IGCSE Physics Forces notes

A force is a push or a pull, measured in newtons (N). Forces can change the size or shape of an object — squeezing a sponge, stretching a rubber band. Forces can also change an object’s velocity: a resultant force may change the object’s speed or its direction of motion, or both.

Forces acting along the same straight line are added or subtracted. Take one direction as positive: a 12 N pull to the right and a 5 N friction force to the left give a resultant of 12 − 5 = 7 N to the right. If the forces cancel exactly, the resultant is zero.

Supplement: the link between resultant force and acceleration is F = ma, with the force and the acceleration in the same direction. A resultant force of 1 N gives a mass of 1 kg an acceleration of 1 m/s².

Supplement: circular motion needs a force too. An object moving in a circle has a force on it that is perpendicular to its motion, always pointing to the centre of the circle. Qualitatively: a bigger force means a bigger speed is possible (same mass and radius); a bigger force allows a smaller radius (same mass and speed); a bigger mass needs a bigger force to hold the same speed and radius. The string of a whirling ball provides that inward force — let go and the ball flies off along a straight line.

Hang weights from a spring and measure the extension — how much longer it is than its unstretched length. The standard experiment: clamp a spring to a stand with a mm rule beside it, record the unstretched length, add loads one at a time, record the new length each time, then plot a load–extension graph. Unloading the weights and re-checking the length shows whether the spring recovered.

For an elastic solid such as a spring, the graph starts as a straight line through the origin: the extension is proportional to the load. Past a certain load the line curves — the spring has been stretched past the point where the simple rule holds.

Supplement: on the straight part, the spring constant k is defined as force per unit extension: k = F/x, measured in N/m. The limit of proportionality is the point on the load–extension graph beyond which extension is no longer proportional to load — the graph starts to curve there. (You do not need the elastic limit in this course.)

Solid friction is the force between two surfaces that sometimes impedes (opposes) motion and produces heating. Rub your hands together — they warm up. Friction between a tyre and the road is useful; friction in a rusty hinge wastes energy and wears the metal. Lubrication separates the surfaces with oil, reducing the friction.

Objects moving through a liquid or through a gas also feel a friction-like force called drag — for example water resistance on a swimmer and air resistance on a cyclist or a falling leaf. Drag grows with speed, which is why cars need more engine power at high speed and why falling objects reach a terminal velocity (Topic 1).

The moment of a force is a measure of its turning effect. Door handles are placed far from hinges, and spanners have long handles, because the further the force acts from the pivot, the bigger the turning effect for the same push. The moment is defined as

This is the principle of moments: for a body in equilibrium, the sum of the clockwise moments about the pivot equals the sum of the anticlockwise moments. Supplement: the same principle works with more than one force on a side — add the moments on each side before comparing. And with no resultant force and no resultant moment, an object is in equilibrium: it does not accelerate and it does not start turning.

1. 1Mark the pivot

   Choose the pivot and label every force with its perpendicular distance from it.

2. 2Moments each side

   Add up clockwise moments and anticlockwise moments separately (Supplement: several forces per side).

3. 3Equate and solve

   Set clockwise = anticlockwise and solve for the unknown force or distance.

Supplement: to demonstrate that an object in equilibrium has no resultant moment, balance a metre rule at its centre on a pivot, hang unequal weights at different distances until the rule stays horizontal, and calculate the moments on each side — they are equal, so the resultant moment is zero, which is why the rule does not rotate.

The centre of gravity of an object is the point through which its whole weight appears to act, whatever the object’s orientation. For a uniform metre rule it is at the 50 cm mark; for a flat shape it can be found by suspension.

1. 1Hang and plumb

   Suspend the irregular card (lamina) freely from a pin at one point. Hang a plumb line from the same point and draw the vertical line on the card.

2. 2Repeat

   Suspend the card from a second, different point and draw that vertical line too.

3. 3Intersect

   The centre of gravity is where the two lines cross. Check by balancing the card on a pin at that point — it stays level.

Stability: an object topples when its centre of gravity moves outside its base. A low centre of gravity and a wide base make an object stable — that is why racing cars are built low and wide, a double-decker bus tilts a long way in a test without toppling, and a loaded suitcase stands upright more easily when the heavy items are packed at the bottom.