echoesof.science · Ages 15–16
Newton's laws and F = m·a
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Forces are vectors: they have a magnitude and a direction. The net external force on an object is the vector sum of all the external forces on it, and we draw them on a free-body diagram, with the object as a single point.
Newton's first law: a body at rest stays at rest, and a body in motion keeps moving at constant velocity, unless a net external force acts on it. This tendency is inertia, and it is proportional to the mass of the object.
Newton's second law: Fnet = m·a. The newton is defined from it: 1 N is the force that gives a 1 kg mass an acceleration of 1 m/s², so 1 N = 1 kg·m/s². For the same force, the acceleration is inversely proportional to the mass. Example: a net force of 51 N on a 240 kg lawn mower gives a = 51/240 ≈ 0.21 m/s².
Experiment: How does acceleration depend on force?
- Measure the mass of the trolley. Put all the slotted masses on the trolley at the start.
- Tie the trolley to the hanger with string over the pulley. Tilt the runway slightly until the trolley, given a small push, rolls at a steady speed (this compensates for friction).
- Move one 20 g mass from the trolley to the hanger. The accelerating force is now about (0.020 kg × 9.8 m/s²) ≈ 0.2 N, while the total mass stays the same.
- Release the trolley from rest. Measure the acceleration with light gates, or time it over a measured distance s and use a = 2s/t².
- Repeat three times, then move the next mass to the hanger. Collect results for 1 to 5 masses on the hanger.
- Plot a against F. Draw a line of best fit and find its gradient; compare it with 1/(total mass).
| Force F (N) | Time t or a, try 1 | Try 2 | Try 3 | Mean a (m/s²) |
|---|---|---|---|---|
| 0.20 | ||||
| 0.39 | ||||
| 0.59 | ||||
| 0.78 | ||||
| 0.98 |
Questions
Draw a free-body diagram for a book resting on a table. Label both forces and explain why the book does not accelerate.
🍎A 1200 kg car accelerates from rest to 15 m/s in 10 s. Calculate its acceleration and the net force needed.
Your experiment: what was the gradient of your a–F graph? What mass does it give, and how does it compare with the measured total mass? Suggest one reason for the difference.
A swimmer pushes backwards on the water. Use Newton's third law to explain how she moves forwards.
Sources for every fact on this sheet: echoesof.science/school/forces-and-motion/sources/