Forces and Acceleration
High-Yield Summary
- A force is any push/pull that can change an object's motion; measured in Newtons (1 N = 1 kg·m/s²).
- Forces are contact (friction, tension, normal force) or non-contact (gravity, magnetic, electrostatic).
- Gravity: F = G(m₁m₂)/r²; weight is gravity acting on mass, W = mg.
- Static friction (0 ≤ fs ≤ μsN) resists the start of motion; kinetic friction (fk = μkN) resists motion already in progress and is usually smaller than max static friction.
- Mass is constant and scalar; weight varies with gravitational field strength and is a vector.
- Center of mass: x_cm = (Σmᵢxᵢ)/(Σmᵢ) — the single point where an object's mass can be treated as concentrated.
Contact vs. Non-Contact Forces
| Contact (direct touching) | Non-Contact (act at a distance) |
|---|---|
| Friction | Gravitational force |
| Tension | Magnetic force |
| Normal force | Electrostatic force |
Gravity and Weight
F = G(m₁m₂) / r² | W = mg
- G = Gravitational constant, ≈ 6.674 × 10⁻¹¹ N·m²/kg²
- m₁, m₂ = Masses of the two objects
- r = Distance between the objects' centers
- g = Acceleration due to gravity, ≈ 9.8 m/s² near Earth's surface
Static vs. Kinetic Friction
| Static Friction (fs) | Kinetic Friction (fk) |
|---|---|
| 0 ≤ fs ≤ μsN | fk = μkN |
| Prevents motion from starting | Opposes motion already happening |
| Maximum value is usually higher | Usually lower than max static friction |
Three General Principles of Friction
- Proportional to normal force — friction increases as normal force increases.
- Independent of contact area — surface area doesn't change friction, given the same normal force and materials.
- Independent of relative velocity (kinetic friction) — stays roughly constant regardless of speed once moving.
Common MCAT Trap
- Mass and weight are often used interchangeably in everyday speech but are not equal on the MCAT — mass is constant everywhere, weight (Fg = mg) changes with local gravitational field strength.
- Kinetic friction is usually less than the maximum static friction — that's why it takes more force to start an object moving than to keep it moving.
Quick Recall
What's the difference between mass and weight?
Why does it take more force to start an object moving than to keep it moving?