The figure shows a ball with mass m = 1.2 kg attached to the end of a thin rod w

Question

The figure shows a ball with mass m = 1.2 kg attached to the end of a thin rod with length L = 1.6 m and negligible mass. The other end of the rod is pivoted so that the ball can move in a vertical circle. (a) What initial speed must be given the ball so that it reaches the vertically upward position with zero speed? What then is its speed at(b) the lowest point and (c) the point on the right at which the ball is level with the initial point? (d) If the ball's mass were doubled, what would the answer to (a) be?

Explanation / Answer

here,

length of rod , l = 1.6 m

mass , m = 1.2 kg

(a)

let the initial speed be v

using conservation of energy

0.5 * m * v^2 = m * g * l

0.5 * v^2 =9.8 * 1.6

v = 5.6 m/s

the initial speed must be given the ball so that it reaches the vertically upward position with zero speed is 5.6 m/s

(b)

the speed at the lowest point be v1

kinetic energy gained = change in potential energy

0.5 * m * v1^2 - 0.5 * m * v^2 = m *g * l

0.5 * v1^2 - 0.5 * 5.6 ^2 = 9.8 * 1.6

v1 = 7.92 m/s

the speed at the lowest point is 7.92 m/s

(c)

both the points at the same level ,

so , both points have same potential energy

then the velocity at right point is 5.6 m/s

(d)

if the ball's mass were doubled

the answer of (a) will remains the same

because it does not depends on the mass of the ball

speed

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