Force of 3 Boxes: Acceleration of System (m1,m2,m3)

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In summary, three blocks of mass 12.5 kg each are on a frictionless surface and are in contact with each other. A force of 91.4 N is applied to block 1, and the acceleration of the system is determined to be 7.312 m/s^2. To find the acceleration in terms of m1, m2, and m3, you need to consider the combined mass of all three blocks. Additionally, to calculate the force of contact between blocks m1 and m2, you can apply Newton's 2nd law to block m1 alone.
  • #1
strugglin-physics
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Three blocks of mass 12.5 kg each, on a frictionless horizontal surface are in contact with each other as shown in the figure below.



A force F = 91.4 N is applied to block 1 (mass m1). Determine the acceleration of the system (in terms of m1, m2, and m3).

I did 91.4 = 12.5a
91.4/12.5 = 7.312 but something is missing to that equation. how do I do it in terms of m1, m2, and m3)?
 

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  • #2
Since all three blocks are in contact you are attempting to accelerate all three of them - i.e. the combined mass.
 
  • #3
That was an obvious answer that I should've gotten, thank you.

Could you give me a pointer on this one too, having to do with the same problem?
Calculate the force of contact that block m1 exerts on m2.
 
  • #4
strugglin-physics said:
Calculate the force of contact that block m1 exerts on m2.
Apply Newton's 2nd law to block m1 alone.
 

1. What is the force of 3 boxes and how is it related to the acceleration of the system?

The force of 3 boxes refers to the combined force exerted by three individual boxes in a system. This force is directly related to the acceleration of the system, as stated by Newton's Second Law of Motion: Force equals mass times acceleration (F=ma). This means that the greater the combined mass of the three boxes, the greater the force and the slower the acceleration of the system.

2. How does the individual mass of each box affect the overall acceleration of the system?

The individual mass of each box has a direct impact on the overall acceleration of the system. According to Newton's Second Law of Motion, the acceleration of an object is inversely proportional to its mass. This means that the greater the mass of an object, the slower its acceleration will be. Therefore, a box with a larger mass will contribute more to the overall mass of the system and result in a slower acceleration.

3. What other factors besides mass can affect the acceleration of the system?

In addition to mass, there are other factors that can affect the acceleration of the system. These include the presence of external forces such as friction, air resistance, and gravity. Friction and air resistance can act as opposing forces, slowing down the acceleration of the system. Gravity, on the other hand, can either increase or decrease the acceleration of the system depending on its direction and magnitude.

4. Is there a relationship between the forces acting on each box and the total force of the system?

Yes, there is a direct relationship between the forces acting on each box and the total force of the system. According to Newton's Third Law of Motion, for every action, there is an equal and opposite reaction. This means that the force exerted by one box on another is equal in magnitude but opposite in direction. Therefore, the total force of the system is the sum of the individual forces acting on each box.

5. How can the acceleration of the system be calculated using the force of 3 boxes?

The acceleration of the system can be calculated by dividing the total force of the system by the combined mass of the three boxes. This can be represented by the formula a = F/(m1+m2+m3), where a is the acceleration, F is the total force, and m1, m2, and m3 are the individual masses of the three boxes. By plugging in the known values for force and mass, the acceleration of the system can be determined.

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