Solve Elevator Problem: Work & Power Required

[tnhoots]

Homework Statement

A skier of mass 69.7 kg is pulled up a slope by a motor-driven cable.
(a) How much work is required to pull him a distance of 59.8 m up a 29.9° slope (assumed frictionless) at a constant speed of 1.90 m/s?
(b) A motor of what power is required to perform this task?
hp

Homework Equations

(a) w=f*change in distance*cos angle
(b) power=work/change in time

The Attempt at a Solution

gravity is the only force in play. so the equation for work would be
w=(9.8m/s^2)(59.8m)(cos29.9)=508.03

take that value and divide it by change in time to get power

*correct?

 

[Dick]

"cos angle" refers to what angle? With respect to your given angle cos is the wrong trig function. You are also missing a mass factor which would have been obvious if you had checked the units on your answer.

 

[chaoseverlasting]

No. w=f.s=m.a.s
You haven't taken the mass of the skier into account. The acceleration will be along the incline (which youve taken incorrectly).

 

[chaoseverlasting]

Power can be calculated by p=fv

 

[tnhoots]

Ok so the F in the problem is 9.8m/s^2. I would use cos0. However, the change in distance is unknown. Using the formula d=time * speed, I found it to be 8.75m. So, now would I use the work formula with the numbers (9.8m/s^2)(8.75m)(cos0). Which equals 85.57J. After I find that I would divide work by time (5secs) to find average power which is 17.15 W...just my thinking??

 

[Jack Nagel]

F is not 9.8 m/s^2. That is a. You are forgetting to take into account mass of the skier. force = mass * acceleration

 

[tnhoots]

Ok-so hopefully this is it:
W=(mass of skier*acceleration)(change in distance)(cos29.9)
W=(132.43)(59.8)(cos29.9)=6865.23.
Then take that value and divide by the time which is 31.55 seconds.
Which equals 217.6 hp

 

[robb_]

The SI unit of power is watts. There are about 746 watts per h.p. but you better look up that number, i am pulling it out of my head.

 

[tnhoots]

Is the way I worked the problem out correct? I just need to convert the 217.6 watts to hp? I have had trouble solving this problem. It would be nice to know if this thinking is correct.

 

[robb_]

The reasoning seems okay to me.

 

[tnhoots]

UGH! I'm still stuck. Any help would be greatly appreciated!

 

[robb_]

Where are you stuck?

 

[tnhoots]

alright...i think I've got it. I have to run to class, but I will post later witht the answer I finally came up with! YAY!

 

[tnhoots]

actually, nevermind that answer was also incorrect. sorry to get our hopes up! Still working...

 

[robb_]

whoops, you shouldn't be looking at the cosine of theta. Sorry, just caught that.