Calculate the angle between the displacement vector and the force vector

1. Mar 25, 2012

Absolutism

1. The problem statement, all variables and given/known data

A force F = 8i-3i N acts on a particle that undergoes a displacement Δr = 2i + j m.
(b) What is the angle between F and Δr? (state your answer to three significant figures)

2. Relevant equations

Angle = cos-1 (A.B/ AB)

3. The attempt at a solution

W=13.1 J
AB= 8.5*2.23= 19
cos-1 (13.1/19)= 46.4

2. Mar 25, 2012

BitterX

I will assume that the force is $F=8\hat{i}-3\hat{j}$

the dot product between F and delta-r:
$(8,-3)\cdot (2,1) = 8\cdot 2 + (-3)\cdot 1 = 13$
the norm of F:
$||F||=\sqrt{8^2 +3^2}$
norm of delta-r :
$||\Delta r|| =\sqrt{1^2+2^2}$
I got 47.12 degrees but it seems you have used different conditions :/

3. Mar 25, 2012

Absolutism

I got 47.121 another time when I did not round, but even that gave me a wrong answer L: I am not sure what's wrong

4. Mar 26, 2012

BitterX

If you are sending it to some kind of online checking system:
a. Check to see if they want it in radians.
b. Check if all of the starting conditions are correct.
c. Take into consideration that they make mistakes too.