Why does the full equation for work done, W=Fdcos⁡𝜃W=FdcosθW, equals, F, d, cosine, theta, include the cosine of an angle?

The full equation for work done, W = Fdcosθ, includes the cosine of an angle to account for the direction of the force in relation to the direction of the displacement.

Here's a step-by-step explanation:

1. Work is defined as the force applied to an object times the distance the object moves as a result of this force. This is represented by the equation W = Fd, where W is work, F is force, and d is displacement.

2. However, this equation assumes that the force is applied in the exact same direction as the displacement. In reality, the force can be applied at an angle, which is where θ comes in.

3. The cosine of the angle (cosθ) is used to determine the component of the force that acts in the same direction as the displacement.

4. Therefore, by multiplying the force by the cosine of the angle, we can calculate the effective force that is doing work on the object. This gives us the full equation for work done: W = Fdcosθ.

5. So, the inclusion of cosθ in the work done equation allows us to calculate work done accurately, even when the force is applied at an angle to the direction of displacement.