Question
PLEASE answer all Parts of the questions:
Estimate the spring constant for a trampoline. Assume a person is standing on the trampoline and oscillating up and down without leaving the trampoline. Hint. Begin by estimating the mass of the oscillator and the period of the motion. Part 1 - Recognize the Principles Which of the following statements or principles will be useful in solving this problem? The amount that the trampoline is depressed will depend on the person's mass. The person and trampoline will act as a simple harmonic oscillator. The spring constant of the trampoline will depend on the person's mass. We can use F = ma to describe the motion of the person. Part 2 - Sketch the Problem The figure below shows a person vibrating up (right side) and down (left side) on a trampoline. According to the problem statement, the person is always in contact with the trampoline so he is not "up in the air" in part B. Part 3 - Identify the Relationships According to the problem statement, the person is always in contact with the trampoline so we can treat the person and trampoline as a mass-spring system in which the mass is always connected to the spring. For such a system, what is the relation for the period of the motion? Part 4- Solve Estimates To use your expression for the period of the trampoline to calculate its spring constant k, you will need to estimate the mass of a person and the period of the oscillation in the figure above. What is a reasonable estimate for the mass of a typical person? What is a reasonable estimate for the period of a trampoline's oscillation? Calculations (use your estimates) Using your estimated values for the mass and period, what is the approximate spring constant of a trampoline? N/m
Explanation / Answer
1) the person will act as a simple harmonic oscillator
3) T = 2 pi sqrt( m/k)
guess T = 2 seconds
m = 50 kg
so
2 = 2*pi*sqrt(50/k)
k= 493
