School › Forces and motion › Ages 15–16
Newton's laws and F = m·a
Net force, inertia, Newton's three laws and weight. Calculations with F = m·a and W = m·g, and a trolley experiment to test how acceleration depends on force.
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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.[1]
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.[2][4]
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.[3][5]
Weight is the gravitational force on a mass: W = m·g, with g = 9.80 m/s² on Earth and 1.67 m/s² on the Moon. So a 60 kg student weighs about 588 N on Earth but only about 100 N on the Moon.[3]
Newton's third law: for every action there is an equal and opposite reaction. The two forces act on different objects: a rocket pushes on the exhaust gas, and the gas pushes on the rocket; a cannon is pushed backwards as it fires the ball forwards.[4]
Moving through air, an object feels drag, which acts opposite to its motion. It arises from the difference in velocity between the object and the air and depends on the object's shape. Together with friction, drag is why real objects need a driving force just to keep a constant speed.[7][2]
Try it: How does acceleration depend on force?
You need
- Dynamics trolley and runway (or a smooth bench)
- Pulley clamped to the end of the bench
- String
- Slotted masses on a hanger (e.g. 5 × 20 g)
- Light gates and data logger, or a stopwatch and metre rule
- Sand tray or padded box to catch the masses
- Balance
Safety
Put a sand tray or padded box under the hanging masses and keep feet away. Clamp the pulley firmly, and stop the trolley with a buffer at the end of the runway. Don't overload the hanger.
What to do
- 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).
What happens, and why?
By moving masses from the trolley to the hanger, the total accelerated mass stays constant while the force changes, so Newton's second law predicts a = F/m: a straight line through the origin with gradient 1/m. Tilting the runway balances friction, so the hanging weight is (close to) the net force. Measured accelerations are usually slightly below F/m because friction and drag are not fully removed.[3][5][2]
Play: Forces and acceleration
Sort each situation: are the forces balanced or unbalanced? Some cards are calculations: work out a = F/m (ignore friction).
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Other ages: Ages 6–7 · Ages 10–11