A heavy ball swings on a string in a circular arc of radius 1 m. The two highest

Question

A heavy ball swings on a string in a circular
arc of radius 1 m.

The two highest points of the ball’s trajectory are Q andQ; at these points the string is
±30? from the vertical. Point P is the lowest point of theball’s trajectory where the string
hangs vertically down. The acceleration of gravity is 9.8 m/s2.

1.)What is the ball’s speed at the point P? Neglect airresistance and other frictional forces. Answer in units of m/s.

2.)What is the magnitude of the ball’s acceleration at thepoint P? Answer in units of m/s2.

3.)What is the magnitude of the ball’s acceleration at thepoint Q? Answer in units of m/s2.

Explanation / Answer

let potential energy at point P=0 let velocity at point P=v kinetic energy at point P=(1/2)*m*v2 potential energy at point Q=m*g*h=m*9.8*1*cos30 kinetic energy at point Q=0 m*9.8*1*cos30=(1/2)*m*v2 v=4.12 m/s (ans 1) centripetal acceleration=v2/r=4.122/1=16.97m/s2 an it's constant through out

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