Work, Energy, and the CWE Theorem

In summary, the conversation discusses a student dropping off a tower while tethered to a bungee cord with specific elasticity. The student's initial total mechanical energy is determined and it is shown that they will arrive at the ground with zero kinetic energy. The maximum speed of the student is at the point when they change direction. It is also discussed whether the same bungee cord would be safe for someone with a different mass, with the conclusion that it would not. There is some confusion about the interpretation of the problem and the correctness of the answers, with some clarification needed on the direction of forces and the use of conservation of energy.
  • #1
FrostScYthe
80
0
A student of mass m drops off a tower of height h, tethered to the bungee cord. The elasticity of the bungee cord is hosen so that its effective spring constant is k = 2mg/h. The jump is begun a zero speed at altitude h with the bungee cord fastened vertically above her, barely taut(with no slack), but under no initial tension.

(a) Choose a convenient coordinate systerm to analyze the problem.

- | h k = 2mg/h kx = F(x). I'm not sure what they are
- | want here because to me we
- | put it all in terms of x
- | as it's the only direction
- | considered.
- |
- O


(b) What is the initial total mechanical energy of the student?
I used the Energy for a simple harmonic oscillator and get..

E = 1/2(k)(x)^2
E = (mgx^2)/2

(c) SHow that the student will arrive at the ground with zero kinetic energy.
... I'm not sure about this one

(d) At what height above the ground is the speed of the student a maximum. I think it's at the point when it changes direction and oscillates back

(e) Will the same bungee cord be safe to use for a jump from the same tower(of height h) for a person with mass m' < m? With mass m' > m? Explain your reasoning.
No for both. The force of the spring doesn't depend on the mass, but only on the displacement and spring constant of the spring.

Is the work correct, not exactly, or absolutely wrong =\
 
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  • #2
(a) If you denote the student's altitude by x, then they want to know when x is zero. Could be when the student is at the top or bottom. They also want to know whether you count forces as positive when pointing up or down.

(b) Since the student is not moving at the beginning, initial total energy = initial potential energy.

(c) You can use conservation of energy. Zero kinetic energy means 'no motion'. See?

(d) I think your answer is wrong. Because when he changes direction, the speed is zero.

(e) I think your answer is wrong. They do not ask for the force in the cord, but whether he hits the ground. Better use the info given in (c)...
 
  • #3


Overall, the response provided seems to be on the right track and shows a good understanding of the concepts involved in the problem. However, there are a few areas that could use some clarification or improvement:

a) The chosen coordinate system seems to be fine, but it would be helpful to label the axes and clearly define what each variable represents. For example, x could represent the displacement from the initial position, while h could represent the height above the ground.

b) The initial total mechanical energy should include both potential and kinetic energy. Since the student starts at rest, the initial kinetic energy should be zero and the total mechanical energy should only be the potential energy at the initial height h.

c) To show that the student arrives at the ground with zero kinetic energy, you can use the conservation of mechanical energy principle. This means that the initial total mechanical energy is equal to the final total mechanical energy (which is just the potential energy at the final height, since the kinetic energy is zero). Therefore, at the ground, the kinetic energy must be zero.

d) The maximum speed of the student will occur at the point when the potential energy is at its minimum and all of the potential energy has been converted to kinetic energy. This occurs when the student is at the lowest point of the oscillation, which is at the ground.

e) The reasoning provided for both cases is incorrect. The spring constant does not depend on the mass, but the acceleration of the student does. A lighter person will experience a higher acceleration and therefore may require a different spring constant to ensure a safe and comfortable jump. Similarly, a heavier person may require a higher spring constant to prevent them from hitting the ground too hard.
 

1. What is work in terms of physics?

Work is defined as the force applied on an object multiplied by the distance it travels in the direction of that force. In other words, it is the energy transfer that occurs when a force is exerted on an object and it moves in the direction of the force.

2. What is energy and how is it related to work?

Energy is the ability of an object to do work. It can exist in many forms such as kinetic, potential, and thermal energy. Work and energy are directly related as work is the transfer of energy from one object to another.

3. What is the Conservation of Work-Energy (CWE) Theorem?

The CWE theorem states that the total amount of work done on an object is equal to the change in its kinetic energy. This means that the work done by all forces acting on an object is equal to the change in its speed or velocity.

4. How is the CWE theorem applied in real-world situations?

The CWE theorem can be applied in various real-world situations, such as calculating the potential and kinetic energy of a roller coaster or determining the amount of work needed to lift an object to a certain height. It can also be used to analyze the efficiency of machines.

5. Can the CWE theorem be violated?

No, the CWE theorem is a fundamental law of physics and has been extensively tested and proven to hold true in all situations. Violation of this theorem would require a violation of the law of conservation of energy, which is one of the most fundamental principles in physics.

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