What Is the Force of Tension Between Mass A and B?

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SUMMARY

The force of tension between Mass A (4 kg) and Mass B (6 kg) in a system with an external tension of 150 N and an acceleration of 2.99 m/s² can be determined using Newton's second law, F=ma. The downward acceleration of Mass C (12 kg) indicates that the tension in the string connecting Mass B and C must counteract the weight of Mass C while also contributing to the overall acceleration of the system. By analyzing the forces acting on each mass, particularly focusing on the lower mass, the correct tension can be calculated systematically.

PREREQUISITES
  • Understanding of Newton's second law (F=ma)
  • Basic knowledge of forces and tension in a pulley system
  • Ability to analyze free body diagrams
  • Familiarity with mass and weight concepts
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  • Calculate the tension in the string between Mass B and C using F=ma
  • Explore the effects of varying mass on tension in multi-body systems
  • Learn about free body diagrams for complex systems
  • Study the principles of static and dynamic equilibrium in physics
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Students studying physics, particularly those focusing on mechanics and tension in multi-body systems, as well as educators seeking to clarify concepts related to forces and acceleration.

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Homework Statement



Force of tension externally is 150N [up]
Acceleration is 2.99 m/s^2 [down]
Mass A is the highest and is 4kg
Mass B is attached to Mass A by a light (negligible) string, Mass B is 6 kg
Mass C is attached to Mass B by a light (negligible) string, Mass C is 12 kg

What is the force of tension on the string between Mass A and B.


Homework Equations



There isn't really a formula for tension I don't think... Which is why I'm confused. I have gotten the wrong answer 3 times already. I am not sure how the relationship between the three bodies works in this system
 
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Have you drawn a large, neat diagram?

You can analyze these types of equations quit methodically. Let's consider the lower mass. It has its own weight pulling down, and a retarding force (tension in that lower rope) pulling upwards. The result of this tug o' war is a force that causes that 12 kg body to accelerate downwards at 2.99m/sec2.

So, you can apply F=ma, to determine the only unknown in this bit of the puzzle, viz., T3 or whatever you want to name the tension in the lower rope.

Now, turn your attention to the middle weight ...

Shortcuts are best avoided until you know what is going on.
 

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