A 90 g bead on a 60 cm long string is swung in a vertical circle about a point 2

Question

A 90 g bead on a 60 cm long string is swung in a vertical circle about a point 200 cm above the floor ( as shown in figure). The tension in the string when the bead is at the very bottom of the circle is 3.4 N. A Very sharp knife is  suddenly inserted, as shown in the ifgure, to cut the stirng  directly below the point of support. How far to the right of the center of the circle does the ball hit the floor?

A 90 g bead on a 60 cm long string is swung in a vertical circle about a point 200 cm above the floor ( as shown in figure). The tension in the string when the bead is at the very bottom of the circle is 3.4 N. A Very sharp knife is suddenly inserted, as shown in the ifgure, to cut the stirng directly below the point of support. How far to the right of the center of the circle does the ball hit the floor?

Explanation / Answer

at bottom,

T = mg + mv^2 /r

3.4 = 0.090 x (9.8 + v^2 /0.60)

v = 4.10 m/s inhorizonal direction

height from ground h = 200 - 60 = 140 cm =1.4 m

in vertical, h = uyt + at^2 /2

1.4 = 0 + 9.8 x t^2 /2

t = 0.535 sec

x = ut = 4.10 x 0.535 = 2.19 m

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