Question

Two people are sitting on playground swings. One is pulled back 4 degrees from the vertical and the other is pulled back 8 degrees. They are both released at the same instant. Will they both come back to their starting points at the same time

Answer 1

The bodies will not come back to their starting point at he same time.

Step-by-step explanation:

Since they are both pulled back at an angle to the vertical, there is a tangential component of acceleration a = gsinθ

When θ = 4 , a = 9.8sin4 = 0.684 m/s²

When θ = 8 , a = 9.8sin8 = 1.364 m/s²

Using s = ut + 1/2at². Where s is the distance covered and t = time taken, u = initial speed = 0 (assumed since they are both released at the same time)

So s = 0 × t + 1/2at² = 1/2at²

s = 1/2at²

t = √2s/a. Now, since s is the same for both swings, it follows that

t ∝ 1/a. Since their accelerations are different, the bodies will not come back to their starting point at he same time.

Answer 2

They will come back at the same time.

Step-by-step explanation:

The angular velocity equation of ω
`= (V)/(r)` where ω is the frequency of the movement, dependent on the angle. But since swings are simple pendulums and their angles of 8 and 4 degrees are small, they will come back to their starting points at the same time.

I hope this answer helps.