A ball with a mass of 200 g is tied to a light string that has a length of 2.20

Question

A ball with a mass of 200 g is tied to a light string that has a length of 2.20 m. The end of the string is tied to a hook, and the ball hangs motionless below the hook. Keeping the string taut, you move the ball back and up until the string makes an angle of 29.0° with the vertical. You then release the ball from rest, and it oscillates back and forth, pendulum style. Use g = 9.80 m/s2.

(a) If we neglect air resistance, what is the highest speed the ball achieves in its subsequent motion?
1____________ m/s

(b) Resistive forces eventually bring the system to rest. Between the time you release the ball and the time the ball comes to a permanent stop, how much work do the resistive forces do? (Use the appropriate sign.)
2_____________J

Explanation / Answer

a) energy at hihest poistion = mgl( 1-cos) 

this energy is equal to Kineatic energy at bottom( highets vleovity)

mgl(1- cos29) = 0.5mv^2

9.8( 2.20)( 0.125) = 0.5v^2

solving for v ,

v = 2.32 m/s apprx

b) work don e= chnage in kE =0J-  0.53824 J= -0.53824 j apprx( work don eby resistiv e force)

work done is negative

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