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Centripetal acceleration and centripetal force

AP.PHYS: CHA‑4.A (EU), CHA‑4.A.2 (EK), CHA‑4.A.2.1 (LO), CHA‑4.A.2.2 (LO), INT‑3.B (EU), INT‑3.B.1 (EK), INT‑3.B.1.3 (LO), INT‑3.B.2 (EK)
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A pendulum consists of a ball with a mass of 0, point, 5, start text, space, k, g, end text attached to the ceiling by a 3, point, 00, start text, space, m, end text massless rope. The ball is released from rest at some initial angle from vertical and freely swings back and forth. The free body diagram of the ball when the pendulum makes an angle of 45, degree from the vertical and has a tension of 21, start text, space, N, end text in the rope is shown below.
Two arrows point out of a central dot. A vertical arrow, labeled F sub M G, points straight down. A diagonal arrow, labeled T, points up and to the right. A thin vertical line extends down from the arrowhead. Between the arrowhead and this line is the label forty five degrees.
Calculate the speed of the mass when rope at this point. Write your answer to 3 significant figures.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
start fraction, start text, m, end text, divided by, start text, s, end text, end fraction