Question

A car with a mass of 1180 kilograms is being driven at 18.2 meters per second when it runs into a tree. If the front of the car is pushed in 41.1 centimeters, what is the magnitude of the force exerted on the car? Include units in your answer. Answer must be in 3 significant digits.

Answer 1

We know that the work is related to the kinetic energy by the work energy theorem:

`W=K_f-K_i`

In this case the final velocity of the car is 0 m/s; with this in mind and plugging the values given for the initial velocty we have:

`\begin{gathered} W=(1)/(2)(1180)(0)^2-(1)/(2)(1180)(18.2)^2 \\ W=-195431.6 \end{gathered}`

Now, we know that the work is given by:

`W=Fd`

plugging the distance and the work done we have:

`\begin{gathered} -195431.6=0.411F \\ F=-(195231.6)/(0.411) \\ F=-4.76*10^5 \end{gathered}`

Since we need the magnitude we drop the sign, therefore the magnitude of the force is:

`F=4.76*10^5\text{ N}`