An object of mass m 1 = 4.00 kg is tied to an object of mass m 2 = 3.70 kg with

Question

An object of mass m1 = 4.00 kg is tied to an object of mass m2 = 3.70 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 = 5.80 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

(a)

the tension in the string T1 is

T1 = - m1g + m1v1^2/ R1

from the relation between velocity and radius

v1 = v2/ R2 * R1 = 5.8/0.5 * 1 = 11.6 m/s

T1 = - ( 4) ( 9.8) + ( 4) ( 11.6)^2/1 m

=499.04 N

-----------------------------------------------

Tension in string 2 is

            T2 = ( m 2 v22 / l  ) + T 1- m2g

                = ( ( 3.7 kg)(5.8 m/s)2 / 0.5 ) + 499- ( 3.7 *9.8 m/s2 )

                = 711.676N

string 2 will break first

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.