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Energy/Work Question

  • #1

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?
 

Answers and Replies

  • #2
1,860
0
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. [itex]F \cdot \Delta s[/itex]). 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.
 

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