A totally inedible cafeteria meatball with mass 40.0 g is attached to the free e

Question

A totally inedible cafeteria meatball with mass 40.0 g is attached to the free end of a 2.50-m piece of string that is attached to the ceiling. The meatball is pulled to the left so that the string makes a 36.9 angle with the vertical and is then released.

A) What is the magnitude of the angular velocity of the meatball the first time the angular acceleration is zero?

B) What is the direction of the angular velocity of the meatball the first time the angular acceleration is zero?(into or out of page?)

C) What is it the second time that z=0? (when it passes highest or lowest point?)

D) At the times described in parts (a) and (b), what is the magnitude of the meatball's radial acceleration?

E) At the times described in parts (a) and (b), what is the direction of the meatball's radial acceleration? (towards or away from center?)

Explanation / Answer

A)

at the lowest point the angular acceleration = 0

potential energy at the iniitial point = U = m*g*L*(1-costheta)

at teh lowest point the ball has KE = 0.5*m*v^2

from energy equation

KE = PE

v = sqrt(2*g*L*(1-costheta))

v = sqrt(2*9.8*2.5*(1-cos36.9)) = 3.13 m/s

angular velocity = w = v/L = 3.13/2.5 = 1.252 rad/s

(B)

out of the page

(C)

time period T = 2*pi*sqrt(L/g)

T = 2*pi*sqrt(2.5/9.8) = 3.2 s

the ball is passes the lowest point after a time t = 3T/4 = 2.4 s <<--answer

(D)

ar = w^2*L = 1.252^2*2.5 = 3.92 m/s^2

(E)

towards the center

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