# Q & A: Motorcycle and Car

Q:
A car and a motorcycle are traveling in the same direction at about 45 MPH. The motorcycle driver weighs 187 pounds and he is wearing very light clothes. The motorcycle changes lines from left to right and hits the car on the front right side. On what direction will both go?
- Dante (age 41)
Randolph, NJ
A:
I'll bet you're trying to get us to do your homework for you, but this question has enough interesting features beyond the standard homework answer that it's worth talking about.

You haven't specified the mass of the car, but it's not that relevant (as long as it's much more than that of the motorcycle and driver). The total momentum of the system points along the road, with only a small sidways component as the motorcyclist changes his lanes. So the momentum after the collision should point down the road, and that's the general direction both the car and the motorcycle should be going after the collision. But, collisions can be complicated, and there are lots of things that could happen:

1) The motorcycle can just bounce off of the car. More likely, the motorcycle will dent the car, lose its momentum transverse to the direction along the road, and move with the car, but not be stuck to it, after the collision. The motorcyclist should try to steer back into his lane if at all possible at this point, eventually slow down, and negotiate with the car's driver whose insurance is going to pay for the dent. Lane changes are usually very slow (sideways velocity components are usually less than 1 mph) so this outcome is actually not too unlikely, but some other scenarios may happen instead:

2) As in 1, the motorcycle bounces off of the car, but loses control. This can happen especially if the part of the motorcycle which makes contact with the car is the handlebar or the front tire. If the front wheel gets turned to the side, it will yank the motorcycle violently in that direction. Which direction that is depends on the details of the collision.

It is not a good idea to turn a motorcycle's front wheel while going 45 MPH down a road -- the motorcycle could flip over, tossing the motorcycle rider at the car or in the other direction, neither of which sounds good, especially since the motorcycle driver is wearing light clothes (always a bad idea when riding a motorcycle). The motorcycle driver could be struck by his motorcycle, abraded by the road, or even run over by the car, or perhaps all three. Because of strong frictional forces with the road (and with the car, especially if it is the rotating tire making contact with the car body or tire), the conservation of momentum argument made in 1) won't apply and bad things can happen. I once saw two motorcycles going down a high-speed expressway, one trailing the other by inches. The front tire of the back motorcycle made contact with the rear tire of the leading motorcycle; the rear motorcycle flipped over backwards, throwing the riders.

3) Only in James Bond and similar movies -- the car could have a latching mechanism which can pick up the motorcycle and carry it away. This would be in our mechanics class a "totally inelastic collision". By the way, if a motorcycle attempts to ride up into the back of a truck by means of a ramp extended from the truck, while going at 45 MPH down a road (they probably do this in James Bond movies), this will almost certainly involve an accident, as the rotation speed of the wheels has to be very different when in contact with the ground and when in contact with the ramp of the moving truck.

Tom

(published on 10/22/2007)