An object of mass m1 = 4.00 kg is tied to an object of mass m2 = 2.90 kg with St

Question

An object of mass m1 = 4.00 kg is tied to an object of mass m2 = 2.90 kg with String 1 of length script i = 0.500 m. The combination is swung in a vertical circular path on a second string, String 2, of length script i = 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, m2 is traveling at v = 4.60 m/s.

(a) What is the tension in String 1 at this instant?
N

(b) What is the tension in String 2 at this instant?
N

(c) Which string will break first if the combination is rotated faster and faster?
string 1 string 2

Explanation / Answer

Given Mass m1 = 4.00 kg          m2 = 2.90 kg Velocity of object 2 is   v 2   = 4.60 m/s Angular velocity of the particle                = v 2 / l                    = 4.60 m/s / 0.500 m                    = 9.2 rad /s Velocity of object 1 is                v 1 = ( 2l )                      = ( 2*0.500 m ) ( 9.2 rad /sec )                      = 9.2 rad /s a) Tension in String 1               T 1 = m 1 v 12 / 2 l   - m1g                    = ( 4.00 kg)( 9.2 rad/s )2 / 2( 0.5 m)   - ( 4.00 kg ) ( 9.8 m/s )                    = 299.36 N ____________________________________________________________ b) Tension in string 2 is             T = ( m 2 v22 / l  ) + T 1- m2g                 = ( ( 2.9 kg)(4.6 m/s)2 / 0.5 ) + 299.36 - ( 2.9 *9.8 m/s2 )                 = 393.668 N ___________________________________________________________ c) String 2 will breaks first.                    = ( 4.00 kg)( 9.2 rad/s )2 / 2( 0.5 m)   - ( 4.00 kg ) ( 9.8 m/s )                    = 299.36 N ____________________________________________________________ b) Tension in string 2 is             T = ( m 2 v22 / l  ) + T 1- m2g                 = ( ( 2.9 kg)(4.6 m/s)2 / 0.5 ) + 299.36 - ( 2.9 *9.8 m/s2 )                 = 393.668 N ___________________________________________________________ c) String 2 will breaks first.

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