Racing to the Finish: A Boy Paddles from Point 1 to Point 7

[physicdummy]

Homework Statement

A boy paddles his bike as fast as he can from point 1 to point 2. At point 2, he releases his feet from the pedal and coasts to point 7.

http://i649.photobucket.com/albums/uu220/mapo_tofu/picture-3.png


a)At which point did he travel fastest?
b)State the energy conversion from point 1 to 2.


________ energy of the boy pedaling --> ________ energy of the bike at point2

Homework Equations

Law of conservation of energy

The Attempt at a Solution

a ) If neglecting friction, then the total energy possessed by the bike should be the same throughout. Hence, the ke at 2-3 and 5-7 are the same and so the speed is the same throughout.

If considering friction, then ke is greatest at 2 so the speed is fastest at 2.


b) kinetic energy of the boy pedalling --> potential energy of the bike

Not sure of the potential energy part... is there a specific name for this
form of potential energy?

 

[cepheid]

a ) If neglecting friction, then the total energy possessed by the bike should be the same throughout. Hence, the ke at 2-3 and 5-7 are the same and so the speed is the same throughout.

This is simply not true. There is a net input of energy to the bike from the rider. Have you ridden a bike before? If you pedal hard enough, you accelerate.

 

[physicdummy]

This is simply not true. There is a net input of energy to the bike from the rider. Have you ridden a bike before? If you pedal hard enough, you accelerate.

So is the bike fastest at point 2 then? Is potential energy present? As you can tell from my name, I'm a dummy when it comes to physics, so I'd appreciate it if you can shed some light on this!

 

[HallsofIvy]

The potential energy of the bike is a constant. Assuming no friction, pedelling will increase velocity and so that energy will go into increasing the kinetic energy. Including friction, some of the energy of pedelling will go into overcoming friction. Yes, without friction, the bike will be fastest at point 2, where the boy stops pedelling and, neglecting friction, will keep that speed. With friction, the bike will still be fastest at point 2 and then will slow down.

 

[rwisz]

I would like to clarify that there is no such thing as "energy of the boy pedaling" or "energy of the bike." Energy is a property of a system, not an individual object. So, the correct way to phrase the energy conversion would be:

Kinetic energy of the boy and the bike at point 1 --> Potential energy of the bike at point 2

The energy conversion here is from kinetic energy (motion) to potential energy (stored energy due to position or height). This is known as a mechanical energy conversion, as it involves the movement of objects.

To answer the question of which point the boy traveled fastest, it would depend on the presence of friction. Without friction, the boy would maintain the same speed throughout, so he would travel at his fastest speed at all points. However, in the real world, friction would slow him down, so he would travel fastest at point 2 where he has the most kinetic energy. At point 7, his kinetic energy would have been converted to potential energy, so he would be moving slower.

I hope this helps clarify the concepts of energy and its conversion in this scenario.