5. An object of mass m1 = 4.00 kg is tied to an String 1, object of mass m2 = 3.

Question

5. An object of mass m1 = 4.00 kg is tied to an String 1, object of mass m2 = 3.00 kg with String 1 of length 1= 0.500 m. , The combination is String 2 swung in a vertical circular path on a second string, String 2, of length, 1=0.500 m. During the motion, the two strings are collinear at all times as shown in Figure. At the top of its motion, m2 is traveling at y =4.00 m/s. (a) What is the tension n String 1 at this instant? (b) What s the tension in String 2 at this instant? (c) Which string will break first if the combination is rotated faster and faster?

Explanation / Answer

angular speed = w = v/l

for m1

v1 = 2l*w = 2l*v/l = 2v = 8 m/s

T1 = m1*v1^2/(2l) = m1*v^2/2l = (4*8^2)/1 = 256 N

for m2

v2 = v = 4 m/s

a = v2^2/l = (4^2)/0.5 = 32 rad/s^2

Fnet = T2 - T1 = m2*a

T2 = T1 + m2*a

T2 = 256+(32*3) = 352 N

T2 > T1

as the system rotates faster and faster the T2 increases and at some speed it breaks

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