# Cross Product, Forces

1. Nov 16, 2007

### mkwok

1. The problem statement, all variables and given/known data
A force F = (5 i - 1 j) N acts on a particle that undergoes a displacement r = (2 i + j) m.
(a) Find the work done by the force on the particle. (Calculate all numerical answers to three significant figures.)

(b) What is the angle between F and r?

* the problem required us to put our answer in 4 sig figs

2. Relevant equations
W=F*R
cross product |F||R|cos$$\theta$$

3. The attempt at a solution

part A,
since W=F*R, so I did: 5*2 + 1(-1) = 9.000 (4 sig figs)

Part B,
cross product |F||R|cos$$\theta$$
|F|=$$\sqrt{26}$$
|R| = $$\sqrt{3}$$
9=$$\sqrt{26}$$$$\sqrt{3}$$cos$$\theta$$
$$\theta$$=cos-1(9/($$\sqrt{26}$$$$\sqrt{3}$$)) = 37.87 degrees

My homework website tells me its wrong, what did I do wrong then?

Last edited: Nov 16, 2007
2. Nov 16, 2007

### robphy

define [and distinguish]: cross product, dot product
define: work

3. Nov 16, 2007

### Dick

That's what I get. But i) it's the dot product, not the cross product and ii) the length of the second vector is sqrt(5) not sqrt(3). My question is how did you get the correct angle?

4. Nov 16, 2007

### Bill Foster

5. Nov 16, 2007

### mkwok

oops. I am so sorry
I really meant the dot product...
the angle is still incorrect though

6. Nov 16, 2007

### Dick

No, it's not. It's correct. Maybe you are supposed to give it in radians? Maybe sig figs? These automated homework checkers should be destroyed.

7. Nov 17, 2007

### Bill Foster

Automatic homework checker? Don't they have TAs anymore?

What the hell are they teaching in colleges these days?

8. Nov 17, 2007

### robphy

Most undergraduate colleges don't have TAs.
Online homework assignments [however imperfect] can encourage students to work outside of class meeting times.
In addition, online homework assignments can be customized and randomized for each student.

9. Nov 17, 2007

### Bill Foster

You know how they encouraged us to work outside class meeting times when I was in college? They made us turn the homework in, gave us pop quizzes, and/or frequent exams.

10. Nov 17, 2007

### robphy

Yep... me, too.
But then again... I really really wanted to learn it... possibly unlike the generic student.

11. Nov 17, 2007

### Dick

True. But they can be pretty difficult to reason with.