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Forces and their direction  IB DP Physics Study Notes

Forces and their direction  IB DP Physics Study Notes - 2025 Syllabus

Forces and their direction  IB DP Physics Study Notes

Forces and their direction  IB DP Physics Study Notes at  IITian Academy  focus on  specific topic and type of questions asked in actual exam. Study Notes focus on IB Physics syllabus with Students should understand

  • Newton’s three laws of motion
  • forces as interactions between bodies
  • that forces acting on a body can be represented in a free-body diagram
  • that free-body diagrams can be analysed to find the resultant force on a system

Standard level and higher level: 10 hours
Additional higher level: There is no additional higher level content

IB DP Physics 2025 -Study Notes -All Topics

IBDP Physics 2025 -Study Notes -All Topics

Newton’s First Law of Motion (Law of Inertia)

Statement: An object remains at rest or continues to move at a constant velocity in a straight line unless acted upon by a net external force.

  • This means that motion doesn’t need a continuous force — only a force imbalance causes a change in motion.
  • Objects resist changes in their state of motion. This resistance is called inertia.
  • The greater the mass of an object, the greater its inertia.

 

Implications:

  • If no net force is applied, an object won’t accelerate (no speeding up, slowing down, or changing direction).
  • This explains why spacecraft continue moving at constant speed in deep space after engines are turned off.

Example:

A book sliding across a table eventually stops due to friction. Without friction, the book would continue sliding forever at constant speed.

▶️ Answer/Explanation

According to Newton’s First Law, the book only slows because friction (a net external force) is acting on it. If friction were zero (e.g., on an air table), it would maintain its velocity indefinitely.

Newton’s Second Law of Motion

Statement:The net external force acting on an object is equal to the rate of change of its momentum with respect to time.

Mathematical Form:

\( F = \dfrac{dp}{dt} \)

  • \( F \): Net force (in newtons, N)
  • \( p \): Momentum \( (p = mv) \)
  • \( \dfrac{dp}{dt} \): Time rate of change of momentum

When Mass is Constant:

If mass \( m \) is constant, then:

\( F = \dfrac{d}{dt}(mv) = m \dfrac{dv}{dt} = ma \)

This gives the commonly used form of Newton’s Second Law:

\( F = ma \)

Key Points:

  • If you apply a greater force on the same object, it accelerates more.
  • If the object is more massive, the same force causes less acceleration.
  • The direction of the acceleration is the same as the direction of the net force.

Example:

You push a 10 kg cart with a force of 20 N. Find the acceleration.

▶️ Answer/Explanation

Using Newton’s Second Law: \( F = ma \Rightarrow a = \frac{F}{m} = \frac{20}{10} = 2 \, \text{m/s}^2 \).

The cart will accelerate at \( 2 \, \text{m/s}^2 \) in the direction of the applied force.

 Newton’s Third Law of Motion

Statement: For every action, there is an equal and opposite reaction.

  • Forces always occur in pairs.
  • If object A exerts a force on object B, then object B simultaneously exerts a force of equal magnitude and opposite direction on object A.
  • These forces act on different bodies, so they do not cancel each other out.

Important: Third-law forces are always equal in magnitude, opposite in direction, and of the same type (gravitational, normal, tension, etc.).

Example:

When you jump, your feet push downward on the ground. The ground pushes you upward with an equal force, allowing you to rise.

▶️ Answer/Explanation

Action: Your legs exert a force downward on the ground.

Reaction: The ground exerts an equal upward force on you, propelling you into the air.

 Forces as Interactions Between Bodies

Forces do not exist in isolation – they are always the result of an interaction between two physical objects. Understanding this is key to mastering Newtonian mechanics.

Definition of a Force: A force is a push or pull resulting from an interaction between two bodies. It is a vector quantity — meaning it has both magnitude and direction.

Forces are mutual: Every force involves two objects. If object A exerts a force on object B, object B simultaneously exerts a force of equal magnitude and opposite direction on object A. This is Newton’s Third Law in action.

Source and receiver: Every force interaction includes:

    • Source: The object causing the force.
    • Receiver: The object experiencing the force.

Two main categories of forces based on interaction type:

    • Contact forces: These arise when two objects are physically touching. Examples:
      • Normal force – upward force from a surface.
      • Friction – resists motion between surfaces.
      • Tension – force transmitted through a string or rope.
    • Non-contact (action-at-a-distance) forces: These occur without physical contact. Examples:
      • Gravitational force – between masses.
      • Electrostatic force – between charged particles.
      • Magnetic force – between magnetic poles or moving charges.

Force pairs never cancel: Even though two forces in an interaction pair are equal and opposite, they do not cancel each other because they act on different objects. For cancellation to occur, the forces must act on the same object.

Forces can be external or internal to a system:

    • External forces affect the motion of a system (e.g., a person pushing a box).
    • Internal forces exist within the system and don’t affect its overall motion (e.g., tension within a rope).

Important consequence: When analyzing motion, we only consider the forces acting on the object of interest — even though those forces are due to interactions with other bodies.

Example:

A book of mass 2.0 kg rests on a horizontal table. Identify all the interaction pairs of forces involved and explain how Newton’s Third Law applies.

▶️ Answer/Explanation

We will analyze the force interactions between the book and other objects (Earth and table):

  • Gravitational Interaction:
    • Force on book by Earth: The Earth pulls the book downward with gravitational force \( F_g = mg = 2.0 \times 9.8 = 19.6 \, \text{N} \).
    • Reaction force: The book pulls the Earth upward with an equal and opposite force of 19.6 N.
  • Normal Interaction:
    • Force on book by table: The table pushes up on the book with a normal force of 19.6 N (assuming equilibrium).
    • Reaction force: The book pushes down on the table with a force of 19.6 N.

In both cases, the interaction forces occur in pairs — one on each object — equal in magnitude and opposite in direction. This is Newton’s Third Law.

Important: These force pairs never cancel each other because they act on different bodies.

 Forces Acting on a Body Can Be Represented in a Free-Body Diagram

A free-body diagram (FBD) is a visual representation used in physics to show all the external forces acting on a single object. The object is usually represented by a simple box or dot, and forces are shown as arrows pointing in the direction in which they act.

  • Each arrow represents a force acting on the object.
  • Arrow direction indicates the direction of the force.
  • Arrow length represents the magnitude of the force (qualitatively).
  • Forces are labeled (e.g., \( F_g \), \( F_N \), \( F_f \), \( F_{applied} \)).
  • Only forces acting ON the object are shown, not forces the object exerts on others.

Example: 

A 5.0 kg block is resting on a horizontal surface. A person applies a horizontal force of 10 N to the right, and there is a frictional force of 4 N opposing the motion. Label the free-body diagram.

▶️ Answer/Explanation

Forces acting on the block:

  • Weight: \( F_g = mg = 5.0 \times 9.8 = 49 \, \text{N} \) downward
  • Normal force: \( F_N = 49 \, \text{N} \) upward (balances weight, assuming no vertical motion)
  • Applied force: \( F_{applied} = 10 \, \text{N} \) to the right
  • Frictional force: \( F_f = 4 \, \text{N} \) to the left

The free-body diagram should have:

  • An arrow pointing down labeled \( F_g = 49 \, \text{N} \)
  • An arrow pointing up labeled \( F_N = 49 \, \text{N} \)
  • An arrow pointing right labeled \( F_{applied} = 10 \, \text{N} \)
  • An arrow pointing left labeled \( F_f = 4 \, \text{N} \)

This diagram helps us understand and calculate the net (resultant) force acting on the block.

Free-Body Diagrams to Find Resultant Force on a System

Free-body diagrams (FBDs) are essential tools in physics to understand how different forces act on a single object. Once all forces are correctly represented, you can analyze the diagram to find the resultant force, which determines the object’s acceleration according to Newton’s Second Law: \( F_{\text{net}} = ma \).

  • Step 1: Draw the Free-Body Diagram (FBD)
    • Sketch the object as a dot or a box.
    • Represent every external force acting on the object with a labeled arrow pointing in the direction of the force.
    • Typical forces include: gravitational force (\( mg \)), normal force (\( N \)), tension, applied force (\( F_{\text{app}} \)), and friction.
  • Step 2: Choose a Coordinate System
    • Usually, the x-axis is horizontal, and the y-axis is vertical.
    • On inclined planes, it helps to tilt the axes along and perpendicular to the surface.
  • Step 3: Resolve Forces Into Components (if necessary)
    • Break angled forces into horizontal (\( x \)) and vertical (\( y \)) components using trigonometry.
    • \( F_x = F \cos \theta \), \( F_y = F \sin \theta \)
  • Step 4: Apply Newton’s Second Law in Each Direction
    • Sum all horizontal forces: \( \Sigma F_x = ma_x \)
    • Sum all vertical forces: \( \Sigma F_y = ma_y \)
    • Set accelerations to zero if the object is at rest or moving with constant velocity.
  • Step 5: Find the Resultant Force
      • If the object moves in 1D, the net force is the algebraic sum of forces in that direction.
      • If the object is in 2D, calculate the net force using the Pythagorean theorem:

    \( F_{\text{net}} = \sqrt{(\Sigma F_x)^2 + (\Sigma F_y)^2} \)

  • Step 6: Calculate Acceleration (if needed)
    • Use Newton’s Second Law: \( a = \frac{F_{\text{net}}}{m} \)

Example:

A box of mass 5 kg is pulled along a rough floor with a force of 40 N at an angle of 30° above the horizontal. The frictional force is 12 N. Find the net force and acceleration.

▶️ Answer/Explanation

Step 1: Break the applied force into components:

\( F_x = 40 \cos(30^\circ) \approx 34.6 \, \text{N} \)

\( F_y = 40 \sin(30^\circ) = 20 \, \text{N} \)

Step 2: Calculate the normal force:

\( F_N = mg – F_y = 49 – 20 = 29 \, \text{N} \)

Step 3: Net horizontal force:

\( F_{\text{net}} = F_x – F_{\text{friction}} = 34.6 – 12 = \boxed{22.6 \, \text{N}} \)

Step 4: Acceleration:

\( a = \frac{F_{\text{net}}}{m} = \frac{22.6}{5} = \boxed{4.52 \, \text{m/s}^2} \)

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