How Is Force Distributed Between Three Boxes on a Frictionless Surface?

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In summary, the conversation discusses finding the force that box 2 exerts on box 1 as three boxes slide together on a frictionless surface. The solution involves using Newton's laws and drawing a free body diagram to identify the forces acting on block 1. The final answer is 5/6 of the applied force, as given by the teacher.
  • #1
dlthompson81
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Homework Statement



Three boxes are in contact and resting on a horizontal, frictionless surface. One box has mass m, the middle box has mass 2m, and the third box has mass 3m. A horizontal force of magnitude F is applied to the first box, and the three boxes slide together across the surface.

Find the force box 2 exerts backward on box 1 as the boxes accelerate across the table, in terms entirely of F.

Homework Equations



F=MA

The Attempt at a Solution



I already know the answer to this is 5/6. The teacher went over it in class, but I don't fully understand it. Can anyone help me out with an explanation of how exactly it works? It would be much appreciated. I have a midterm Monday, and I'm sure this will be on it. Thanks for the help.
 
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  • #2
The answer is 5/6 (F).

Can you find the acceleration of the system of blocks in terms of F and m? Then draw a free body diagram of block 1. This is essential. In a free body diagram, you show all forces acting on the block. These forces are contact forces like applied forces, friction, normal forces, as well as action at a distance forces like gravity (weight) forces. Once you identify these forces, use Newton's laws. In this FBD of block 1, apply Newton's 2nd law in the x direction to solve for the force of block 2 on block 1.
 
  • #3
Ok I think I may have this figured out.

The acceleration is A=F/6M

The force exerted back on block 1 is 5/6.

So that is the mass of 2 and 3 which is 5M * A

5M(F/6M) = 5/6F

So, for say the force exerted back on block 2 from block 3 it would be:

3M(F/6M)= 3/6F Is that right or am I still lost?
 
  • #4
dlthompson81 said:
Ok I think I may have this figured out.

The acceleration is A=F/6M
yes, good.
The force exerted back on block 1 is (5/6)(F).
That answer was given you by the teacher..you are trying to find it, not know it.
So that is the mass of 2 and 3 which is 5M * A

5M(F/6M) = 5/6F

So, for say the force exerted back on block 2 from block 3 it would be:

3M(F/6M)= 3/6F Is that right or am I still lost?
You went from trying to find the force of block 2 on 1, to finding the force of block 3 on 2? You must pretend no answer was given you. Look at block 1. There is an applied force F acting on it to the right, and a force of block 2 on 1 acting to the left. What is the net force acting on block 1? Then F_net =mA, where you calculated A correctly. Solve for the force of 2 on 1. Now see if you get the correct answer, as was given to you by the teacher.
 
  • #5


I would like to first clarify the question and the given information. The homework statement describes a situation where three boxes with different masses are in contact and resting on a horizontal, frictionless surface. A horizontal force of magnitude F is applied to the first box, and the three boxes slide together across the surface.

The homework equation provided, F=MA, is the fundamental equation used to describe the relationship between force, mass, and acceleration. In this situation, the force F is applied to the first box, which has a mass of m. The middle box has a mass of 2m, and the third box has a mass of 3m.

Now, to find the force that the second box exerts backward on the first box, we can use Newton's Third Law of Motion, which states that for every action, there is an equal and opposite reaction. In this case, the force applied to the first box (action) will result in an equal and opposite force exerted by the second box on the first box (reaction).

To determine the magnitude of this force, we can use the equation F=MA, where F is the force exerted by the second box, M is the mass of the second box, and A is the acceleration of the system. Since all three boxes are sliding together, they have the same acceleration. Therefore, we can write the equation as F=(2m)(a), where a is the acceleration of the system.

Now, we need to find the value of acceleration a. This can be done by considering the total mass of the system, which is m+2m+3m=6m. We know that the net force applied to the system is F, and using Newton's Second Law of Motion, we can write F=(6m)(a). Solving for a, we get a=F/6m.

Substituting this value of a in the equation F=(2m)(a), we get F=(2m)(F/6m)=F/3. Therefore, the force exerted by the second box on the first box is F/3. This means that the force box 2 exerts backward on box 1 as the boxes accelerate across the table is 1/3 of the applied force F.

To convert this into terms entirely of F, we can write it as 1/3F or simply F/3. Therefore, the force exerted by the
 

Related to How Is Force Distributed Between Three Boxes on a Frictionless Surface?

1. What is force?

Force is a physical quantity that can cause an object to accelerate or change its motion. It is measured in Newtons (N) and is represented by the formula F = ma, where F is force, m is mass, and a is acceleration.

2. How does force affect three boxes?

Force can affect three boxes in different ways depending on the magnitude and direction of the force. If the force applied to the boxes is in the same direction as their motion, it will cause them to accelerate. If the force is applied in the opposite direction, it will slow down the boxes. If the force is applied at an angle, it will cause the boxes to move in a curved path.

3. What are the three types of forces?

The three types of forces are contact forces, non-contact forces, and frictional forces. Contact forces are those that require physical contact between two objects, such as when pushing or pulling an object. Non-contact forces are those that act at a distance, such as gravitational and magnetic forces. Frictional forces are caused by the interaction between two surfaces and can either oppose or support motion.

4. How does Newton's Third Law apply to three boxes?

Newton's Third Law states that for every action, there is an equal and opposite reaction. This means that when a force is applied to one of the boxes, it will exert an equal and opposite force on the other boxes. For example, if one box is pushed to the right, the other two boxes will also experience a force to the left.

5. How can I calculate the net force on three boxes?

To calculate the net force on three boxes, you need to add all the individual forces acting on the boxes. If the forces are in the same direction, you can simply add them together. If they are in opposite directions, you need to subtract the smaller force from the larger force. The resulting net force will determine the overall motion of the boxes.

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