Calculating Tension and Speed in Circular Motion: A Tether Ball Example

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SUMMARY

The discussion focuses on calculating the tension in the cord and the speed of a tether ball in circular motion. Given a tether ball with a mass of 0.5 kg attached to a 1.5 m cord at a 20-degree angle from the vertical, the tension in the cord and the speed of the ball remain constant during its circular motion. The key concepts include the relationship between centripetal force and tension, which are critical for solving the problem accurately.

PREREQUISITES
  • Circular motion dynamics
  • Centripetal force calculations
  • Trigonometric functions for angle resolution
  • Newton's laws of motion
NEXT STEPS
  • Calculate tension in circular motion using the formula T = mg/cos(θ) + mv²/r
  • Determine speed of the ball using the formula v = rω, where ω is angular velocity
  • Explore the effects of varying angles on tension and speed in circular motion
  • Study the principles of centripetal acceleration and its relation to tension
USEFUL FOR

Physics students, educators, and anyone interested in understanding the mechanics of circular motion and tension in systems like tether balls.

Lalasushi
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A tether ball of mass 0.5kg is attached to a vertical pole by a cord 1.5m long. Assume the cord attaches to the centre of the ball. If the cord makes an angle of 20 degrees with the vertical, then:
a) what is the tension in the cord?
b) what is the speed of the ball?

im having trouble with this question. I am assuming that the ball is nearly at the top of its swing...just 20 degrees away from it...can anyone help me with part a)? I am not sure if it has anything to do with centripetal force...
 
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You have misunderstood the situation:
The tether ball moves in a circular orbit in the HORIZONTAL plane, to which the the vertical is the normal direction.

In this situation, you will find that the speed of the ball and the tension in the cord are CONSTANTS throughout the circular motion.
 

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