The figure shows a thin rod, of length L = 1.10 m and negligible mass, that can

Question

The figure shows a thin rod, of length L = 1.10 m and negligible mass, that can pivot about one end to rotate in a vertical circle. A heavy ball of mass m = 140 kg is attached to the other end. The rod is pulled aside to angle 0 = 17° and released with initial velocity v Overscript right-arrow EndScripts Subscript 0 = 0. (a) What is the speed of the ball at the lowest point? (b) Does the speed increase, decrease, or remain the same if the mass is increased?

Chapter 08, Problem 018 The figure shows a thin rod, of length L1.10 m and negligible mass, that can pivot about one end to rotate in a vertical circle. A heavy ball of mass m = 140 kg is attached to the other end. The rod is pulled aside to angle = 170 and released with initial velocity V 0 = 0, (a) what is the speed of the ball at the lowest point? (b) Does the speed increase, decrease, or remain the same if the mass is increased? (a) Number Units

Explanation / Answer

Given L = 1.10 m

mass m = 140 kg

angle 0 = 17°

let the origin is at the bottom of the rod in vertical position

if the mass israised through a vertical height 'h' then

h = l - (l*cos(0))

h = l * (1-cos(0))

the potential energy is P.E = m * g l * (1-cos(0))

when it reaches bottom the kinetic energy is K.E = 1/2 * m * v^2

from conservation of energy

K.E = P.E

1/2 * m * v^2 = m * g * l * (1-cos(0))

we get v = sqrt(2 * g * l * (1-cos(0))--------------(1)

v = sqrt(2 * 9.8 * 1.1 * (1-cos(17))

v = 0.97 m/s-------------Answer

b) from expression (1) it is very clear that 'v' does not depend on mass so

If the mass is increased the speed 'v' remains same

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