The three laws
Newton's first law: an object keeps its state of motion, at rest or at constant velocity, unless a net force acts on it. This tendency is called inertia, and mass is its measure. Newton's second law: the net force on an object equals its mass times its acceleration, ΣF = m a, and the acceleration points in the direction of the net force. A newton is the force that gives a 1 kg mass an acceleration of 1 m/s². Newton's third law: when object A pushes on object B, B pushes back on A with a force equal in size and opposite in direction. The two forces act on different objects, so they never cancel each other.
Mass versus weight
Mass is how much matter an object has, in kilograms. Weight is the gravitational force on it: W = m g, about 9.8 N for each kilogram. A 65 kg person weighs about 637 N at the Earth's surface.
Common forces
- Normal force N: the push of a surface perpendicular to the surface. It is not always equal to the weight. In an elevator accelerating up, N = m (g + a).
- Tension T: the pull along a rope or string.
- Friction f: a force along the surface that opposes sliding. Kinetic friction is f = μₖ N. Static friction can be as large as μₛ N before sliding begins.
Free-body diagrams and the method
- Pick one object and draw only the forces acting on it.
- Choose axes, often along and perpendicular to the motion. On a ramp, tilt the axes with the ramp.
- Write ΣF = m a along each axis and solve.
On a frictionless ramp at angle θ, the acceleration along the ramp is g sin θ, whatever the mass.
Worked example
A 8.0 kg block is pulled across a floor by a horizontal 50 N force. The kinetic friction coefficient is 0.20. Use g = 9.8 m/s².
- Normal force: N = m g = 8.0 × 9.8 = 78.4 N.
- Friction: f = 0.20 × 78.4 = 15.7 N.
- Net force: 50 − 15.7 = 34.3 N.
- Acceleration: a = 34.3 / 8.0 = 4.29 m/s².
If the same force were applied at constant speed, the friction would equal the push and the net force would be zero.
Connected objects
For two blocks joined by a rope, apply the second law to each and use the fact that they share the same acceleration. Adding the equations often removes the tension. If a mass m₂ hangs and pulls a mass m₁ across a frictionless table, a = m₂ g / (m₁ + m₂).
Common mistakes
- Thinking that motion needs a force. Constant velocity needs zero net force.
- Pairing the third-law forces on the same object.
- Using mass where weight is needed, or the reverse.
- Drawing a force that does not have a source object.