Chapter 6: How Forces Affect Motion

A force is a push or a pull. It can start or stop motion, change speed, change direction or change shape. A force has both magnitude (how strong) and direction (which way), so both must be stated. The SI unit of force is the newton (N), and a spring balance measures it. The weight of an object is the force with which the Earth pulls it. Some forces need contact, such as a kick, while others, such as gravity, act from a distance.

Forces on an object can be balanced or unbalanced. Two forces that are equal in size and opposite in direction are balanced and cancel each other. The net force is the single force that has the same effect as all the forces together. Along one line, forces in the same direction add, and forces in opposite directions subtract, and the net force points along the larger force. If the net force is zero, the forces are balanced. If it is not zero, the forces are unbalanced and the motion changes.

Friction is the force that arises between two surfaces in contact and opposes their relative motion. Its direction is opposite to the motion, or to the tendency to move. It depends on the nature of the surfaces: rough surfaces give more friction than smooth ones. A box pushed gently does not move because friction balances the push, and it starts to move only when the push exceeds the maximum friction. Friction helps us walk, grip and brake. If all friction vanished, a moving object would keep moving at constant velocity.

Newton's first law says that an object at rest stays at rest, and an object in motion keeps moving with constant velocity, unless a net force acts on it. This tendency to resist a change of motion is called inertia. If the net force is zero, the acceleration is zero. A velocity-time graph of such motion is a horizontal line, and a position-time graph is a straight line. A net force is needed only to change the velocity, not to keep an object moving.

Newton's second law says that the acceleration of an object is directly proportional to the net force and inversely proportional to its mass. In symbols, F = ma, or a = F ÷ m. The direction of the acceleration is the direction of the net force. One newton is the force that gives a mass of 1 kg an acceleration of 1 m/s², so 1 N = 1 kg·m/s². Doubling the force doubles the acceleration, and doubling the mass halves it.

The weight of an object is F = mg, where g ≈ 9.8 m/s² is the acceleration due to gravity, the same for every mass at a place. The second law also tells us the force needed to change velocity: first find the acceleration a = (v − u) ÷ t, then use F = ma. A longer stopping time means a smaller acceleration and therefore a smaller force, so catching with pulled-back hands, airbags and landing mats reduce the force. On a velocity-time graph, a steeper line means a larger net force.

Newton's third law says that for every action there is an equal and opposite reaction. The two forces always come in a pair, they are equal in magnitude and opposite in direction, and they act on two different objects, so they never cancel each other. The law holds for contact forces and for forces at a distance. Equal forces can still give unequal accelerations because the masses differ, as with a gun and its bullet or the Earth and a falling fruit.

A system is a group of objects considered together. Forces from outside the system are external forces, and forces between the parts are internal forces. Internal forces come in equal and opposite pairs and cancel inside the system, so only external forces decide the acceleration of the whole. For two boxes joined by a string, pulled by a force F on a smooth floor, the acceleration is a = F ÷ (m1 + m2). The pull of the string is called tension.