W = F * d * cos(θ)
where:
* W is the work done
* F is the magnitude of the force
* d is the magnitude of the displacement
* θ is the angle between the force vector and the displacement vector
Explanation:
* Force component in the direction of displacement: The force vector can be resolved into two components: one parallel to the displacement (F * cos(θ)) and one perpendicular to the displacement (F * sin(θ)). Only the component of the force parallel to the displacement does work.
* Work done by the parallel component: The work done by the parallel component of the force is equal to the magnitude of the component multiplied by the displacement.
* Cosine function: The cosine function is used to find the component of the force parallel to the displacement.
Key Points:
* The angle θ is the angle between the force vector and the displacement vector, not the angle between the force vector and the horizontal or vertical axis.
* Work done is a scalar quantity, meaning it has magnitude but no direction.
* The work done is positive if the force and displacement are in the same direction and negative if they are in opposite directions.
Example:
A force of 10 N is applied to an object at an angle of 30 degrees to the direction of displacement. The object is moved 5 meters. Calculate the work done.
* F = 10 N
* d = 5 m
* θ = 30 degrees
W = 10 N * 5 m * cos(30°) = 43.3 J
Therefore, the work done on the object is 43.3 Joules.
