You must design a device for shooting a small marble vertically upward. The marb

Question

You must design a device for shooting a small marble vertically upward. The marble is in a small cup that is attached to the rim of a wheel of radius0.270 m ; the cup is covered by a lid. The wheel starts from rest and rotates about a horizontal axis that is perpendicular to the wheel at its center. After the wheel has turned through 20.0 rev, the cup is the same height as the center of the wheel. At this point in the motion, the lid opens and the marble travels vertically upward to a maximum height h above the center of the wheel.

If the angular acceleration is constant, what must it be so that the marble reaches a height of 12 m?

Explanation / Answer

height reached, h = 12 m

let v is the speed of marble when ot leaves the wheel,

Apply conservation of energy

initial,kinetic energy = final potentail energy

(1/2)*m*v^2 = m*g*h

v = sqrt(2*g*h)

= sqrt(2*9.8*12)

= 15.34 m/s

required angular speed, w = v/r

= 15.34/0.27

= 56.8 rad/s

we know, wo = 0

anglau dispalcement, theta = 20 rev = 20*2*pi rad = 125.7 rad

let alfa is the required angular acceleration,

use, w^2 - wo^2 = 2*alfa*theta

==> alfa = (w^2 - wo^2)/(2*theta)

= (56.8^2 - 0^2)/(2*125.7)

= 12.83 rad/s^2 <<<<<<<<<<-------------Answer

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