Problem 19 - Chemistry: The Central Science

Question

(a) What is work? (b) How do we determine the amount of work done, given the force associated with the work?

Step-by-Step Solution

Answer

(a) Work is the energy transferred to or from an object through the application of force along a displacement. (b) To determine the amount of work done, use the formula \(W = F × d × \cos(\theta)\), where \(W\) represents the work done, \(F\) represents the magnitude of the force applied, \(d\) represents the displacement, and \(\theta\) represents the angle between the force and displacement vectors.

Step 1: (a) Definition of Work

In physics, work is defined as the energy transferred to or from an object through the application of force along a displacement. In simple words, it represents the energy transferred when a force is applied to an object, and the object moves along the direction of the force.

Step 2: (b) Calculation of Work Done

The amount of work done on an object is calculated using the formula: Work \(W = F × d × \cos(\theta)\) Where: - \(W\) represents the work done, - \(F\) represents the magnitude of the force applied, - \(d\) represents the distance over which the force is applied (displacement), and - \(\theta\) represents the angle between the force vector and the displacement vector. In order to calculate the amount of work done, follow the steps below: 1. Determine the magnitude of the force applied (\(F\)). 2. Determine the distance over which the force is applied (displacement, \(d\)). 3. Determine the angle (\(\theta\)) between the force vector and the displacement vector. 4. Plug the values obtained in steps 1, 2, and 3 into the work done formula and calculate the result. Note that if the force and displacement vectors are in the same direction, the angle \(\theta\) will be 0°, and the \(\cos(0)\) term will be 1, simplifying the work done formula to: Work \(W = F × d\)