An object of mass m 1 = 4.00 kg is tied to an object of mass m 2 = 4.40 kg with

Question

An object of mass m1 = 4.00 kg is tied to an object of mass m2 = 4.40 kg with String 1 of length = 0.500 m. The combination is swung in a vertical circular path on a second string, String 2, of length = 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?

Choose:

string 1

string 2   

Explanation / Answer

a) By v = r
=> = v/r = 4.60/0.5
=> = 9.2 rad/sec

Thus the velocity of the m1 will be= r = 1 x 9.2= 9.2 m/s
Thus by T = mv^2/r - mg
=>T1 = [4 x (9.2)^2]/1 - 4 x 9.8  
=>T1 = 299.36 Newton

(b) By T = mv^2/r - mg
=>T = [4.40 x (4.60)^2]/0.5 - 4.40 x 9.8 43.12
=>T = 143.088 Newton

=>T2 = T1 + T
=>T2 = 442.448 Newton

(c) String 2

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