Conservation of Energy Confusion

In summary, the person crouches a distance C and then has a push-off phase. He then has a takeoff distance H, where H is the difference between the maximum jump height and the end of the crouch distance.
  • #1
yosimba2000
206
9
Question:
A person wants to jump in the air. To do so, he has to crouch a distance C. He then has a push-off phase, where the he accelerates upwards by a distance C. At the end of push-off, he then achieves takeoff (airborne). The end of his takeoff distance is H, and H is the difference between maximum jump height and end of crouch distance.

My professor says the Cons of E. equation is FC = mgH + WC, with this reasoning:

"The total energy you need to take off at the moment of the take-off = F (reaction force) X C (distance).
The total energy you spend during the push-off till the take off = potential energy to reach the jumping distance, H (mgH) + kinetic energy to overcome the gravity of the person (WC).
Therefore, FC = mgH + WC"

I don't quite understand his reasoning for this. Is there something more intuitive anyone can share?
 
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  • #2
At the top of the leap, speed is zero, so there is zero kinetic energy.

Your gravitational potential energy at the top is higher than at the floor. That difference is the quantity of energy you must put into the leap. Conservation of energy is the principle you use to easily solve this problem.

Work at it a little more and you will be able to solve for the speed you have as your feet leave the ground.
 
  • #3
I am able to solve it using mgh = 0.5mv^2, but this way seems to be much faster.
So my potential energy at the top is mgH, right? That says my total energy input is FC-WC, but I still don't see why this is true. Gravity is pulling down on the person at all times, so the total energy by gravity should be mgH. And in order to move, I need to put in some Force over the total distance H that exceeds gravitational force so I can have a net movement. That energy is FH. Together, that puts me at potential energy mgH. So I'm saying FH+mgH=mgH. Which means FH=0. I'm confused
 
  • #4
yosimba2000 said:
And in order to move, I need to put in some Force over the total distance H that exceeds gravitational force so I can have a net movement.

We are neglecting friction here, so the leap is "free fall." In free fall, you do not need force to move, you need force to accelerate/decelerate.

While the person is in the air, the only force on him is gravity and he is accelerating downward the whole time. As his feet leave the ground, he has maximum kinetic energy. The kinetic energy becomes potential energy as he ascends, reaching zero kinetic energy at the top of the leap. During the leap, the sum of kinetic plus potential energies is constant.
 
  • #5
ok so all the energy I put in right before being airborne is my maximum kinetic energy. This energy is the force by my muscles, and in order to accelerate up, I must oppose gravitational force, and then add some more force to start to move up. So I have to put in energy WC+ FC, and that equals mgh, right? This is what I originally thought when doing my HW, but apparently it is wrong. I don't see why it is wrong.
 
  • #6
yosimba2000 said:
ok so all the energy I put in right before being airborne is my maximum kinetic energy. This energy is the force by my muscles, and in order to accelerate up, I must oppose gravitational force, and then add some more force to start to move up. So I have to put in energy WC+ FC, and that equals mgh, right? This is what I originally thought when doing my HW, but apparently it is wrong. I don't see why it is wrong.

The energy that you are putting in during the take off is equal to FC. That is the force from your muscles times the distance over which that force acts. Gravity acts in the opposite direction, opposing this force. WC is the energy that gravity is removing during take off. The net kinetic energy that you have at the instant your feet leave the ground is the difference, WC - FC, not the sum.
 
  • #7
Trying to do all this stuff with just words makes my head hurt. It really needs some diagrams and graphs. I think if you draw a graph of position, acceleration, KE, PE, gravity force, and foot force versus time, that you will be able to see the whole picture answer your own questions.

It sounds like you have the ideas correct, you're just getting confused with the bookkeeping.
 

1. What is conservation of energy confusion?

Conservation of energy confusion refers to the misunderstanding or misinterpretation of the principle of conservation of energy, which states that energy cannot be created or destroyed, only transferred or converted from one form to another. This confusion may arise due to misconceptions about how energy works or how it is conserved in different systems.

2. Why is conservation of energy an important concept?

Conservation of energy is a fundamental principle in the field of physics and has many practical applications. It helps us understand and predict the behavior of various systems, from simple objects to complex systems like the universe. It also plays a crucial role in the development of sustainable energy sources and technologies.

3. What are some common misconceptions about conservation of energy?

One common misconception is that energy can be created or destroyed, which goes against the principle of conservation of energy. Another misconception is that energy is a tangible substance that can be stored or transferred. In reality, energy is an abstract concept that describes the ability of a system to do work.

4. How can we avoid confusion about conservation of energy?

To avoid confusion, it is important to have a clear understanding of the principle of conservation of energy and its applications. It is also helpful to familiarize oneself with the different forms of energy and how they are converted or transferred in different systems. Seeking clarification from experts and conducting research can also help to clear up any confusion.

5. What are some real-life examples of conservation of energy?

Some real-life examples of conservation of energy include a pendulum swinging back and forth, a roller coaster moving from its highest point to its lowest point, and a ball rolling down a hill. In all these cases, the total amount of energy remains constant, even though it may change forms. Another example is the energy-efficient design of buildings and appliances, where energy is conserved by reducing waste and optimizing usage.

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