Please show all your work clearly or I won\'t rate!! A lever arm rotates upward

Question

Please show all your work clearly or I won't rate!!

A lever arm rotates upward with an angular velocity of 4 rad/s and an angular acceleration of 3 rad/s2. It is observed that a 1 kg box has a velocity of 0.5 m/s relative to the arm and away from the pivot point when the arm is at 20 degree with the horizontal. What is the acceleration of the box relative to the arm at this point? Assume the coefficient of friction between the box and arm to be 0.15. 21.4 m/s" 18.0 m/s2 23.3n/s2 19.5 m/s: 16.1 m/s:

Explanation / Answer

This is a nice problem

At first i forgot to take coriolis acceleration into account and ended up with wrong answer.

after struggling for some time ,finally i got it.   :)

take components of weight along the plane and perpendicular to plane
g = 10  (for 9.8 also ans coming out to be almost same)
along the plane = mgsin(20)=3.42
normal to plane = mgcos(20)

take normal to plane :

m*(ay+ac) =N -mgcos(20)

ay = 1.5*3 = 4.5

ac = coriolis acceleration = 2*w*v = 4
N =17.9

frictional force f =N = 2.685 N

centrifugal force = mw^2r = 24 N

block will move up the incline

ma = m^2r -mgsin(20) - N = 18  (aprox)

a = 18m/s^2

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