Ball tied to string- centripetal force

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SUMMARY

The discussion focuses on calculating the dynamics of a ball with a mass of 1.5 kg twirled in a vertical circle of radius 1.2 m at a constant speed. The period of the motion is 1.3 s. Key calculations include the speed of the ball, centripetal acceleration, centripetal force, and tension in the string at both the top and bottom of the circle. It is established that the formula for centripetal force is m*(v^2/r) and that it differs from the tension in the string.

PREREQUISITES
  • Understanding of uniform circular motion
  • Knowledge of centripetal acceleration
  • Familiarity with free body diagrams
  • Basic physics equations related to force and tension
NEXT STEPS
  • Calculate the speed of an object in circular motion using T = 2πr/v
  • Explore the relationship between centripetal force and tension in strings
  • Learn about free body diagram analysis in circular motion
  • Investigate the effects of varying mass and radius on centripetal force
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and circular motion, as well as educators seeking to clarify concepts of centripetal force and tension in strings.

Dannystu
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Homework Statement



A ball, mass m = 1.5 kg is twirled at constant speed v at the end of a massless string in a vertical circle of radius r = 1.2 m. The period for this uniform circular motion is T = 1.3 s. Free body diagrams for the ball at the top and at the bottom of the circle are shown.
a. Compute the speed v of the ball.
b. Compute the ball’s centripetal acceleration.
c. Compute the “centripetal force” on the ball.
d. When the ball is at the top (point A in the figure) compute the tension FTA in the string.
e. When the ball is at the bottom (point B in the figure) compute the tension FTB in the string.



Homework Equations



I understand all the parts except for question c, is the formula for centripetal force m*(v^2/r)? Or is it the same as the The tension in the string?
 
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Dannystu said:
I understand all the parts except for question c, is the formula for centripetal force m*(v^2/r)?
Yes.
Or is it the same as the The tension in the string?
No, they are not the same.
 
thanks a lot Doc!
 

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