Calculating Work Using W=f*d*Cos(theta)

[laxboi33]

Homework Statement

W= f * d * Cos (theta)

Homework Equations

The Attempt at a Solution

In an object moving in the x-direction how do you know when to use zero as theta or 180 as theta? From the problems I've solved I find that when there is negative acceleration or a force stopping the object then the theta is 180. When the object is in a constant velocity or it is accelerating the theta seems to be zero. Can someone explain to me when to use zero or 180 for theta in objects moving in the x-direction? Also, in what case would you use 90 degrees as theta?

thanks.

 

[rock.freak667]

The angle θ is measured counter clockwise from the +ve x-direction. So if θ=0, then the force is acting in the +ve x-direction.

If θ=180, then the force is acting in the -ve x-direction. (This is why in the case of friction θ=180).

If θ=90, then the force is acting perpendicular to the mass it is acting on. This may mean that the force and displacement are at 90 degrees to each other and thus the work done = 0J

 

[tomcue]

It is important to remember that theta represents the angle between the force vector and the displacement vector. In the case of an object moving in the x-direction, the force vector and the displacement vector are parallel, meaning the angle between them is either 0 or 180 degrees. When the object is moving with constant velocity or accelerating in the x-direction, the force vector is in the same direction as the displacement vector, so theta would be 0 degrees. When there is a force stopping the object or causing negative acceleration, the force vector is in the opposite direction of the displacement vector, so theta would be 180 degrees.

In the case of an object moving in a direction other than the x-axis, such as at an angle, you would use 90 degrees as theta when the force is perpendicular to the displacement vector. This can also be seen in the equation for work, as Cos(90) = 0, meaning the force and displacement vectors are perpendicular and do not contribute to the work done.

Ultimately, the value of theta will depend on the specific scenario and the relationship between the force and displacement vectors. It is important to carefully analyze the situation and determine the appropriate angle to use in the equation.