Newton's second law

You already know two things from experience:

• A gentle push gives a small acceleration; a strong push gives a big one.
• The same push moves a light object more easily than a heavy one.

Testing it. A cart is pulled the same distance from rest by a cup hanging over a pulley:

• Double the cup's mass (a bigger pulling force) and the cart takes less time: it accelerates more. (We compare using a₂/a₁ = T₁²/T₂².)
• Double the cart's mass (same force) and it takes longer: it accelerates less.

The results are a little less than exactly double or half, because of friction and small errors in measuring.

Newton's second law: the acceleration is in the direction of the net force; it is proportional to the force (more force, more acceleration) and inversely proportional to the mass (more mass, less acceleration):

a = F/m, or F = ma.

What is 1 newton? The force that gives a 1 kg mass an acceleration of 1 m s⁻². To feel it: hold a 100 g mass on your palm. You are pushing up with about 1 N.

Weight. Near the Earth's surface, F = mg, where g = 9.8 m s⁻² (use 10 for quick estimates). g is the same for every object, heavy or light.

Momentum is mass × velocity: how much "oomph" a moving thing has. A stone resting in your hand doesn't scare anyone; the same stone thrown fast does. The fuller form of the second law says: the rate of change of momentum is proportional to the net force.