Final answer:
The force constant for each elastic band can be calculated using Hooke's law, and it is approximately 267.96 N/m. The time for one complete bounce of the child is approximately 0.954 seconds. The child's maximum velocity during the bounce is approximately 0.634 m/s.
Step-by-step explanation:
The force constant of an elastic band can be calculated using Hooke's law, which states that the force exerted by a spring is directly proportional to its extension. In this case, each elastic band stretches 0.240 m while supporting 1/3 of the child's weight. So, the force constant for each elastic band can be calculated by dividing the weight of the child by the extension:
Force constant = (Child's weight / Extension)
For example, if the child weighs 6.55 kg and the extension is 0.240 m, the force constant for each elastic band would be:
Force constant = (6.55 kg × 9.8 m/s²) / 0.240 m = 267.96 N/m
The time for one complete bounce of the child can be calculated using the formula:
Time = 2π√(Mass / Force constant)
Using the given mass (6.55 kg) and the force constant (267.96 N/m), we can calculate the time:
Time = 2π√(6.55 kg / 267.96 N/m) ≈ 0.954 seconds
The child's maximum velocity during the bounce can be calculated using the formula for simple harmonic motion:
Maximum Velocity = Amplitude × √(Force constant / Mass)
With an amplitude of 0.240 m, a force constant of 267.96 N/m, and a mass of 6.55 kg, we can calculate the maximum velocity:
Maximum Velocity = 0.240 m × √(267.96 N/m / 6.55 kg) ≈ 0.634 m/s