Acceleration of a system with three blocks

Click For Summary
SUMMARY

The acceleration of a system consisting of three blocks with masses 9kg, 4kg, and 6kg can be accurately calculated using Newton's second law, F=ma. The initial attempt failed to account for gravitational forces acting on the 4kg block, which is crucial for correct calculations. By including the gravitational force for all blocks, the correct acceleration can be determined. The final equations for each block must reflect all forces acting upon them, including tension and gravity.

PREREQUISITES
  • Understanding of Newton's second law (F=ma)
  • Knowledge of free body diagrams
  • Basic principles of gravity and tension in systems
  • Ability to solve linear equations
NEXT STEPS
  • Review the application of Newton's second law in multi-body systems
  • Study free body diagram techniques for complex systems
  • Learn about tension forces in pulley systems
  • Explore gravitational effects on different masses in motion
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and dynamics, as well as educators seeking to clarify concepts related to forces and motion in multi-body systems.

duplaimp
Messages
33
Reaction score
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?
 
Physics news on Phys.org
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.
 
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:
 

Similar threads

  • · Replies 13 ·
Replies
13
Views
2K
  • · Replies 11 ·
Replies
11
Views
3K
  • · Replies 33 ·
2
Replies
33
Views
2K
  • · Replies 2 ·
Replies
2
Views
4K
Replies
6
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
Replies
10
Views
2K