Dot Physics

Super Fast Motorcycle

ZapperZ already beat me to this, but if it is worth doing once it is worth doing again. Here is a video of an electric motorcycle that can apparently go from 0 to 60 mph in 1 second.

What acceleration would this have? If you want, you can look at my stuff on kinematics, but this case is pretty straight forward. Really, as straight forward as one could get. Let me start with the definition of acceleration: (in the x-direction since this is a 1-d problem)

i-8b606394ee679fa86103c91c2821767b-a-motorcycle.jpg

I know both the change in speed and the time, so this is easy. I can make it even easier using google. The acceleration is 60 mph/s. Google can convert this to m/s2. Or it can be done the longer way:

i-7ac2f08952a6ecc13fe6b655ae040ea6-unit-conversion-for-accel.jpg

That seems large. How about a free-body diagram of the motorcycle while it is accelerating:

i-eafa407ea13407fa363a622466648be3-motorcycle-fbd.jpg

Two questions: What kind of coefficient of friction would you need to do this and what kind of forces would be exerted on the rider? The usual model for static friction looks like this:

i-f5852000e32c3dc2e8fb7ab00f5b8940-model-for-friction.jpg

Where N is the normal force on the bike, which would have a magnitude of mg in this case (m is the mass of the bike plus person and g is the local gravitational constant). Using Newton’s second law in the x-direction, I can write:

i-e61d0a14339b952ecc71c5da47c799f4-mu-equals.jpg

(note: I switched from friction being less than or equal to, to being equal. If that confuses you, check this out)

So, if the acceleration is greater than 9.8 m/s2, then the coefficient of friction would have to be larger than one. Ok. Enough about friction. What about the guy? The guy would have a very similar free body diagram. The only difference would be that the friction force would be replaced by some other force. Say the force of the handle bars pulling on him (but also the seat).

i-f2f0bb979f16eba32acc8a612f156904-f-on-rider.jpg

If the person has a mass of 70 kg, what would this force be? In the x-direction:

i-49283454cf62d21207d84e58c48dd52c-net-force-on-rider.jpg

That is pretty large, compare that to his (or her) weight of (70 kg)(9.8 N/kg) = 686 Newtons.

Comments

  1. #1 Motorbike helmets
    June 17, 2009

    Awesome, very fast indeed. I love the video but not very good at physics.