⚙️ Strand A: Dynamics

Course: SPH4U — Physics, Grade 12, University Preparation
Focus: Forces, Newton's laws, friction, circular motion, and two-dimensional analysis

1. Newton's Laws of Motion

1st Law (Inertia): An object at rest stays at rest, and an object in motion stays in uniform motion, unless acted upon by a net external force.
2nd Law: ΣF = ma — net force equals mass times acceleration.
3rd Law: For every action, there is an equal and opposite reaction.

2. Key Equations

ΣF = ma   |   F_g = mg   |   f = μN
F_c = mv²/r   |   a_c = v²/r   |   T = 2πr/v

3. Free Body Diagrams

Object on Flat Surface m F_N F_g = mg F_a f Object on Inclined Plane mg F_N θ mg sinθ (along plane) mg cosθ (perpendicular)

4. Circular Motion

Centripetal acceleration always points toward the center of the circular path. The centripetal force is not a separate force — it's the net force directed inward (e.g., tension, gravity, friction, normal force).

📝 Worksheet — Strand A: Dynamics

1. [K/U — 3 marks] A 5.0 kg box is pushed across a horizontal surface with an applied force of 30 N. The coefficient of kinetic friction is 0.25.

a) Draw a free body diagram showing all forces.

b) Calculate the net force on the box.

c) Calculate the acceleration.

2. [K/U — 3 marks] A 2.0 kg object hangs from a string attached to the ceiling of an elevator. Calculate the tension in the string when the elevator:

a) Moves upward with acceleration 3.0 m/s²

b) Moves downward with acceleration 2.0 m/s²

c) Moves at constant velocity

3. [Thinking — 4 marks] A 1500 kg car rounds a banked curve of radius 80 m. The road is banked at 15° and there is no friction.

a) Draw a free body diagram for the car on the banked curve.

b) Determine the speed at which the car can safely round the curve.

4. [Thinking — 4 marks] Two blocks (m₁ = 4.0 kg, m₂ = 6.0 kg) are connected by a string over a frictionless pulley (Atwood machine).

a) Draw free body diagrams for both blocks.

b) Determine the acceleration of the system.

c) Determine the tension in the string.

5. [Communication — 3 marks] Explain why a car rounding a curve on a flat road can only go so fast before sliding outward. Include: the role of friction as the centripetal force, what happens when μmg < mv²/r, and why banking the road helps.

6. [Application — 4 marks] A satellite orbits Earth at an altitude of 350 km (ISS orbit). Earth's radius is 6.37 × 10⁶ m and g at that altitude is approximately 8.8 m/s².

a) What provides the centripetal force?

b) Calculate the orbital speed.

c) Calculate the orbital period.

SPH4U — Physics, Grade 12 | Strand A: Dynamics | Ontario Curriculum 2008