Any help would be appreciated. I just don\'t get how to work this out. Thanks! C

Question

Any help would be appreciated. I just don't get how to work this out. Thanks!

Consider a ball of mass m = 0.333 kg on a 0.555 m string being whirled in a vertical circular path as shown in the diagram below. When the ball is at the top of the circle, it has a speed of 2.55 m/s.

(a) When the ball is at the top of the circle, what is the tension in the string?

magnitude = N

direction =

(b) What minimum speed should the ball have at the top of the circle to continue in its circular motion?
Answer is in m/s

Explanation / Answer

a)

r = radius = L = 0.555 m

m = mass of ball = 0.333 kg

v = speed = 2.55 m/s

at the top , force equation is given as

T + mg = mv2/r

T + (0.333) (9.8) = (0.333) (2.55)2/(0.555)

T = 0.64 N

direction : downwards

b)

minimum speed is when T = 0

so mg = mv2/r

v = sqrt(rg) = sqrt(0.555 x 9.8) = 2.33 m/s

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