Solving Work and Energy Questions: Skier of Mass 67kg

[islanderman7]

Homework Statement

A skier of mass 67 kg is pulled up a slope by a motor-driven cable.
(a) How much work is required to pull him 40 m up a 30° slope (assumed frictionless) at a constant speed of 1.7 m/s?

m= 67kg
Delta y= 40m
Theta= 30 degrees
v= 1.7m/s

Homework Equations

I know that:

F=ma
W= F cos(Theta) (Delta y)

The Attempt at a Solution

I am solving for the force:
F=ma
F= 67 (1.7)
F= 113.9 N/m

With F solved I use my Work Equation:
W= F cos(Theta)(Delta y)
W= 113.9 (cos30) (40)
W= 3945.61 J
W= 3900 J

My answer differs from the correct answer by 10% to 100%

What am I doing wrong? Am I using the wrong equations?

 

[Mindscrape]

So you know that he has to be pulled up a distance of 40*sin(30). Work is the force times the component of the directional change projected onto the force (i.e. $F \cdot \Delta s$). Where does this lead you? (Hint: your directional thinking is wrong.)

Don't just use equations, know where they come from. Yes, it's hard if it's your first time, but you really can't just plug and chug and expect to get away it.

 

[Moetasim]

Your equations and approach seem to be correct. The difference in your answer may be due to rounding errors or slight variations in the given values. It is also possible that the correct answer was calculated using more precise values or a different method. It would be helpful to double check your calculations and also consider any assumptions or approximations made in the problem.