Resistive Force

1. Sep 21, 2008

JJones_86

1. The problem statement, all variables and given/known data
A bicyclist rides 7.8 km due east, while the resistive force from the air has a magnitude of 2.4 N and points due west. The rider then turns around and rides 5.3 km due west. The resistive force from the air on the return trip has a magnitude of 4.5 N and point due east.

a) Find the work done by the resistive force during the round trip.
_____ J
b) Based on your answer to part (a), is the resistive force a conservative force?
Yes
No

2. Relevant equations
W=F*D

3. The attempt at a solution
W1=2.4N*7800M = 18720 J
W2=4.5N*5300M = 23850 J

Total Work = W1+W2 = 42570 J

I know my setup is wrong, can someone give me some hints? Thanks

2. Sep 21, 2008

LowlyPion

Why do you think that is wrong? Work is the integral of the scalar product of force and displacement isn't it?

3. Sep 21, 2008

Mattowander

For part a, your setup is mostly not right. However, keep in mind that if a force is applied and the displacement is in the opposite direction, then that force is doing negative work. (I.E. if you lift something straight up, gravity is doing negative work)

4. Sep 21, 2008

JJones_86

Well I know its not right because I'm getting the wrong answer

Ok, but am I using the right equations?

5. Sep 21, 2008

Mattowander

Yes you seem to be using the right equation. Check your sig figs if you're getting the wrong answer.

6. Sep 21, 2008

JJones_86

Ok so are you saying that my Forces should be negative since it's going in the opposite direction?

7. Sep 21, 2008

Mattowander

It depends on which direction you take to be negative. What I'm saying is that in both cases, the WORK done by the restrictive force must be negative because the direction of the restrictive forces is opposite the direction of displacement.

8. Sep 21, 2008

JJones_86

Is it possible to have a negative joule though?

W1=-2.4N*7800M = -18720 J
W2=-4.5N*5300M = -23850 J

Im sorry, I'm just really confused right now.

9. Sep 21, 2008

Mattowander

10. Sep 21, 2008

JJones_86

Ok, so my answer would be..

W1=-2.4N*7800M = -18720 J
W2=-4.5N*5300M = -23850 J

Total Work = W1+W2 = -42570 J?

11. Sep 21, 2008

Mattowander

The number is right. However, not both of the forces are negative.

If you define East to be positive, then the first 2.4N will be negative. However, the second force 4.5N is pointing East and so must also be positive. When the bike rider changes direction, he is first going towards a positive direction and then towards a negative direction. That is why the Work in either case is negative.

12. Sep 21, 2008

JJones_86

Oh ok, i see

So it would be
W1=2.4N*7800M = 18720 J
W2=-4.5N*5300M = -23850 J

Total Work = W1+W2 = -5130 J

But if I were to make the 2.4N the negative force, and the 4.5 postive, i would get a +5130 J, so would the final answer just be 5130 J, no matter the sign?

13. Sep 21, 2008

Mattowander

What I'm saying is that the forces are not always negative. The DISPLACEMENTS however can be negative. If you define East to be the positive x direction, then traveling west would mean your displacement is negative.

W1=-2.4N*7800M = -18720 J
W2=4.5N*-5300M = -23850 J
Total Work = W1 + W2 = -42570J

You had the right answer before but you arrived at it using wrong assumptions. I just wanted to make sure you understand that whether or not the displacement or force is negative depends upon the direction it is in.

14. Sep 21, 2008

JJones_86

Ok, I feel dumb now, lol. So the answer is -42570J, so the answer to part B is No, right? Because conservative would mean the difference would be 0, correct?

Last edited: Sep 21, 2008
15. Sep 21, 2008

Mattowander

Assuming that sig figs do not count then yes, both those answers seem correct.

16. Sep 21, 2008

JJones_86

Ok, thank you very much for your help, I really appreciate it!

17. Sep 21, 2008

Mattowander

No problem, anytime.

18. Sep 29, 2009

Cluless

I have the same problem with different numbers. The distance is 5.0 km and the resistive force is 3.0 N. I solved using the equation W=(Fd)2 and got 30,000 J, but I do not understand how to determine if the resistive force is a conservative force. Help?