Solving Marble in Container Problem: Find Forces at A, B & C & Between Marbles

[539ay868h]

Hi all. I am stuck at this question for quite some time. Not really sure on how to go about solving it. Please help! Thanks in advance.

Two uniform 77.4-g marbles 2.23 cm in diameter are stacked as shown in the figure in a container that is 2.70 cm wide.

a) Find the force that the container exerts on the marble at the point of contact A.
b) Find the force that the container exerts on the marble at the point of contact B.
c) Find the force that the container exerts on the marble at the point of contact C.
d) What force does each marble exert on the other?

 

[Doc Al]

It's a statics problem, so what does that tell you? Start, as usual, by identifying all the forces acting on each marble. Hint: Use symmetry to figure out the point where the marbles touch.

 

[539ay868h]

I took the width of the container to minus the 2 radius of the marbles to get the horizontal length of the right-angle triangle (the blue line in the image).

2.7-2.23=0.47cm

then i took used cos(theta)=0.47/2.23
theta = 77.8

is this the correct approach?

 

[orthovector]

great problem

 

[Doc Al]

I took the width of the container to minus the 2 radius of the marbles to get the horizontal length of the right-angle triangle (the blue line in the image).

2.7-2.23=0.47cm

then i took used cos(theta)=0.47/2.23
theta = 77.8

is this the correct approach?

Excellent! Keep going.