Calculating Horse Power Output for a Sled on an Inclined Hill

[mybrohshi5]

Homework Statement

A sleigh and driver with a total mass of 130 kg are pulled up a hill with a 15 degree incline by a horse

If the overall retarding frictional force is 800 N and the sled moves up the hill with a constant velocity of 5.0 km/h,
what is the power output of the horse? (Express in horsepower, of course.)

Homework Equations

P=W/t
P=F*(v)

The Attempt at a Solution

I first converted the 5 km/h to m/s

5km/h = 1.389 m/s

Not sure what to do now. I know there is a retarding force of 800N and i know the velocity so i want to say i can find the force by the horse to travel at that velocity with that retarding force but I am not sure how. cause then i believe if that force is found i could multiply that by the velocity to get the power in watts then convert to horsepower.

thanks for any help :)

 

[lightgrav]

it is a "block on a ramp, with friction" ; sum the force components parallel to the ramp.

or , see how much PE changes each second,
and how much Work is done against friction each second .

 

[mybrohshi5]

I think i am supposed to solve it using PE and Work because that is what my professor just went over.

The thing is i feel like i don't have enough information to find the Power.

I know potential energy is = m(g)(h)

Im just not sure how to apply that to this problem.

and to find the Work done against friction if the distance is not known how do i find this?

Would i use

W = change in kinetic energy

W = 1/2mv_f^2 - 1/2mv_i^2

v_i = 0 so

W = 1/2mv_f^2

Thanks for the help :)

 

[mybrohshi5]

I understand it using the component forces parallel to the incline.

I used: Ff + Fgx - Fh = 0

800 + 130(9.8)sin(15) = Fh

Fh = 1129.7

P = 1129.7(1.389)

P = 1569.2 watts or 2.1 horsepower.

But I would also really like to know how to use PE and W to find it though :) any tips?

 

[mybrohshi5]

Could i get some help with this next part. I thought i did it right but its wrong :(

Suppose that in a spurt of energy, the horse accelerates the sled uniformly from 5.0 km/h to 19 km/h in 6.0 s. What is the horse’s maximum instantaneous power output? Assume the same force of friction.

I found the acceleration

a = 5.278 - 1.389 / 6
a = 0.648

then i found the force of the horse (Fh)

Ff + Fgx - Fh = ma

800 + 130(9.8)sin15 - 130(0.648) = Fh

Fh = 1045.495

then i found the power

P = Fh * V_avg

P = 1045.495 ( 5.278 - 1.389 / 2)

P = 2032.96 W

P = 2.1 hp

that was wrong so i thought maybe since it says the max power output i thought to use just the velocity max so...

P = 1045.495(5.278) = 5518 W

P = 7.4 hp

but that was wrong also :(

Any suggestions? Thank you