A series of small packages, each with a mass of 4 kg, are discharged from a conveyor belt as shown. Assume that the coefficient of static friction between each package and the conveyor belt is 0.4.
Determine the force exerted by the belt on a package just after it has passed Point A
I attached the picture below
F = ma
The Attempt at a Solution
So I began by drawing a FBD:
-W: Weight pointed downwards
-N: Normal pointed upwards
-f: Friction pointed left
-B: Force from the belt pointed right.
From what I understand, we are trying to solve for B.
Also, it is about to enter a circular region, which makes me think that the net acceleration is -mv^2/r in the y direction and dv/dt in the x direction.
So, I began by solving the forces in the y direction:
-mv^2/r = -W + N
-(4)(1^2)/(0.250) = -(4)(9.81) + N
--> N = 23.24 N
From there, I setup the equation in the x direction:
dv/dt = B - (u)N
dv/dt = B - (0.4)(23.24)
Now the thing is, I assumed that the speed is consistent which would imply B = (0.4)(23.24) = 9.296 N.
However, this answer was wrong, so I am not sure how to approach it from here.
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