Conservation of energy of a bike uphill

In summary: The principle of conservation of energy state that energy cannot be created or destroyed, only changed.
  • #1
ubuntu2
7
0
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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  • #2
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?
 
  • #3
The total energy of the object changes.
 
  • #4
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?
 
  • #5
Kinetic energy and potential energy.
 
  • #6
No actually, the system did not accept KE(final)-KE(initial) neither.
 
  • #7
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?
 
  • #8
I am aware of that, I was just trying to avoid writing a confusing text.
 
  • #9
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?
 

Related to Conservation of energy of a bike uphill

1. What is the principle of conservation of energy?

The principle of conservation of energy states that energy cannot be created or destroyed, but can only be transformed from one form to another. This means that the total amount of energy in a closed system remains constant.

2. How does conservation of energy apply to a bike going uphill?

When a bike is going uphill, it is working against the force of gravity. As the bike climbs, its potential energy increases because it is gaining height. At the same time, the bike's kinetic energy decreases as it moves slower due to the work being done against gravity. However, the total energy of the bike remains the same, following the principle of conservation of energy.

3. Can a bike gain energy while going uphill?

No, according to the principle of conservation of energy, energy cannot be created. The bike may gain potential energy as it climbs, but this energy comes at the expense of the bike's kinetic energy. The total energy of the bike remains the same.

4. What factors affect the conservation of energy on a bike going uphill?

The conservation of energy on a bike going uphill is affected by the weight of the bike and the rider, the steepness of the hill, and the resistance from the bike's brakes and air resistance. The heavier the bike and rider, the steeper the hill, and the more resistance from the brakes and air, the more energy will be required to climb the hill.

5. How does the conservation of energy impact the speed of a bike going uphill?

As the bike climbs uphill, its potential energy increases, and its kinetic energy decreases. This means that the bike will slow down as it climbs. However, the total energy of the bike remains the same, so once the bike reaches the top of the hill and starts descending, it will regain its lost speed due to the conversion of potential energy back into kinetic energy.

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