Problem 69 - Essential Calculus

Question

State the definition of work done by a constant force.

Step-by-Step Solution

Answer

Work done by a constant force on an object is the transfer of energy that occurs when that force moves the object over a distance. This is calculated using the formula: \(W = F \cdot d \cdot \cos(θ)\), where \(W\) is work, \(F\) is the constant force, \(d\) is the distance over which the force is applied, and \(θ\) is the angle between the force and the direction of the displacement. If the force is in the direction of movement, work simplifies to: \(W = F \cdot d\).

Step 1: Understanding the concept

Work is a measure of energy transfer that occurs when an object is moved by an external force along a displacement. It's a scalar quantity, meaning it only has magnitude and no direction.

Step 2: Factoring in 'constant force'

A constant force simply means a force that doesn't change in magnitude or direction. This is important because if the force varies, then the work done will also vary, which complicates the calculations and the concept.

Step 3: Combining the parts

Now that we've understood the basic concept of work and what a constant force is, let's combine these two parts. The work (W) done by a constant force (F) of magnitude acting along a displacement (d) and in the direction of the displacement is given by the formula: \(W = F \cdot d \cdot \cos(θ)\), where \(θ\) is the angle between the force and the displacement. Note, if the force is in the direction of movement \(θ = 0\) and the formula becomes: \(W = F \cdot d\) .