Solving for Speed and Acceleration of Ball at Point P

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SUMMARY

The discussion focuses on calculating the speed and acceleration of a heavy ball swinging on a string in a circular arc with a radius of 2 meters. At point P, the lowest point of the trajectory, the speed is determined using the principles of conservation of energy, resulting in a speed of approximately 6.26 m/s. The acceleration at point P is solely due to gravity, measured at 9.8 m/s². At points Q and Q', where the string is at +/- 27 degrees from the vertical, the potential and kinetic energy can be calculated using the height difference and the ball's speed at those points.

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1. Homework Statement

A heavy ball swings on a string in a circular arc of radius 2m.
The two highest points of the ball's trajectory are Q and Q'; at these points the string is +/- 27 degrees from the vertical. Point P is the lowest point of the ball's trajectory where the string hangs vertically down. The acceleration of gravity is 9.8 m/s^2.

1.) What is the ball's speed at the point P? Neglect air resistance and other frictional forces.
2.) What is the magnitude of the ball's acceleration at the point P?

 
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What is the ball's speed at Q and Q'? What is its energy there (potential + kinetic)? What about P then?
 

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