# Work Done by a Constant Force (Q6 page 188 of Cutnell and Johnson)

1. Aug 15, 2014

### gcombina

6.A person pulls a toboggan for a distance of 35.0 m along the snow with a rope directed 25.0° above the snow. The tension in the rope is 94.0 N.

a) How much work is done on the toboggan by the tension force?

Ok, so W = (F cos Θ) s
= (94.0 cos 25°) 25 m
= WRONG ANSWER

I know the answer is 94.0 times distance but that would equal WORK right (fs)

why are they doing (94.0 N)(35.0 M) = Force???

**this is really frustrating , why are they including distance as force?

Last edited: Aug 16, 2014
2. Aug 15, 2014

### olivermsun

So what does it say in terms of a "right" answer or solution?

Why does your solution have 94.0 twice?

3. Aug 16, 2014

### Staff: Mentor

Hi gcombina. What does that "s" in your formula stand for? What units would it have?

Also, what are the units of that "W"?

4. Aug 16, 2014

### gcombina

this is the "right" answer

W = (94.0 N) (35.0 m) cos 25.0 = 2980 J

5. Aug 16, 2014

### gcombina

it was my mistake, i corrected it already.

6. Aug 16, 2014

### gcombina

basically, this is the right answer => (94.0 N) (35.0 m) cos 25° =2980 J

this is formula (F cos θ)s I always use, but now they are using (Fs cos θ), where is this formula comes from?????

I though W = (F cos θ)s and NOT (Fs cos θ)

7. Aug 16, 2014

### Orodruin

Staff Emeritus
Uhmmmm ... It is the same. Multiplication is commutative so it does not matter what order you multiply things in.

8. Aug 16, 2014

### Staff: Mentor

Do these give the same answer?

9. Aug 18, 2014

### gcombina

no, they don't give the same answer

Fs cos θ => (94.0 N) (35.0 m) cos 25° =2980 J

AND

F cos θ => (94.0 N) cos 25° = 85.19 J

10. Aug 18, 2014

### Nathanael

Check your units. You wrote Joules but it is actually Newtons.

I think you meant "(F cos θ)s"? In which case, you do get the same answer.

11. Aug 18, 2014

### haruspex

The distance is 35m, not 25m.

12. Aug 18, 2014

### Staff: Mentor

There is something very fundamental that you are misunderstanding, but I'm having difficulty identifying what.

They aren't. It's difficult to see why you might think they are.

F s cosθ = Force x distance x cosθ

13. Aug 18, 2014

### olivermsun

Starting from the beginning, step by step:

W = (F cos Θ) s

The distance is s = 35.0 m
The force in the direction that the distance is measured over is F cos Θ = (94.0 N)(cos 25°)

W = (F cos Θ) s = (94.0 N)(cos 25°)(35.0 m) = 2980 N m = 2980 J.

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