🧠 Understanding the Physics of Pulling Systems: Free Body Diagram Breakdown

In physics, analyzing the motion of pulling systems is a fundamental skill that appears in standardized tests like the MCAT and other pre-medical exams. The system often involves two masses connected by a string over a pulley—one on a table and one hanging freely. Understanding how forces act on each mass through Free Body Diagrams (FBDs) is critical to solving these types of problems.

🔍 Key Components

Concept	Description
Mass m₁	Rests on a table; subject to friction, normal force, and tension.
Mass m₂	Hangs freely; experiences tension upward and gravity downward.
Tension (T)	The force transmitted through the string connecting m₁ and m₂.
Friction (μN)	Resists the motion of m₁ sliding on the table surface.
Normal Force (N)	The support force acting perpendicular to the surface under m₁.
Gravitational Force (mg)	Acts downward on both masses, driving the system’s acceleration.

🧮 Force Equations

For mass m₁ (on the table):

• Horizontal:

  T − μm1​g = m1​a

• Vertical:

  N = m1g

For mass m₂ (hanging):

• Vertical:

  m2​g − T = m2a

By solving these two equations simultaneously, one can find tension (T) and acceleration (a).

🧠 Exam Tip

Always draw the Free Body Diagram before jumping into calculations. It clarifies which forces apply and in which direction. Choosing a positive direction consistently (like downward in this example) will help avoid sign errors.

🧪 MCAT-Style Practice Question

A 2 kg mass (m₁) rests on a table with a coefficient of kinetic friction of 0.2. It is connected by a string over a pulley to a 1.5 kg hanging mass (m₂). What is the acceleration of the system?

• A) 1.5 m/s²

• B) 2.0 m/s²

• C) 0.5 m/s²

• D) 0.8 m/s²

Solution:
Use the force equations above, plug in the values, and solve for acceleration (a).

✅ Correct Answer: D) 0.8 m/s²

💡 Conclusion

Understanding the physics of pulling systems involves visualizing force interactions clearly. By breaking down each mass’s Free Body Diagram and applying Newton’s laws, one can solve any pulley-based question with confidence. Keep practicing and you’ll ace this topic on exam day.

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