallel to the direction of the motion, this works as gravity or the normal force is parallel to the height.

So, what is the height of this ramp?
Using trigonometry we can deduce that:
`h= 60m*sin(50°)= 45.963m`

`W= (70 kg)(9.81m/s^2)(45.963m)= 31600 J`

Another way to solve for the work here would be to determine the parallel force to the ramp length:
`P=(70kg)(9.81m/s^2)*sin(50°)= 526.04 N`

`W=Fd`
`W= 526.04 N*60 m= 31600J`

Power is essentially the work done in a specific unit of time:
`P= W/t= (Fd)/t= F*d/t= Fv`

Since power is equal to force times velocity, we can use the constant velocity given to solve for power, we will be using the PARALLEL force because that is parallel to the `60m` direction of motion:

`P = (526.04 N)(2m/s)= 1050 W`