Newton's First and Second Laws: F = m a and the Required Practical

Don't read anything yet. Watch each object: is it Newton's first law or the second? Is the speed changing, the direction, or neither? Where there's a resultant force, work out the acceleration. Then switch to the second tab and run the required practical.

Newton's First Law

So a car on a straight, level road at a steady speed has driving force = resistive forces. A skydiver at terminal velocity has air resistance = weight. Balanced doesn't mean stopped: it means the velocity doesn't change.

Velocity changes in two ways

Velocity is speed in a given direction, so it changes if the speed changes, if the direction changes, or both. Any change in velocity needs a resultant force: that's Newton's second law.

The tendency of an object to stay at rest or keep moving at a steady velocity is called its inertia.

Newton's Second Law

A resultant force makes an object accelerate. How much it accelerates depends on how big the force is and how much mass is being pushed.

It is the resultant force that goes in the equation — the single force left over once you have combined everything acting on the object. If the resultant force is zero, the acceleration is zero, and the object stays still or carries on at constant velocity.

The two things the equation is telling you

Read a = F ÷ m twice, holding one thing constant each time:

The required practical tests the first row: keep the mass fixed, change the force, and see whether the acceleration really is proportional to it.

The required practical — the one thing everyone gets wrong

A trolley on a bench is pulled by a string that runs over a pulley, with masses hanging on the end. Here is the trap:

• The force pulling the system along is the weight of the hanging masses only (F = m_hanging × g). A mass sitting on the trolley is held up by the trolley, so it pulls on nothing.
• The mass in F = m a is everything that is accelerating — the trolley, the string, and every mass, whether it is on the trolley or on the hanger.

Getting the acceleration out of the light gate

The trolley is released from rest at the same point every time, so u = 0. The light gate gives the speed v as the card cuts the beam, and the timer gives t, the time from release to the gate.

The graph, and where the mass is hiding

Plot acceleration (y) against force (x) and draw a straight line of best fit through the origin. Because a = (1/m) × F, that line has:

The line goes through the origin because no force means no acceleration. If your line misses the origin, something systematic is wrong — usually friction.

Friction, and how to compensate for it

Friction between the wheels and the bench opposes the motion, so the real resultant force is smaller than the weight you hung on the string. The measured acceleration comes out too low and the line does not pass through the origin.

The fix is to compensate for friction: tilt the runway by raising the far end slightly, until the trolley rolls at a constant speed when given a gentle push with nothing hanging on the string. At that tilt, a component of the trolley's weight exactly cancels friction, so the only resultant force left is the one you add on the string.

Inertial mass

Rearranged the other way, m = F ÷ a defines the inertial mass of an object.

Calculation questions want the same four lines every time. Write them out even when you can do it in your head — the marks are for the working, not the number.

Both laws, F = m a and the practical explained out loud — useful for a last-minute recap, or if you'd rather hear it than read it.

Both laws, F = m a and the practical explained out loud — useful for a last-minute recap, or if you'd rather hear it than read it. The video is on its way.