Question

In the work energy equations in the x-direction the cos is usually ____, unless stated otherwise

a) 1
b) 0
c) 0.5
d) π

Answer 1

In work-energy equations, the cosine of the angle between force and displacement is usually 1 for motion in the x-direction, indicating maximum work done since the force is parallel to displacement.

Step-by-step explanation:

In the context of work-energy equations in physics, the cosine (cos) of the angle between the force vector and the displacement vector determines the work done in a particular direction. For motion in the x-direction, cosine is usually 1, which means the force is parallel to the displacement and the entire magnitude of the force contributes to the work done. However, if the force is perpendicular to the displacement, cosine will be 0, resulting in zero work (W = Fd cos θ).

For instance, carrying a briefcase horizontally with a constant force at a constant speed will result in no work done on the briefcase since the displacement is perpendicular to the applied force (cos 90° = 0). On the other hand, if a person is pushing a lawn mower forward, and the force applied is in the direction of the motion, the cosine of angle θ (theta) will be 1 as the angle is 0°, leading to maximum work done (W = Fd cos 0).