In the formula, W = Fdcosθ, where W is the work done by a Force, F, to create displacement, d, what is the definition of θ?
In the formula W = Fdcosθ, θ represents the angle between the force vector, F, and the displacement vector, d.
In the formula W = Fdcosθ, θ represents the angle between the direction of the applied force, F, and the direction of the displacement, d. It is important to determine the correct angle when using this formula because the work done on an object can vary depending on the angle at which the force is applied.
To find the value of θ, you need to measure or determine the angle between the force vector and the displacement vector. It is commonly measured in degrees (°) or radians (rad). There are several ways to determine the angle:
1. Direct Measurement: If you have a diagram or physical representation of the situation, you can directly measure the angle using a protractor or measuring tool.
2. Trigonometric Functions: If you know the lengths of the sides of a right triangle formed by the force and displacement vectors, you can use trigonometric functions such as sine, cosine, or tangent to calculate the angle. For example, if you know the lengths of the sides adjacent to and opposite θ, you can use the tangent function (tanθ = opposite/adjacent) to find the angle.
3. Vector Dot Product: If you have the components of the force and displacement vectors, you can use the dot product to find the angle. The dot product of two vectors is given by the formula F · d = |F| |d| cosθ, where |F| represents the magnitude of the force vector and |d| represents the magnitude of the displacement vector. Rearranging this formula, you can solve for θ by taking the inverse cosine of (F · d) / (|F| |d|).
By using these methods, you can determine the value of θ and plug it into the formula to calculate the work done by the force.