Question

Dirk pushes on a packing box with a horizontal force of \(66.0 \mathrm{N}\) as he slides it along the floor. The average friction force acting on the box is \(4.80 \mathrm{N} .\) How much total work is done on the box in moving it $2.50 \mathrm{m}$ along the floor?

Short answer

Answer: The total work done on the box is 153 J (joules).

Step-by-step solution

Define the given variables

We are given the following information: - Dirk's pushing force: \(F_{push} = 66.0 \mathrm{N}\) - Friction force: \(F_{friction} = 4.80 \mathrm{N}\) - Distance moved: \(d = 2.50 \mathrm{m}\)

Calculate the work done by Dirk's pushing force

The work done by a force is given by the formula \(W = F \times d\). Since Dirk's pushing force is acting in the same direction as the distance moved, we can directly use the formula: \(W_{push} = F_{push} \times d = 66.0 \mathrm{N} \times 2.50 \mathrm{m} = 165 \mathrm{J}\) (joules)

Calculate the work done by the friction force

The friction force is acting opposite to the direction of the distance moved. Therefore, we need to take the negative sign into account when calculating the work done: \(W_{friction} = -F_{friction} \times d = -4.80 \mathrm{N} \times 2.50 \mathrm{m} = -12.0 \mathrm{J}\)

Calculate the total work done on the box

The total work done is given by the sum of the work done by each force: \(W_{total} = W_{push} + W_{friction} = 165 \mathrm{J} + (-12.0 \mathrm{J}) = 153 \mathrm{J}\) The total work done on the box by Dirk's pushing force and the friction force while moving it \(2.50 \mathrm{m}\) along the floor is \(153 \mathrm{J}\).