Question

A force f=fxi fyj acts on a particle that undergoes a displacement of s=sxi syj. Find the angle between f and s?

1) 0 degrees
2) 45 degrees
3) 90 degrees
4) 180 degrees

Answer 1

To calculate the angle between force vector f and displacement vector s, we use their dot product. With given values, the dot product (or the work done) is 39 J, but the angle is not determined with the provided information.

Step-by-step explanation:

To find the angle between the force vector f and the displacement vector s, we use the dot product of the two vectors. The dot product is defined as f · s = |f| |s| cos(θ), where θ is the angle between the vectors, and |f| and |s| are the magnitudes of the vectors f and s, respectively.

Given the force f is fxi + fyj and displacement s is sxi + syj, the dot product is fxsx + fysy. For the values provided, the force is (3 N)i + (4 N)j and the displacement is (5 m)i + (6 m)j, so the work done, which is the dot product, is (3 N)(5 m) + (4 N)(6 m) = 15 + 24 = 39 J.