At what angle should the ball suspended on the thread be deflected so that when it passes the equilibrium position
November 23, 2020 | education
| At what angle should the ball suspended on the thread be deflected so that when it passes the equilibrium position, its acceleration is 5 m / s2?
Given:
a = 5 m / s square
Decision:
rejecting the ball, we raised it to a height h
At this point, it has a potential energy mgh
Then this energy turns into kinetic. At the lowest point, all potential energy has passed into kinetic energy.
Means mvsquare / 2 = mgh
vsquare / 2 = gh
vsquare = 2gh = 2g (R-Rcos alpha) = 2gR (1-cos alpha)
Acceleration is related to speed by the formula
a = vsquare / R
Hence
v square = aR
Then
2gR (1-cos alpha) = aR
2g (1-cos alpha) = a
1-cosalpha = a / (2g)
cos alpha = 1-a / (2g)
alpha = arccos (1-a / (2g)) = arccos (1-5 / (2 * 9.8)) = 41.8 degrees
Answer: 41.8 degrees.
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