A ball with a mass of 280 g is tied to a light string that has a length of 2.20

Question

A ball with a mass of 280 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 31.0° 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(in 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.)

Explanation / Answer

the height from equilibrium position upto which its moved = 2.2 - 2.2cos31
= 0.3142 metre
when it achieves highest speed, the potential energy is totally converted to kinetic energy
1/2 mv2 = mgh

v2 = 2gh = 2x9.8x0.3142 = 6.16

v=2.48 m/s

when the bob comes to rest, the net work done must be equal to the initial potential energy,

Now the displacement of bob is always opposite to the resistive force, therefore the work done is negative.

work done by resistive forces = -mgh = -0.28 x 9.8 x 0.3412 = -0.936J

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