Ug n/20 Side View Top View A large circular disk of mass m and radius R is initi
ID: 1446531 • Letter: U
Question
Ug n/20 Side View Top View A large circular disk of mass m and radius R is initially stationary on a horizontal icy surface. A person of mass m/2 stands on the edge of the disk. Without slipping on the disk, the person throws a large stone of mass m/20 horizontally at initial speed vo from a height h above the ice in a radial direction, as shown in the figures above. The coefficient of friction between the disk and the ice is . All velocities are measured relative to the ground. The time it takes to throw the stone is negligible. Express all algebraic answers in terms of m, R, uo- and fundamental constants, as appropriate. (a) Derive an expression for the length of time it wl take the stone to strike the ice. (b) Assuming that the disk is free to slide on the ice, derive an expression for the speed of the disk and person immediately after the stone is thrown (c) Derive an expression for the time it wil take the disk to stop sliding.Explanation / Answer
a) Here, h = 0 * t + 1/2 * g * t2
=> t = sqrt(2h/g) -------------------> length of time to strike ice .
b) Applying conservation of momentum
=> (m/20) * Vo = (m + m/2) * V
=> V = Vo/30 ---------------> speed of disk and person
c) time taken by disk to stop sliding = Vo/(30µg)
d) Appling conservation of momentum
=> m/20 * Vo * R = (1/2 * m * R2 + m/2 * R2 ) * w
=> m/20 * Vo * R = (m * R2) * w
=> w = Vo/(20R) ----------------------> angular speed after stone is thrown
e) Appling conservation of momentum
=> m/20 * Vo * R/2 = (1/2 * m * R2 + m/2 * R2/4 ) * w
=> m/40 * Vo * R = (5/8 * m * R2) * w
=> w = Vo/(25R) ----------------------> angular speed after stone is thrown
=> For the new position angular velocity is less than angular velocity found in part d) .
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