Q & A: Motorcycle Car Collision

Hi there, I am having an online 'discussion' about speed. If a motorbike is travelling at 300 kilometres per hour and a car is travelling at 100 kilometres per hour and they are both heading in the same direction, what speed would they be doing if the bike hit the car? I'm no good at physics, but my guess is at least 300! I feel that if the bike hit the car at 300 kph, the bike may probably go through the car, maybe not completely. The other party says that the bike would do hardly any damage to the car! Thanks and I hope this question isn't too stupid:)
- Vicki Kendrigan (age 50)
Mildura, Victoria, Australia

Hi there, The question certainly isn't stupid... In fact it's probably too complex for me to answer with much certainty!

In Physics we like to simplify things as much as possible, and what I see in your question is a conservation of momentum problem. That is, the initial momentum off all objects is equal to the final momentum,
p_ini = p_fin
Our initial momentum comes from the bike and the car separately so we add their momenta
p_ini=p_bike+p_car
Momentum is classically defined as mass*velocity. So what our final equation is going to look like is:
m_bike*v_bike+m_car*v_car=m_(bike+car)*v_final
Or
v_final=(m_bike*v_bike+m_car*v_car)/m_(bike+car)

You gave the velocities so lets get some numbers for the masses. 
We'll take the weight of a Harley Davidson "Forty-Eight" at about 250 Kg for our bike. And we'll use the weight of a Toyota Camry SE for our car at about 1500 Kg.
We'll also add 85 kg to the bike and 170 to the car giving them 1 and 2 passengers respectively.

So we have:
v_final=(300Km/h*335Kg +100Km/h*1670Kg)/2005 Kg = 133 Km/h

Now this is a very idealized situation where the two collide and remain joined. Obviously in a real situation things can get much more complicated.  The motorcyclist is likely to be thrown off the bike, and it's impossible to know what the driver will do afterwards that may either help or hinder.  But if we want some idea, another thing we can look at is the kinetic energy involved.

KE=1/2 m*v²
Again this we add the initial energies and compare to the final.
KE_ini= 1/2*335*(300^2)+1/2*1670*(100^2)=23425000 Kg(Km/h)²
or about 1.8 megajoules.

KE_fin=1/2*2005*(133^2) = 17733222.5 Kg(Km/h)² or about 1.4 megajoules

So we have a difference of 400,000 Joules, but where did it go?
Well that's the "crash."  That energy goes into damaging both the car and the motorcycle, into the sound of the accident, and anything else you can think of involved in a vehicular collision.

All I can tell you for sure is that 400,000 joules will run a 100watt incandescent light bulb for about an hour, or that it's the amount of caloric energy in a banana.
I can't really say for sure what gets damaged and how much is done, but if I was forced to pick a side, I'd say the car at least would probably still be drivable after the accident.

Thanks for the question,
Mike Boehme

(published on 04/19/2012)