An object of mass m_1 = 4.00 kg is tied to an object of mass m_2 = 3.50 kg with

Question

An object of mass m_1 = 4.00 kg is tied to an object of mass m_2 = 3.50 kg with String 1 of length l = 0.500 m. The combination is swung in a vertical circular path on a second string, String 2, of length f = 0.500 m. During the motion, the two strings are collinear at all times as shown in the figure. At the top of its motion, m_2 is traveling at v = 4.70 m/s. What is the tension in String 1 at this instant? Does the mass of m_2 affect the force needed to make mi travel in a circle? What is the tension in String 2 at this instant? N Which string will break first if the combination is rotated faster and faster?

Explanation / Answer

w = v / r = 4.70 / 0.5 = 9.4 rad/s

using Fnet = ma on m1 :

T1 + m1g = m1 (w^2 r )

T1 + (4 x 9.81) = 4 ( 9.4^2 * (0.5 + 0.5))

T1 + 39.24 = 353.44

T1 = 314.2 N ......Ans

b) on m2:

T2 + m2g - T1 = m2 ( w^2 r)

T2 + (3.50 x 9.81) - 314.2 = 3.50 ( 9.4^2 * 0.5)

T2 - 279.86 = 154.63

T2 = 434.49

c) as we can see T2 > T1

so string 2 will break first

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