A 21-kg child swings on a playground swing 3.4 m long. What is the period of her motion? If her brother, who weighs twice as much as she does,rides on the swing instead, what is the period of the motion?
I'm sure your text or class notes has the pendulum period (P) formula
P = 2 pi sqrt (L/g)
Note that it is independent of mass.
To find the period of the swing's motion, we can use the formula for the period of a simple pendulum:
T = 2π * √(L/g)
where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity (9.8 m/s² on Earth).
For the first situation, where the child swings on the playground swing, we have:
L = 3.4 m
g = 9.8 m/s²
Substituting these values into the formula, we can calculate the period of motion:
T = 2π * √(3.4/9.8)
Using a calculator, we find that the period is approximately 2.99 seconds.
Now, for the second situation, where the brother who weighs twice as much as the child rides on the swing, we need to account for the change in weight.
Given that the brother weighs twice as much, his weight would be 2 * 21 kg = 42 kg.
Using the same formula, with the new weight:
T = 2π * √(L/g)
but now with:
L = 3.4 m
g = 9.8 m/s²
weight of the brother = 42 kg
Substituting these values into the formula, we can calculate the new period of motion:
T = 2π * √(3.4/9.8)
Using a calculator, we again find that the period is approximately 2.99 seconds.
Therefore, for both the child and the brother, the period of motion on the swing is approximately 2.99 seconds.