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
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:
They will come back at the same time.
Explanation:
The angular velocity equation of ω[tex]= \frac{V}{r}[/tex] 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.
Answer:
The bodies will not come back to their starting point at he same time.
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.