How Is Maximum Kinetic Energy Calculated for an Electric Bicycle with a Rider?

[Dongorgon]

Homework Statement

An engineer was to design a bicycle that can be powered only by an electric motor. The bicycle can carry an 80kg rider at a maximum speed of 6m/s. Under these conditions the maximum distance the bicycle can cover before the battery needs to be recharged is 32km. The bicycle has a mass of 30kg. Calculate the maximum kinetic energy of the bicycle and rider when the rider is not pedalling.

The Attempt at a Solution

Assuming that no resistance force acts, what I've done is to consider the work done as equal to the change in kinetic energy over the entire displacement.
From this: WD=110x9.8x32000=34496000J
Hence, KEmax=34496000J
Which also is the entire stored energy of the battery.
Is this a correct way, and would this answer be sufficient? Thanks

 

[haruspex]

You seem to have involved g somehow, but there's no mention of vertical movement. What's your logic for that?
OTOH, you have not used the info re 6m/s, which does seem to be highly relevant.
(Are there more parts to the question?)

 

[Dongorgon]

Yeah, through working out the KE via 1/2mv^2 it obtains a value of 1980J. But for some reason, this seems far too small considering this energy can carry the rider 32km also? Would I be correct in thinking this value for KE is also the total energy stored by the battery?
Also, there are no more parts, just that. Thanks for the fast reply.

 

[haruspex]

Yeah, through working out the KE via 1/2mv^2 it obtains a value of 1980J. But for some reason, this seems far too small considering this energy can carry the rider 32km also?

The max KE is not the energy required to carry the rider 32km. That might be the case if all the energy in the battery were converted to KE straight away and thereafter it's just carried along by its KE. The reason I asked if there are more parts is that the 32km does not seem to be relevant. But it's not unusual for irrelevant information to be provided as a test of whether the solver can figure out what is.

 

[Nickie]

for the help!

I would say that your approach to solving this problem is correct. By considering the work done as equal to the change in kinetic energy, you have correctly calculated the maximum kinetic energy of the bicycle and rider. This answer is sufficient, but it would be helpful to also mention the units of the answer (Joules) and explain the significance of this value in terms of the performance of the bicycle. Additionally, you may want to consider the efficiency of the electric motor and how it affects the maximum distance the bicycle can cover before the battery needs to be recharged. Overall, your solution is well-reasoned and demonstrates a good understanding of the principles of kinetic energy.