4.4 Newton's laws of motion

For a body of mass m, ΣF=ma. The acceleration points in the direction of the resultant, not necessarily in the direction of the largest individual force.

Draw a free-body diagram, resolve along convenient axes and include friction, tension, weight and reactions only when they act on the chosen body.

A 5 kg block with 20 N right and 8 N left has resultant 12 N right and acceleration 2.4 m s⁻² right.

Action–reaction pairs belong to different bodies and cannot be cancelled inside one body’s force equation.

Mass m is measured in kilograms and remains the same in a given object; weight W=mg is a force in newtons and depends on local gravitational field strength g.

Use mass in F=ma and weight as a force in vertical equations. A scale reading is a contact force and may differ from mg during acceleration.

A 3 kg object weighs about 29.4 N where g=9.8 m s⁻²; its mass is still 3 kg on the Moon.

Mass and weight are not interchangeable, and “weighing zero” in free fall does not mean mass disappears.

For constant acceleration, v=u+at, s=ut+½at², v²=u²+2as and s=½(u+v)t. Choose equations containing the known quantities.

State the positive direction and use signed displacement, velocity and acceleration consistently. If acceleration changes, split the motion or use a different method.

From rest with a=3 m s⁻² for 4 s, v=12 m s⁻¹ and s=24 m.

These equations are not valid for variable acceleration, and distance is not always equal to displacement.

For linked particles, an inextensible string over a smooth pulley gives equal magnitude accelerations and tension throughout the string. Newton’s second law is written separately for each mass.

Draw one diagram per particle, choose a common positive direction and use the string constraint only after writing the force equations.

A hanging mass and a block on a smooth table have the same acceleration; their combined equations can eliminate the internal tension.

Equal tension does not mean equal net force or equal mass; the particles can accelerate together with different forces.