Answer to Question #128546 in Classical Mechanics for Zaina

Question

A force F=(3 i + 4 J + 5 k) newtons is applied on a 500 g object to move it a displacement D=(5 i+ 4 j + 3k) meters, find the angle between the force F and the displacement d, if the work done by f is 46J?

Answer 1

$$W=\vec{F}\cdot \vec{D}=FD\cos(\theta)$$

Thus,

$$F=\sqrt{3^2+4^2+5^2}=5\sqrt{2}\\ D=\sqrt{3^2+4^2+5^2}=5\sqrt{2}$$

Hence,

$$46=50\cos(\theta)\implies \theta=\cos^{-1}(23/25)$$