The Physics of Hitting an Elk With You Car

By Heather Frank

This summer when I was on a road trip with my Dad in the Grand Canyon we hit an Elk with our car at 4:30 in the morning while driving in the dark at 45 mph. Although the car was totaled and the Elk died, my Dad and I were unharmed since we were wearing our seatbelts and the airbags deployed.

In order to analyze the forces that we felt during the accident I had to make a few estimations. I assumed that M_CAR=2000 kg, M_ELK=225 kg, V₁ of the car before the accident was 45 mph (20 m/s) and V₂ is the velocity of the car and elk after colliding. I treated this as an inelastic collision because after we hit the Elk we carried the Elk on the hood of our car for about .5 seconds. Then we traveled an additional 15m before coming to a stop. After finding the Velocity of the Car and the Elk after the collision (V₂) I was able to find the W_NC done on the car to make it stop by looking at the change in Kinetic Energy. This W_NC was a combination of the work done by the friction between the tires and the road and the work done by the car brakes to come to the stop. Finally, I looked at the Force exerted on my Dad and I during the accident and how that force was significantly decreased by us wearing seatbelts and the deployment of the airbags, which increased the time that we experienced a change in momentum. 

MV_CAR+MV_ElK=MV_{CAR AND ELK}

(2000)(20)+0=(2225)(V) Vfinal of Car and Elk= 18m/s

Then Elk fell off car and car traveled for additional 15 m.

Change in KE=W_NC=1/2m(v_f²-v₀²)

W_NC=1/2(2000)(0-18²)= -324000 J

This is combination of Ffr and Work done by brakes of car over 30m.

W_NC=Ffrd+Fbraked

324000=(.7)(2000)(9.8)(15)+ Fbrake(15)

Fbrake= 7880 N A LOT OF FORCE!

 Also it is important to note that the reason we did not sustain injury from the accident is because the Force exerted on us (change in momentum over time) was significantly decreased by the airbags and the seatbelts, by increasing the time in which we felt the change in momentum.

NOTE: These numbers are all estimates. I have a foggy memory of the accident and my times and distances might be slightly off but the ideas of Physics apply to this scenario.