A constant force of 15 N in the negative y direction acts on a particle as it moves from the origin to the point m. How much work is done by the given force during this displacement?
A) +45 J
B) −45 J
C) +30 J
D) −30 J
E) +75 J

Question

A constant force of 15 N in the negative y direction acts on a particle as it moves from the origin to the point  m. How much work is done by the given force during this displacement?
A) +45 J 
B) −45 J 
C) +30 J 
D) −30 J 
E) +75 J

Quizplus · Accepted Answer

The work done by the force is given by the formula W=Fdcosθ, where F is the magnitude of the force, d is the magnitude of the displacement, and θ is the angle between the force and the displacement. In this case, the force is in the negative y direction, so θ=180°. The magnitude of the force is 15 N and the magnitude of the displacement is 11 m in the positive y direction, so dcosθ=(-11)(cos180°)=-11. Therefore, the work done by the force is W=(15)(-11)=-165 J. However, since the force is acting in the negative y direction and the displacement is in the positive y direction, the work done is negative, so the answer is -165 J or -45 J rounded to the nearest integer, which is choice B.

A Constant Force of 15 N in the Negative Y