Work, Energy, and the CWE Theorem

  • #1
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 =\

Answers and Replies

  • #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)...