9  Forces and Interactions

9.1 Syllabus inquiry question

  • How do interactions between objects produce changes in motion?
Feynman Insight

From The Feynman Lectures on Physics, Vol I, Chapter 9:

A force is not a property of a single object. It is a description of an interaction between two objects, and it always has a direction.

9.2 Learning Objectives

  • Identify contact and field forces.
  • Draw and interpret free-body diagrams.
  • Calculate weight and normal force in simple cases.
  • Determine net force and equilibrium conditions.

9.3 Content

9.3.1 Types of forces

Forces arise from interactions between objects. We classify them into two categories:

Contact forces require physical touching:

  • Normal force (N): Perpendicular push from a surface
  • Friction (f): Parallel to surface, opposes relative motion
  • Tension (T): Pull through a rope, string, or cable
  • Applied force (F): Push or pull from an external agent

Field forces act at a distance:

  • Gravitational force (Weight, W): Attraction toward Earth’s centre
  • Electric force: Between charged objects
  • Magnetic force: Between magnets or moving charges

The SI unit of force is the newton (N), where 1 N = 1 kg·m/s².

9.3.2 Interactive: Force Categories

Explore different types of forces acting on objects:

Interpreting the diagram:

  • Red vector (W): Weight pulling downward
  • Blue vector (N): Normal force pushing upward from surface
  • Green vector (F): Applied force pushing right
  • Purple vector (f): Friction opposing the motion

9.3.3 Weight and normal force

Weight is the gravitational force on a mass:

\[W = mg\]

where \(g = 9.8\) m/s² near Earth’s surface.

Normal force is the surface’s response to being compressed. On a horizontal surface at rest, the normal force balances weight:

\[N = W = mg\]

Key Distinction
  • Mass (m) is the amount of matter, measured in kilograms (kg)
  • Weight (W) is a force, measured in newtons (N)

An astronaut’s mass is the same on Earth and the Moon, but their weight differs because \(g\) differs.

9.3.4 Free-body diagrams

A free-body diagram (FBD) shows only the forces acting on a single object. Rules for drawing:

  1. Represent the object as a dot or simple shape
  2. Draw all forces as arrows starting from the object
  3. Label each force with its name and magnitude
  4. Include only forces acting on the object, not forces it exerts

9.3.5 Interactive: Building a Free-Body Diagram

Consider a box being pushed across a floor. The free-body diagram shows all forces on the box:

The net force is the vector sum of all forces. In this example:

  • Vertical: \(N - W = 0\) (equilibrium vertically)
  • Horizontal: \(F - f = 25 - 10 = 15\) N to the right

9.3.6 Equilibrium

When the net force is zero, the object is in equilibrium:

\[\vec{F}_{net} = \sum \vec{F} = 0\]

An object in equilibrium is either:

  • Static equilibrium: At rest
  • Dynamic equilibrium: Moving with constant velocity
Newton’s First Law Preview

An object in equilibrium will remain at rest or continue moving at constant velocity. This is Newton’s First Law, covered in the next section.

9.3.7 Interactive: Equilibrium vs Acceleration

Compare the net force when forces are balanced versus unbalanced:

9.4 Worked Examples

9.4.1 Example 1: Weight and normal force

A 6.0 kg box rests on a horizontal floor. Find the weight and normal force.

Solution:

  1. Weight: \(W = mg = 6.0 \times 9.8 = 58.8\) N downward

  2. At rest on a level surface, the net vertical force is zero

  3. Therefore: \(N = W = 58.8\) N upward

9.4.2 Example 2: Net force in one dimension

Two horizontal forces act on a trolley: 14 N east and 9 N west.

Solution:

  1. Choose east as positive

  2. Net force: \(F_{net} = 14 - 9 = 5\) N east

  3. The trolley accelerates east (in the direction of net force)

9.4.3 Example 3: Tension in a hanging mass

A 2.5 kg mass hangs at rest from a light rope. Find the tension.

Solution:

  1. Net force is zero (equilibrium)

  2. Forces: Weight down, Tension up

  3. \(T = W = mg = 2.5 \times 9.8 = 24.5\) N upward

9.5 Common Misconceptions

Common Misconceptions

  • Misconception: Weight and mass are the same. Correction: Mass is measured in kg, weight in N. Weight depends on location; mass does not.

  • Misconception: The normal force always equals weight. Correction: This is only true on horizontal surfaces with no other vertical forces. On slopes or with additional forces, \(N \neq W\).

  • Misconception: Opposing forces always cancel. Correction: Forces only cancel if they act on the same object with equal magnitudes and opposite directions.

  • Misconception: A free-body diagram should show all forces in the problem. Correction: Show only forces acting on the chosen object, not forces it exerts on others.

9.6 Practice Questions

9.6.1 Easy (2 marks)

A 4.0 kg object rests on a table. Calculate its weight.

  • Use \(W = mg\) (1)
  • Correct value: \(W = 4.0 \times 9.8 = 39.2\) N with units (1)

Answer: 39.2 N (or 39 N)

9.6.2 Medium (4 marks)

A box is pulled with 30 N east while friction acts 12 N west. Determine the net force and describe the motion.

  • Correct net force calculation: \(F_{net} = 30 - 12 = 18\) N (2)
  • Direction of net force: east (1)
  • Statement that box accelerates east (1)

Answer: Net force is 18 N east. The box accelerates to the east.

9.6.3 Hard (5 marks)

A 10 kg crate is pulled upward by a cable with 140 N tension. Determine the net force and state whether the crate accelerates or is in equilibrium.

  • Weight calculation: \(W = 10 \times 9.8 = 98\) N (1)
  • Net force calculation: \(F_{net} = 140 - 98 = 42\) N upward (2)
  • Correct statement: crate accelerates upward (1)
  • Optional: Calculate acceleration \(a = 42/10 = 4.2\) m/s² (1)

Answer: - Weight = 98 N down - Net force = 140 - 98 = 42 N upward - The crate accelerates upward at 4.2 m/s²

9.7 Multiple Choice Questions

Test your understanding with these interactive questions:

9.8 Summary

Key Takeaways
  • Forces describe interactions between objects and always have direction
  • Contact forces (normal, friction, tension) require physical contact
  • Field forces (gravity, electric, magnetic) act at a distance
  • Weight is \(W = mg\) where \(g = 9.8\) m/s²
  • Free-body diagrams show all forces acting on one object only
  • Equilibrium means \(\vec{F}_{net} = 0\) (at rest or constant velocity)

9.9 Self-Assessment

Check your understanding:

After studying this section, you should be able to: