Conservation of energy of a bike uphill

AI Thread Summary
The discussion revolves around calculating the total external work done on Jonathan and his bicycle as he rides uphill. The expected answer is -mgh, but the system requires a solution without using the gravitational constant g. Participants emphasize the importance of considering both kinetic and potential energy changes during the ascent. There is confusion regarding the system's restrictions on using certain constants and how to express the energy changes solely in terms of initial and final velocities. The conversation highlights the need for clarity in applying the conservation of energy principle to this scenario.
ubuntu2
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Homework Statement
Jonathan is riding a bicycle and encounters a hill of height h. At the base of the hill, he is traveling at a speed vi. When he reaches the top of the hill, he is traveling at a speed vf. Jonathan and his bicycle together have a mass m. Ignore friction in the bicycle mechanism and between the bicycle tires and the road.
What is the total external work done on the system of Jonathan and the bicycle between the time he starts up the hill and the time he reaches the top? (Use any variable or symbol stated above as necessary.)
The attempt at a solution
I know the answer should be -mgh; but the system does not accept it as I am supposed to give an answer without using the constant g.

What do you think the answer is? Thank you.
 
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ubuntu2 said:
Homework Statement
Jonathan is riding a bicycle and encounters a hill of height h. At the base of the hill, he is traveling at a speed vi. When he reaches the top of the hill, he is traveling at a speed vf. Jonathan and his bicycle together have a mass m. Ignore friction in the bicycle mechanism and between the bicycle tires and the road.
What is the total external work done on the system of Jonathan and the bicycle between the time he starts up the hill and the time he reaches the top? (Use any variable or symbol stated above as necessary.)
The attempt at a solution
I know the answer should be -mgh; but the system does not accept it as I am supposed to give an answer without using the constant g.

What do you think the answer is? Thank you.
If an external force does work on an object, what changes?
 
The total energy of the object changes.
 
ubuntu2 said:
The total energy of the object changes.
Indeed. So what in terms of the energy of the bike, what is changing as Jon rides up the hill?
 
Kinetic energy and potential energy.
 
No actually, the system did not accept KE(final)-KE(initial) neither.
 
ubuntu2 said:
No actually, the system did not accept KE(final)-KE(initial) neither.
I expect that you will need to write an expression in terms of vi and vf. You also need to account for the change in potential energy.

HINT: What does the principle of conservation of energy state?
 
I am aware of that, I was just trying to avoid writing a confusing text.
 
ubuntu2 said:
I am aware of that, I was just trying to avoid writing a confusing text.
I am a little confused that the system will not allow you to use the constant, g. That is the acceleration due to gravity, no?
 

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