Newton's Third Law/ Circular Motion

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SUMMARY

The discussion focuses on calculating the speed required for mass m1 to rotate in a circular motion while mass m2 remains at rest. The tension T in the string is determined to be equal to the weight of m2 (T = m2g). The net force acting on m1 is equal to this tension, leading to the equation a = m2g / m1. By substituting acceleration a with v^2 / r, the final formula derived is v = sqrt(rm2g / m1), confirming the correctness of the approach.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Familiarity with circular motion concepts
  • Knowledge of tension in strings and forces acting on masses
  • Basic algebra for manipulating equations
NEXT STEPS
  • Study the application of Newton's Second Law in circular motion scenarios
  • Explore the concept of centripetal force and its relationship with tension
  • Learn about the dynamics of systems involving pulleys and hanging masses
  • Investigate real-world applications of circular motion in engineering
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Physics students, educators, and anyone interested in understanding the principles of circular motion and tension in connected mass systems.

dekoi
Question:
Mass m1 on the frictionless table is connected by a string through a hole in the table to a hanging mass m2. With what speed must m1 rotate in a circle of radius r if m2 is to remain hanging at rest?

My answer:

Fnetym2 = T - m2g
For m2, a = 0
Therefore,
0 = T - m2g
T = m2g

Fnetxm1 = T
m1a = T
m1a = m2g
Therefore,
a = m2g / m1

Since a = v^2 / r, v = sqrt(ra)

Therefore,
v = sqrt(rm2g / m1)

Is this correct?
 

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Looks correct to me.
 

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