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

In summary, the conversation discusses a statics problem involving two stacked marbles in a container. The question asks for the force exerted on the marbles at different points and the force each marble exerts on the other. The approach to solving the problem involves identifying all the forces acting on each marble and using symmetry to determine the point of contact. One participant suggests using trigonometry to find the angle of the force.
  • #1
539ay868h
2
0
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?
 

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  • #2
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.
 
  • #3
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?
 

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  • #4
great problem
 
  • #5
539ay868h said:
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.
 

1. What is the "Marble in Container Problem" and why is it important to solve?

The Marble in Container Problem refers to a physics problem where marbles are placed in a container and the forces between the marbles and the container are analyzed. This problem is important to solve because it helps us understand the principles of force and motion, which have many real-world applications.

2. How do you find the forces at points A, B, and C in the Marble in Container Problem?

The forces at points A, B, and C can be found by using Newton's Third Law of Motion, which states that for every action, there is an equal and opposite reaction. This means that the forces at these points are equal in magnitude but opposite in direction.

3. What is the importance of understanding the forces between marbles in the container?

Understanding the forces between marbles in the container allows us to predict their motion and behavior, which can have practical applications in fields such as engineering and design. It also helps us understand the basic principles of force and motion, which are fundamental to many other branches of science.

4. What factors can affect the forces between marbles in the container?

The forces between marbles in the container can be affected by factors such as the mass and velocity of the marbles, the shape and material of the container, and any external forces acting on the container or the marbles.

5. How can I solve the Marble in Container Problem if I don't know the exact forces at each point?

If the exact forces at each point are unknown, you can use the equations of motion and Newton's Second Law to calculate the forces. These equations take into account the mass and acceleration of the marbles, as well as the net forces acting on them, and can help you determine the forces at points A, B, and C. Alternatively, you can use experimental data to estimate the forces and verify your calculations.

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