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IB DP Physics Newton’s laws of motion Study Notes - 2025 Syllabus

IB DP Physics Newton’s laws of motion Study Notes

IB DP Physics Newton’s laws of motion 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 guiding questions of

  • the nature and use of the following contact forces

    ◦ normal force FN is the component of the contact force acting perpendicular to the surface that counteracts the body
    ◦ surface frictional force Ff acting in a direction parallel to the plane of contact between a body and a surface, on a stationary body as given by Ff ≤ μsFN or a body in motion as given by Ff = μdFN where μs and μd are the coefficients of static and dynamic friction respectively
    ◦ tension
    ◦ elastic restoring force FH following Hooke’s law as given by FH = –kx where k is the spring constant
    ◦ viscous drag force Fd acting on a small sphere opposing its motion through a fluid as given by Fd = 6πηrv where η is the fluid viscosity, r is the radius of the sphere and v is the velocity of the sphere through the fluid
    ◦ buoyancy Fb acting on a body due to the displacement of the fluid as given by Fb = ρVg where V is the volume of fluid displaced

     

  • the nature and use of the following field forces

    ◦ gravitational force Fg is the weight of the body and calculated is given by Fg = mg
    ◦ electric force Fe
    ◦ magnetic force Fm

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

Contact Forces

1. Normal Force \( F_N \)

  • This is the force exerted by a surface perpendicular (normal) to the surface, supporting an object resting on it.
  • It prevents solid objects from passing through each other.
  • If a body is on a horizontal surface with no vertical acceleration, then \( F_N = mg \).
  • If other vertical forces act (like tension or extra load), normal force adjusts accordingly: \( F_N = mg – F_{\text{up}} \) or \( F_N = mg + F_{\text{extra}} \).

\( F_N = \text{component of contact force perpendicular to the surface} \)

2. Frictional Force \( F_f \)

  • Friction acts parallel to the surface and opposes motion or attempted motion.
  • Static friction: prevents motion, adjusts up to a limit: \( F_f \leq \mu_s F_N \)
  • Kinetic (dynamic) friction: acts when body is sliding: \( F_f = \mu_d F_N \)
  • \( \mu_s \) (static coefficient) is typically larger than \( \mu_d \).

 \( \text{If body is stationary: } F_f \leq \mu_s F_N \)

\( \text{If body is sliding: } F_f = \mu_d F_N \)

A graph between the applied force and types of friction is shown in the figure above.

Here,

  • OD represents that the body is at rest.
  • OA represents static friction.
  • AD represents the maximum static friction called limiting friction.
  • The region beyond D represents that the body is in motion.
  • CB represents kinetic friction.

3. Tension Force \( T \)

  • Tension occurs in strings, cables, or ropes pulling on an object.
  • It is always directed along the string, away from the object.
  • Assumed to be uniform in a massless, inextensible string.
  • Tension balances forces in systems like elevators, pulleys, hanging masses.

\( T = \text{Force transmitted through a taut string} \)

4. Elastic Restoring Force \( F_H \)

  • Applies when an object like a spring is stretched or compressed from equilibrium.
  • According to Hooke’s Law: \( F_H = -kx \), where:
    • \( k \) = spring constant (stiffness)
    • \( x \) = displacement from equilibrium
  • Negative sign indicates force is always opposite to displacement.

\( F_H = -kx \)

5. Viscous Drag Force \( F_d \)

  • Applies when a small spherical object moves through a viscous fluid (slow speed regime).
  • Given by Stokes’ Law: \( F_d = 6 \pi \eta r v \), where:
    • \( \eta \) = viscosity of fluid
    • \( r \) = radius of sphere
    • \( v \) = velocity through the fluid
  • Opposes motion and increases with speed.

\( F_d = 6 \pi \eta r v \)

6. Buoyant Force \( F_b \)

  • Upward force experienced by an object submerged in fluid due to displaced fluid.
  • Based on Archimedes’ principle: \( F_b = \rho V g \)
  • Where:
    • \( \rho \) = density of fluid
    • \( V \) = volume of fluid displaced
    • \( g \) = gravitational field strength

\( F_b = \rho V g \)

Example

A 5 kg block is placed on a frictionless incline that makes a 30° angle with the horizontal. Calculate the normal force acting on the block.

▶️ Answer/Explanation

∙ Weight of the block: \( F_g = mg = 5 \times 9.8 = 49 \, \text{N} \)

∙ On an incline, the normal force is the component of weight perpendicular to the surface: \( F_N = F_g \cos\theta \)

\( F_N = 49 \cos(30^\circ) = 49 \times 0.866 = \boxed{42.4 \, \text{N}} \)

Example 

A 10 kg crate slides across a floor with coefficient of kinetic friction \( \mu_d = 0.3 \). Find the frictional force acting on it.

▶️ Answer/Explanation

∙ Normal force \( F_N = mg = 10 \times 9.8 = 98 \, \text{N} \)

∙ Kinetic friction formula: \( F_f = \mu_d F_N = 0.3 \times 98 = \boxed{29.4 \, \text{N}} \)

Example

A 3 kg object hangs at rest from a rope. Find the tension in the rope.

▶️ Answer/Explanation

∙ At rest, tension balances weight: \( T = F_g = mg = 3 \times 9.8 = \boxed{29.4 \, \text{N}} \)

Example

A spring with spring constant \( k = 150 \, \text{N/m} \) is stretched by 0.2 m. Calculate the restoring force.

▶️ Answer/Explanation

∙ Hooke’s Law: \( F_H = -kx = -150 \times 0.2 = \boxed{-30 \, \text{N}} \)

∙ Negative sign indicates force is directed opposite to the displacement.

Example

A cube of volume \( 0.01 \, \text{m}^3 \) is fully submerged in water (\( \rho = 1000 \, \text{kg/m}^3 \)). Find the buoyant force.

▶️ Answer/Explanation

∙ Archimedes’ principle: \( F_b = \rho V g = 1000 \times 0.01 \times 9.8 = \boxed{98 \, \text{N}} \)

Field Forces

1. Gravitational Force \( F_g \)

  • Acts between any two masses. On Earth, it’s simply the weight of the object.
  • Always directed toward the center of mass (e.g., Earth’s center).
  • Given by \( F_g = mg \)

\( F_g = mg \)

\( g = \) The standard value for the acceleration due to gravity on Earth’s surface is approximately 9.8 m/s² (meters per second squared).

2. Electric Force \( F_e \)

  • Acts between electric charges.
  • Attractive for opposite charges, repulsive for like charges.
  • Given by Coulomb’s Law: \( F_e = \frac{k q_1 q_2}{r^2} \) where \( k \) is Coulomb’s constant.

\( F_e = \frac{k q_1 q_2}{r^2} \)

3. Magnetic Force \( F_m \)

  • Acts on moving charges in a magnetic field.
  • Direction given by right-hand rule.
  • Magnitude: \( F_m = qvB \sin \theta \), where:
    • \( q \) = charge
    • \( v \) = velocity of charge
    • \( B \) = magnetic field strength
    • \( \theta \) = angle between velocity and magnetic field

\( F_m = qvB \sin \theta \)

Example

What is the gravitational force acting on a 7 kg object on Earth?

▶️ Answer/Explanation

∙ Weight = \( F_g = mg = 7 \times 9.8 = \boxed{68.6 \, \text{N}} \)

Example

Two charges \( q_1 = 2 \times 10^{-6} \, \text{C} \) and \( q_2 = -3 \times 10^{-6} \, \text{C} \) are 0.1 m apart in air. Find the magnitude of the electric force between them. (Take \( k = 9 \times 10^9 \, \text{Nm}^2/\text{C}^2 \))

▶️ Answer/Explanation

\( F_e = \frac{k |q_1 q_2|}{r^2} = \frac{9 \times 10^9 \times (2 \times 10^{-6})(3 \times 10^{-6})}{(0.1)^2} \)

\( F_e = \frac{54 \times 10^{-3}}{0.01} = \boxed{5.4 \, \text{N}} \)

Example

A proton with charge \( q = 1.6 \times 10^{-19} \, \text{C} \) moves at \( 3 \times 10^6 \, \text{m/s} \) perpendicular to a magnetic field of \( 0.2 \, \text{T} \). Find the magnetic force.

▶️ Answer/Explanation

∙ Magnetic force: \( F_m = qvB = 1.6 \times 10^{-19} \times 3 \times 10^6 \times 0.2 \)

\( F_m = \boxed{9.6 \times 10^{-14} \, \text{N}} \)

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