Eleventh Grade · Science · week 10

Newton's Second Law: F = ma

Apply Newton's second law to relate net force, mass, and acceleration, and distinguish mass from weight.

Newton's first law describes what happens with zero net force; his second law describes what happens with a nonzero net force -- and gives it a precise, powerful equation: F_net = m*a, or acceleration equals net force divided by mass (a = F_net / m). A bigger net force produces a bigger acceleration; a bigger mass, pushed by the same force, produces a smaller acceleration. The unit of force, the newton (N), is actually defined from this equation: 1 N is the force needed to accelerate a 1 kg mass at 1 m/s^2 (1 N = 1 kg*m/s^2).

This is also the week to nail down mass versus weight, a mix-up that follows people for life. Mass is the amount of matter in an object, measured in kilograms, and it does not change no matter where the object is. Weight is the FORCE of gravity on that mass, measured in newtons, found from W = m*g -- and it very much depends on location, since g is different on the Moon or Mars. A 70 kg astronaut has the same 70 kg mass everywhere in the universe, but weighs about 686 N on Earth and only about a sixth of that on the Moon.

📋 For the teacher
Teach it (10–15 min):
  • This week's lab: attach a rubber band to a small wagon or box and pull it so the rubber band always stretches to the same length (a rough way to hold the applied force constant), timing how quickly it picks up speed with a light load versus a much heavier load. More mass, same force, slower pickup -- F=ma made visible.
  • Drill the newton's definition explicitly: "1 newton is exactly the push it takes to accelerate 1 kilogram by 1 meter per second, per second" -- connecting the abstract unit to the equation that defines it.
  • Use a bathroom scale as a segue into weight: it actually measures the force your body exerts on it (your weight), not your mass directly, which is why a scale reads differently in a fast-accelerating elevator (a preview of a coming lesson).
  • When two forces act on the same object, always have them draw a quick sketch with arrows before combining anything -- opposing arrows subtract, same-direction arrows add, and skipping the sketch is where sign errors creep in.
Talk about it:
  • What does Newton's second law say happens when you double the net force on an object? When you double the mass instead?
  • How is the newton, as a unit, actually defined?
  • Why does an astronaut's mass stay the same on the Moon while their weight changes?

Mastery looks like: They compute net force, mass, or acceleration using F=ma given the other two quantities, and correctly distinguish mass (kg, constant) from weight (N, location-dependent).

Common stumbles: Using weight (in newtons) where mass (in kilograms) belongs in F=ma, or vice versa; forgetting to combine multiple forces into a single net force before applying the equation.

Homework for this lessonType it, write it with a stylus, or print it for pencil & paper.open →
Records attendance + 15 min of Science for this learner.
← Back to todayAll coursesYear planner