5.2 Forces and Motion
Key Takeaways
- Newton's three laws — inertia, F = ma, and action-reaction — together predict how an object's motion changes whenever forces act on it.
- Universal forces include gravity (always attractive, depends on mass and distance), the electromagnetic force (electric and magnetic interactions), and the strong and weak nuclear forces that operate only inside the nucleus.
- Velocity is a vector (magnitude plus direction) while speed is scalar; acceleration is the rate of change of velocity, so a turning object at constant speed is still accelerating.
- Free-body diagrams isolate one object and draw every force acting on it, making vector addition straightforward and exposing the net force that Newton's second law uses.
- Simple machines (lever, pulley, inclined plane) trade force for distance: the input work equals the output work, so a smaller force over a larger distance produces the same mechanical advantage.
Universal Forces
Four fundamental forces govern every interaction in the universe. For the TExES 4-8 classroom, the focus is on the three named in the competency: gravitational, electrical, and magnetic (the electromagnetic force unifies the latter two), with brief awareness of the strong and weak nuclear forces that act only inside the nucleus.
| Force | Acts between | Nature | Relative strength (at nuclear range) |
|---|---|---|---|
| Gravitational | All masses | Always attractive; infinite range | Weakest (~10^-38) |
| Electromagnetic | Charges and magnets | Attractive or repulsive; infinite range | Strong (~1/137 of strong) |
| Strong nuclear | Quarks and nucleons | Holds nucleus together; ~1 fm range | Strongest (1) |
| Weak nuclear | Many particles | Mediates radioactive decay; ~0.01 fm range | Weaker than EM (~10^-6) |
Gravity is the only force a 4-8 student feels all day. Newton's law of universal gravitation says every mass attracts every other mass with a force F = G(m₁m₂)/r², where G = 6.674 × 10⁻¹¹ N·m²/kg². Because gravity follows an inverse-square law, doubling the distance between two masses drops the force to one-quarter. Near Earth's surface this reduces to F_gravity = mg with g ≈ 9.8 m/s².
Electrical force acts between charges: like charges repel, opposite charges attract. Coulomb's law mirrors Newton's: F = k(q₁q₂)/r², with k ≈ 8.99 × 10⁹ N·m²/C². Magnetic force is the relativistic partner of the electric force — a moving charge or spin creates a magnetic field, and a magnetic field exerts a force only on moving charges, given by F = qvB sinθ.
Scalars and vectors, the kinematic equations, free fall, and motion graphs are developed in the previous section, "Describing Motion: Kinematics and Motion Graphs."
The Vector Nature of Force
Force is a vector, so the net force on an object is the vector sum of all individual forces. A free-body diagram isolates one object and draws each force as an arrow from the object's center, scaled by magnitude. Perpendicular forces are usually resolved into x and y components: F_net,x = ΣF_x and F_net,y = ΣF_y, then F_net = √(F_net,x² + F_net,y²).
Consider a book on a ramp at angle θ. The weight mg points straight down. Resolve it into a component along the ramp (mg sinθ, the downhill pull) and perpendicular to the ramp (mg cosθ, matched by the normal force). When friction is negligible, the book accelerates at a = g sinθ — independent of mass, which is why Galileo's rolling balls and Apollo's hammer-and-feather drop fall together.
Newton's Three Laws of Motion
First Law — Inertia
An object at rest stays at rest, and an object in motion stays in motion at constant velocity, unless acted on by a net external force. Inertia is the resistance to change in motion and is measured by mass. A seat belt works because, without it, a passenger's body obeys the first law and keeps moving forward when the car stops.
Second Law — F = ma
The net force on an object equals its mass times its acceleration: F_net = ma. Force is in newtons (N), where 1 N = 1 kg·m/s². This is the working equation of mechanics.
Third Law — Action–Reaction
For every action force there is an equal and opposite reaction force. The forces act on different objects, so they never cancel for a single object. A rocket pushes gas downward; the gas pushes the rocket upward — the rocket accelerates even in vacuum because the reaction force acts on the rocket itself.
Worked Example: Calculating Force and Acceleration
A 1,200 kg car speeds up from 15 m/s to 25 m/s in 4.0 s. Find the net force.
- Acceleration: a = (v − v₀)/t = (25 − 15)/4.0 = 2.5 m/s².
- Net force: F = ma = 1,200 × 2.5 = 3,000 N.
If the same car later coasts to a stop in 5.0 s from 25 m/s, the deceleration is a = (0 − 25)/5.0 = −5.0 m/s², and the braking force (from friction of the tires and brake pads) is F = 1,200 × (−5.0) = −6,000 N (negative sign means opposite to motion).
Friction
Friction is a contact force that opposes relative sliding between surfaces. Static friction (up to μ_s·N) prevents motion; kinetic friction (μ_k·N) acts once sliding begins. μ_k is typically less than μ_s, which is why it is harder to start a crate sliding than to keep it moving. On a 4-8 demo, a block dragged across sandpaper versus waxed wood gives students a tangible feel for the coefficient of friction.
A 1,500 kg car accelerates from rest to 20 m/s in 5 seconds. What net force does the engine produce?
The six simple machines, mechanical advantage, and efficiency are developed in the next section, "Simple Machines, Work Input, and Mechanical Advantage."
Cross-Disciplinary Connections
- Blood flow: The heart exerts pressure (a force per area) that drives blood through vessels. Bernoulli's principle (faster fluid, lower pressure) explains partial plaque collapse and the lift on airplane wings; Newton's second law underlies why a narrowed, plaque-coated artery demands greater pressure to deliver the same flow.
- Geologic processes: Gravity drives mass wasting (landslides, creep, slumps). The downhill component mg sinθ sets the threshold at which a slope fails — adding water reduces friction and lowers the safe angle, an idea students can model with a sandpile.
- Tectonics: Convection in the mantle exerts shear forces on plates; Newton's third law means a plate dragging on its neighbor feels an equal and opposite stress.
For the TExES 4-8 classroom, the goal is not to derive Bernoulli but to show that the same F = ma and force-vector reasoning students use on a textbook problem also predicts how blood moves in a vein and how a hillside slides after a rain.