Conservation of energy of a bike uphill

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Homework Help Overview

The problem involves a cyclist, Jonathan, riding uphill on a bicycle and analyzing the work done on the system as he ascends a hill of height h. The discussion centers around the conservation of energy principles, specifically relating to kinetic and potential energy changes without using the gravitational constant g.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the expected answer for the total external work done, with some suggesting it should be -mgh, while others note the requirement to avoid using g. Questions arise about the implications of external work on energy changes and the need to express energy changes in terms of initial and final velocities.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of energy changes as Jonathan rides up the hill. Some guidance has been offered regarding the conservation of energy, but there is no explicit consensus on the correct expression to use without the gravitational constant.

Contextual Notes

Participants are constrained by the requirement to avoid using the constant g in their answers, which has led to confusion and multiple interpretations of the problem setup and assumptions regarding energy changes.

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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