Acceleration of a system with three blocks

In summary, the conversation discusses the acceleration of a system and uses the equations F=ma and Newton's 2nd Law to solve for it. The free body diagrams are also mentioned, with the correct inclusion of gravity for all blocks. Ultimately, the right answer is achieved.
  • #1
duplaimp
33
0

Homework Statement


888aSSy.jpg


What is the acceleration of this system?

Homework Equations


F=ma


The Attempt at a Solution


I tried the following:

Let blocks with mass 9kg, 4kg and 6kg be m9, m4, m6
This is the free body diagrams I drawn:

flDzVEo.png


Then I applied Newton's 2nd Law:
F = ma

(For m9) mg-TR=9a
(For m4) TR-TL=4a
(For m6) TL-w*sin(30)=6a

I solved for a and it didn't gave the right answer.
What I am doing wrong?
 
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  • #2
duplaimp said:
(For m9) mg-TR=9a
Good.

(For m4) TR-TL=4a
What about gravity?

(For m6) TL-w*sin(30)=6a
Good.

Gravity applies to m4 just like it does to m6.
 
  • #3
Doc Al said:
Gravity applies to m4 just like it does to m6.

I didn't included that because as m4 is "in the middle" I thought it wasn't necessary but it seems I was wrong. Now it gives the right acceleration.
Thank you! :biggrin:
 

Related to Acceleration of a system with three blocks

1. What is acceleration of a system with three blocks?

Acceleration of a system with three blocks refers to the rate of change of velocity of the entire system, which is made up of three blocks attached to one another. It is a measure of how quickly the system's speed is increasing or decreasing.

2. How is acceleration calculated for a system with three blocks?

To calculate acceleration of a system with three blocks, you would need to use Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration. The net force can be found by summing up all the individual forces acting on the three blocks in the system.

3. What factors can affect the acceleration of a system with three blocks?

The acceleration of a system with three blocks can be affected by the mass of the blocks, the net force acting on the system, and any external forces such as friction or air resistance. The type of surface the blocks are on and the angle of the incline can also impact the acceleration.

4. How does the acceleration change if the mass of one block is increased?

If the mass of one block in the system is increased, the overall acceleration of the system will decrease. This is because the increased mass will require a greater force to accelerate, and the net force acting on the system will decrease.

5. Can the acceleration of a system with three blocks ever be zero?

Yes, it is possible for the acceleration of a system with three blocks to be zero. This would happen if the net force on the system is equal to zero, meaning that all the forces acting on the blocks are balanced and cancel each other out. In this case, the system would either be at rest or moving at a constant velocity.

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