MATH SOLVE

8 months ago

Q:
# Knowing that the block in the figure moves 25 m from A to B, and a force F of magnitude equal to 80 N is applied to it and it forms an angle θ with the horizontal (without figure) and the friction between the surface and the block is negligible. What measure does the angle θ have, if the net work done on the block in said path is -1200 J?

Accepted Solution

A:

$$ W=Fd\cos\theta $$
W = work done = 1200 J
F = force applied= 80 N
d = displacement = 25m
$$ \cos\theta=\frac{W}{Fd}\xrightarrow{}\frac{1200}{80\times25}\xrightarrow{}\frac{3}{5} $$
$$ \theta=\cos^{-1}\left(\frac{3}{5}\right) $$
$$ \theta=53^{\circ} $$
Therefore, the angle between force vector and displacement vector is 53°.