A 21 kg child swings on a playground swings 3.6 m long. What is period of her motion?
2) If her older brother, who weighs twice as much as she does, rides in the swing instead, what is the period of the motion? Assume the center of mass to be at the position of the seat in both cases.....please I need help me
To find the period of motion for the child swinging on the playground swings, we can use the formula:
T = 2*pi*sqrt(L/g)
where T is the period, L is the length of the swing, and g is the acceleration due to gravity.
For the first case, where the child weighs 21 kg, we can input the values into the formula:
L = 3.6 m
g = 9.8 m/s^2 (average acceleration due to gravity)
T = 2*pi*sqrt(3.6/9.8)
T ≈ 2*pi*sqrt(0.367)
Calculating further:
T ≈ 2*pi*0.606
T ≈ 3.81 seconds
Therefore, the period of motion for the child swinging on the playground swings is approximately 3.81 seconds.
Now, let's move on to the second case where the older brother, who weighs 2 * 21 kg = 42 kg, rides in the swing. The only thing that changes in this case is the mass of the person swinging. The length of the swing and the center of mass remain the same.
Using the same formula as before, we have:
L = 3.6 m
g = 9.8 m/s^2
T = 2*pi*sqrt(L/g)
T = 2*pi*sqrt(3.6/9.8)
T ≈ 2*pi*sqrt(0.367)
Calculating further:
T ≈ 2*pi*0.606
T ≈ 3.81 seconds
Therefore, the period of motion for the older brother swinging on the playground swings is also approximately 3.81 seconds.