How Long Does It Take to Accelerate a Motorcycle from 0 to 100 km/hr?

[jrenman]

Homework Statement

You must find the time it takes to accelerate (at constant applied torque) a motorcycle from 0 to 100 km/hr,

given:
Rider mass: 75 kg
Bike total mass: 190 kg
Torque at crankshaft of motor: 105 Nm
Front and rear wheel masses (10 kg and 17 kg respectively)
Radius of wheels: 0.25 m (includes tire)
Radius of wheel hubs: 0.075 m

Wheel composed of 4 straight, uniform spokes. 1/3 of the wheel mass is in the hub, 1/3 in the spokes, and 1/3 in the rim (includes tire).
Ratio of transmission primary drive gear to crankshaft gear radii: 2.5. Ratio of rear sprocket to front sprocket radii: 2.5.

Once you find an equation for the acceleration (and therefore the time), compare the increased performance that would result from the following two modifications to the bike:

a) Lowering the non-rotating mass by 5 kg, and increasing the torque by 5 Nm [this is what you would get by changing the exhaust system).

b) Reducing the front and rear wheel masses by 2 kg and 5 kg respectively, and their moments of inertia by 50% each (this is what you would get by changing the wheels).

Homework Equations

N_ext = mR_(centre of mass) x a_com + I_com$$\alpha$$
??

The Attempt at a Solution

I think I am supposed to find the time from 0->100km/hr, then calculate an equation in terms of masses and moments of inertia(?) of wheels and then...
I'm not sure where to start really or what steps to take to get in the right direction.

Any help and advice would be wonderful.
Thanks in advance!

 

[Filip Larsen]

It may help to draw a diagram with the various relevant parts of the motorcycle and environment and how they each relate to each other. For instance, if one part transfer power to another part, then what physical variables (like torque, force, angular speed, speed) and characteristics (like mass, moment of inertia, etc) are involved in that transfer). You may need to make assumptions (remember to explain those in your solution) as to how some of the parts relate to each other if the problem text does not specify the details. You should now be able to analyse how to answer the question in the context of your model, like what equations you have to solve to get the answer.

Regarding your specific question, you do need to establish a model of your bike before you can answer the 0 to 100 km/h question. Then the other two questions require you to change your model and (re-)calculate how that affects the acceleration time.