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A 20 g mass is attached to a 120 cm long string. The angle (alpha) is...

A 20 g mass is attached to a 120 cm long string. The angle (alpha) is measured to be 18 degrees. What is the speed of the mass?

The answer is 1.09 m/s but I just don't know how to get it.

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Answer #1

here,

mass , m = 20 g

m = 0.02 kg

length , l = 1.2 m

alpha = 18 degree

let the speed of mass be v

for the circular motion

let the tension in the string be t

t * cos(aplha) - m*g = 0

t * cos(18) - 0.02 * 9.8 = 0

t = 0.206 N

equating the forces horizontally

t*sin(alpha) - m*v^2/(l * sin(alpha)) = 0

0.206 * sin(18) - 0.02 * v^2 /(1.2 * sin(18)) = 0

v = 1.09 m/s

the speed of mass is 1.09 m/s

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