How Forces Affect Motion · Lesson 7 of 8
Forces Acting on a System of Objects
“Choosing a whole system can make internal force pairs disappear from the calculation and reveal the motion simply.”
• Treat connected objects as a single system. • Distinguish internal forces from external forces. • Identify tension in a connecting string. • Calculate the acceleration of a connected system. • Explain when internal forces must still be considered.
Two boxes connected by a string may appear to require two separate force calculations. Yet if they move together, they share one acceleration. By drawing a boundary around both boxes and the string, we can study the combined system. This choice often turns a complicated interaction into one direct application of the second law.
Connected Objects And Tension
Tension is the pulling force transmitted through a stretched string, rope, cable, or similar connector.
When an external force pulls one box, the string pulls the second box. The string also pulls back on the first box. These two tension forces form an interaction pair and have opposite directions on the two boxes. If each box is analysed separately, tension must be included.
Choosing The System
An internal force is a force exerted by one part of a chosen system on another part of the same system.
An external force is a force exerted on the chosen system by something outside its boundary.
For the system containing both boxes and the string, the two tension forces are internal. They are equal and opposite and do not change the total momentum of the entire system. The applied pull comes from outside the boundary and is external. It determines the system’s horizontal acceleration when resistance is absent.
Acceleration Of The System
If masses m₁ and m₂ move together, the total mass is m₁ + m₂. On a frictionless horizontal surface with external horizontal force F, the second law gives the common acceleration.
Problem
Boxes of 2 kg and 3 kg are connected on a frictionless floor. A horizontal external force of 20 N pulls the system. Find their acceleration.
- 1.Choose both boxes and the string as the system.
- 2.Add the masses: 2 kg + 3 kg = 5 kg.
- 3.Identify the net external horizontal force: 20 N. Internal tension is not included for the whole system.
- 4.Use a = F/(m₁ + m₂).
- 5.Substitute: a = 20/5 = 4 m s⁻².
- 6.Both boxes accelerate at 4 m s⁻² in the direction of the pull.
Vertical External Forces
Gravity and the floor act from outside the two-box system. The total weight is (m₁ + m₂)g downward, and the combined normal force is upward. If there is no vertical acceleration, these external vertical forces balance. Their net vertical contribution is zero, while the horizontal external force remains unbalanced.
When To Analyse Parts Separately
Treating the whole system is best for finding common acceleration. To find tension, force on a particular connector, or motion of one part relative to another, isolate an individual object after the common acceleration is known. The tension then becomes an external force for that smaller chosen system.
Problem
In the previous example, suppose the 20 N force pulls the 3 kg box, which pulls the 2 kg box through the string. Find the tension.
- 1.Use the whole system result: a = 4 m s⁻².
- 2.Now isolate the 2 kg box.
- 3.On that box, the only horizontal force is tension in the direction of acceleration.
- 4.Apply T = ma = 2 × 4.
- 5.The tension is 8 N.
- 6.Check using the 3 kg box: 20 N − 8 N = 12 N, and 12/3 = 4 m s⁻², so the result is consistent.
A Systematic Strategy
Draw a boundary around the proposed system. Classify every force crossing the boundary as external. Treat forces between parts inside the boundary as internal. Add the masses inside the boundary, calculate the net external force, and apply the second law. Change the boundary only when a question asks about a particular internal force.
Quiz
Which description best matches Tension?
Which description best matches Internal Force?
Which term matches this description: Tension is the pulling force transmitted through a stretched string, rope, cable, or similar connector.
Which term matches this description: An internal force is a force exerted by one part of a chosen system on another part of the same system.
Which statement is a key takeaway from this lesson?
Practice Problems
- Explain why tension is internal for a two-box system but external for one box alone.
- Calculate the acceleration of connected 4 kg and 6 kg boxes pulled by 30 N on a frictionless floor.
- Name the external vertical forces on the two-box system.
- Explain why choosing a useful system can simplify a problem.
Key Takeaways
• The chosen boundary determines whether a force is internal or external. • Tension is internal when both connected objects and the string are included. • Whole-system acceleration depends on net external force and total mass. • Internal forces must be included when an individual part is isolated. • A good system choice simplifies complicated motion without changing the physics.
The final lesson connects all three laws, friction, graphs, formulas, and system analysis through structured revision and practice.