An object undergoes a displacement x while a force F acts on it. If F does zero work, then the angle between F and x must be
90
To determine the angle between the force F and displacement x, we need to understand the concept of work.
Work is defined as the product of the force applied on an object and the displacement of the object in the direction of the force. Mathematically, work (W) is calculated using the formula:
W = F * x * cos(theta)
where F is the magnitude of the force, x is the displacement, and theta is the angle between the force and the displacement.
Given that the force F does zero work, it means that the work done is zero. Thus, the equation becomes:
0 = F * x * cos(theta)
To find the angle theta, we can rearrange the equation as follows:
cos(theta) = 0
Now, let's think about the range of values for the cosine function. The cosine of an angle can vary from -1 to 1, inclusive. However, in this case, the cosine of theta is 0. Therefore, there are two possible values for theta when cos(theta) = 0:
1. When theta = 90 degrees or π/2 radians: In this case, the force F and displacement x are perpendicular to each other, resulting in zero work done.
2. When theta = 270 degrees or 3π/2 radians: In this case, the force F and displacement x are also perpendicular but in the opposite direction, still resulting in zero work done.
So, the angle between F and x must be either 90 degrees (or π/2 radians) or 270 degrees (or 3π/2 radians) if F does zero work.