This unit, 20–25% of the multiple-choice section, applies forces and Newton's three laws to gravity, friction, springs, drag and circular motion. Physics C adds calculus: you find a center of mass by integration and the velocity under a resistive force by separating variables.
- system
- Whatever objects you decide to treat together. Interactions among its parts set its properties, and it may trade energy or mass with everything around it.
- Example: Three coupled railcars can be one system: to find how fast the whole train speeds up, the couplings between cars don't matter.
- force
- One object's push or pull on another, a vector with size and direction. Every force has a source outside the object; an object can't exert a net force on itself.
- Example: A puck gliding on frictionless ice feels only the ice's upward push and Earth's pull; no separate 'force of motion' keeps it going.
- Newton's third law
- Forces come in pairs: if A exerts a force on B, B exerts one on A of the same size, pointing the opposite way: F_A on B = −F_B on A.
- Example: A rocket's engine pushes exhaust gas backward with 5000 N, so the gas pushes the rocket forward with 5000 N.
- net force
- The vector sum of all the forces exerted on a system. Add the forces along each axis separately, with signs for direction, then combine the components.
- Example: On level ice, ropes pull a sled with 6 N east and 8 N north: the net horizontal force is √(36 + 64) = 10 N.
- Newton's second law
- The net external force on a system, divided by its mass, gives the acceleration of its center of mass: a = ΣF/m. The acceleration points the same way as ΣF.
- Example: A net force of 4500 N forward on a 1500 kg car gives a = 4500/1500 = 3 m/s² forward.
- Newton's law of universal gravitation
- Two masses attract along the line between their centers of mass: F_g = Gm₁m₂/r², G = 6.67 × 10⁻¹¹ N·m²/kg². Twice the distance, one-fourth the force.
- Example: Two asteroids, 500 kg and 600 kg, 2 m apart: F_g = (6.67 × 10⁻¹¹)(3 × 10⁵)/2² ≈ 5.0 × 10⁻⁶ N.
- kinetic friction
- Friction on a surface sliding over another: F_f = μ_k F_N, opposite the sliding. The contact area doesn't affect it; μ_k depends on the two materials.
- Example: A 50 kg sled pulled horizontally on level snow with μ_k = 0.10 feels 0.10 × 500 = 50 N of friction, opposite its sliding.
- Hooke's law
- An ideal (massless) spring pulls or pushes in proportion to how far it is stretched or squeezed from its relaxed length, back toward equilibrium: F_s = −kΔx.
- Example: A spring with k = 400 N/m compressed 0.03 m pushes outward with 400 × 0.03 = 12 N.
- resistive force
- A velocity-dependent force that points opposite the object's velocity, such as air or water drag. A simple model is F_r = −kv, where k is a positive constant.
- Example: A ball moving through syrup at 4 m/s with k = 0.5 kg/s feels 0.5 × 4 = 2 N of drag, backward.
- centripetal acceleration
- The acceleration component toward the center of a circular path, a_c = v²/r. One force, several forces or force components (as on a banked curve) can cause it.
- Example: A car takes a 40 m radius curve at 20 m/s: a_c = 20²/40 = 10 m/s², toward the curve's center.
- center of mass of separate objects
- The point found by weighting each part's position by its mass: x_cm = Σmᵢxᵢ/Σmᵢ. A symmetric system has it on its symmetry lines; it leans toward heavier parts.
- Example: Masses 1 kg at x = 0, 2 kg at 1 m, 1 kg at 4 m: x_cm = (0 + 2 + 4)/4 = 1.5 m.
- contact force
- A force between objects that touch, such as a normal force, friction or tension. It is the large-scale result of electric forces between atoms.
- Example: A climber hanging on a rope feels the rope's tension, a contact force, and gravity, which acts without touching.
