Conservation of energy / work problem

In summary, the conversation is about someone seeking help with a problem involving finding the difference between the top and bottom of a hill, and asking for clarification on the algebraic steps they may have missed. The answer involves identifying the variables and factoring an equation.
  • #1
adams_695
16
1
Homework Statement
Call the system the bicycle and the rider. Use the work-energy equation and W = Fd. Assume the cyclist and air do not heat up. The work-energy equation is Kf + Ugf = Ki + Ugi + W.
Relevant Equations
Kinetic energy & gravitational energy
Answer- Physics .jpg
Attempt 1- Physics.jpg
Attempt 2- Physics.jpg

If someone could advise what I've done wrong it would be much appreciated. How have they eliminated the initial and final for y, and simplify only to y? Also, how did they simplify to a positive 2? What algebraic steps have I missed? Thanks for your help.
 
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  • #2
I would not call that a problem statement. What is the actual question?
 
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  • #3
haruspex said:
I would not call that a problem statement. What is the actual question?
695672E7-6A77-4F8D-8425-24ED89C62321.png


Sorry here it is. Question 9. Thanks!
 
  • #4
You are told the top of the hill is 30m higher than the bottom of the hill. So what is yi-yf?
 
  • #5
haruspex said:
You are told the top of the hill is 30m higher than the bottom of the hill. So what is yi-yf?

30m-0m.

Is this how I went wrong when solving algebraically in the image of my working?
 
  • #6
There was nothing wrong in what you worked out. As haruspex pointed out, identify yi and yf in your own algebra and you are done.
 
  • #7
adams_695 said:
30m-0m.

Is this how I went wrong when solving algebraically in the image of my working?
The last line of your working has the terms -2gyf+2gyi. Factorise.
 

1. What is the law of conservation of energy?

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

2. How is energy conserved in a work problem?

In a work problem, the work done on an object is equal to the change in its kinetic energy. This means that the amount of work done on an object is equal to the amount of energy it gains or loses.

3. What is the formula for calculating work?

The formula for calculating work is W = F x d, where W is work, F is the force applied, and d is the displacement of the object. The unit for work is joules (J).

4. Can energy be lost or gained in a work problem?

No, according to the law of conservation of energy, energy cannot be gained or lost in a work problem. The work done on an object is always equal to the change in its kinetic energy, so the total amount of energy remains constant.

5. How does the law of conservation of energy apply to real-world situations?

The law of conservation of energy applies to all physical systems, including real-world situations. For example, energy is conserved when an object falls from a height, as its potential energy is converted into kinetic energy. The same principle applies to other systems, such as a car engine converting chemical energy into kinetic energy to move the car.

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