Calculating Work on a Car

A car is travelling along a straight horizontal road. A force of \(\text{500}\) \(\text{N}\) is applied to the car in the direction that it is travelling, speeding it up. While it is speeding up is covers a distance of \(\text{20}\) \(\text{m}\). Calculate the work done on the car.

Step 1: Analyse the question to determine what information is provided

• The magnitude of the force applied is \(F=\text{500}\text{ N}\).

• The distance moved is \(\Delta x\) = \(\text{20}\) \(\text{m}\).

• The applied force and distance moved are in the same direction. Therefore, the angle between the force and displacement is \(\theta=0^\circ\).

These quantities are all in SI units, so no unit conversions are required.

Step 2: Analyse the question to determine what is being asked

• We are asked to find the work done on the car. We know from thedefinition that work done is \(W={F}\Delta x\cos\theta\).

Step 3: Next we substitute the values and calculate the work done

\begin{align*} W& = {F}\Delta x\cos\theta\\ & = \left(500\right)\left(20\right) \left(\cos 0\right)\\ & = \left(500\right)\left(20\right) \left(1\right)\\ & = \text{10 000}\text{ J} \end{align*}

Remember that the answer must be positive, as the applied force and the displacement are in the same direction. In this case, the car gains kinetic energy.

The same car now slows down when a force of \(\text{300}\) \(\text{N}\) is applied opposite to the direction of motion while it travels \(\text{25}\) \(\text{m}\) forward. Calculate the work done on the car.

Step 1: Analyse the question to determine what information is provided

• The magnitude of the force applied is \(F=\text{300}\text{ N}\).

• The distance moved is \(\Delta x\) = \(\text{25}\) \(\text{m}\).

• The applied force and distance moved are in the opposite direction. Therefore, the angle between the force and displacement is \(\theta=180^\circ\).

These quantities are all in the correct units, so no unit conversions are required.

Step 2: Analyse the question to determine what is being asked

• We are asked to find the work done on the car. We know from the definition that work done is \(W={F}\Delta x\cos\theta\)

Step 3: Next we substitute the values and calculate the work done

\begin{align*} W& = {F}\Delta x\cos\theta\\ & = \left(300\right)\left(25\right) \left(\cos 180\right)\\ & = \left(300\right)\left(25\right) \left(-1\right)\\ & = -\text{7 500}\text{ J} \end{align*}

Note that the answer must be negative as the applied force and the displacement are in opposite directions. This means that the energy is being lost by the car. This may be energy lost as heat to the environment. Energy conservation still holds, the energy has just been transferred to a larger system that contains the car.