Two uniform 67.9-g marbles 2.45 cm in diameter are stacked as shown in the figur

Question

Two uniform 67.9-g marbles 2.45 cm in diameter are stacked as shown in the figure (Figure 1) in a container that is 2.82 cm wide.

Part A: Find the force that the container exerts on the marble at the point of contact A.

Part B: Find the force that the container exerts on the marble at the point of contact B. (Answer is 1.33 N)

Part C: Find the force that the container exerts on the marble at the point of contact C. (Should be same as Part A)

Part D: What force does each marble exert on the other?

Problem 11.79 Two uniform 67.9-g marbles 2.45 cm in diameter are stacked as shown in the figure (Figure 1) in a container that is 2.82 cm wide. Figure 1of 1

Explanation / Answer

Normal force by C on marbel = Nc
Normal force between two marbles = N
Normal force at A, B = Na, Nb

angle of N with horizontal = theta
cos(theta) = (d -2r)/2r = (2.82 - 2.45*2/2)/2*2.45
theta = 85.669 deg

Force balance on marble 1,2

Na = Ncos(theta)
Nb = 0.0679*9.8 + Nsin(theta)
Nc = Ncos(theta)
0.0679*9.8 = N*sin(theta)

N = 0.66732 N

A) Na = Ncos(theta) = 0.05039 N
b) Nb = 0.66542 + Nsin(theta) = 1.33 N
c) Nc = Ncos(theta) = 0.05039 N
d) N = 0.6673 N

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