Forces

A force is simply a push or a pull, measured in Newtons (N). Since forces have both a size (magnitude) and a direction, they are vector quantities. Common forces you'll encounter include weight (gravity), friction, air resistance, and tension. The key to understanding motion is the 'resultant force', which is the overall force on an object once you've combined all the individual forces acting on it. Sir Isaac Newton's First Law of Motion states that an object's motion will not change unless a resultant force acts on it. This means if the forces are balanced (the resultant force is zero), a stationary object will remain stationary, and a moving object will continue to move at a constant speed in a straight line (constant velocity). A change in motion (acceleration) only happens when forces are unbalanced.

Newton's Second Law of Motion describes what happens when forces are unbalanced. It connects resultant force (F), mass (m), and acceleration (a). The law states that the acceleration of an object is directly proportional to the resultant force acting on it and inversely proportional to its mass. Mass can be thought of as a measure of an object's 'inertia' – its resistance to changing its state of motion. A larger mass requires a larger force to achieve the same acceleration. The relationship is summarised by the most important equation in mechanics: Resultant Force = mass × acceleration. Remember, the 'F' in this equation is always the *resultant* force, not just one of the forces acting.

It's crucial not to confuse mass and weight. Mass is the amount of 'stuff' (matter) in an object and is measured in kilograms (kg). Your mass is the same whether you are on Earth, on the Moon, or in deep space. Weight is the force of gravity acting on an object and is measured in Newtons (N). Your weight depends on where you are – it's a measure of how strongly gravity is pulling on your mass. The force of weight is calculated using the equation: Weight = mass × gravitational field strength. The gravitational field strength, 'g', is the force of gravity per unit mass. On Earth, g is approximately 10 N/kg (or more precisely 9.8 N/kg).

Friction is a force that opposes motion between surfaces in contact. Air resistance is a type of friction that affects objects moving through the air. A key characteristic of air resistance is that it increases as the object's speed increases. This leads to the concept of terminal velocity. Consider a skydiver:

1. Just after jumping, their speed is low, so air resistance is negligible. The only major force is their weight, so they accelerate downwards at approximately g (about 10 m/s²).
2. As their speed increases, air resistance increases, acting upwards. This opposes their weight, so the resultant downward force decreases, and their acceleration reduces.
3. Eventually, they fall so fast that the upward force of air resistance becomes equal in size to their downward force of weight. The forces are now balanced, the resultant force is zero, and they stop accelerating. They now fall at a constant, maximum speed called terminal velocity.

Momentum is a measure of an object's 'quantity of motion'. It is a vector quantity that depends on both an object's mass and its velocity. A lorry moving slowly can have the same momentum as a fast-moving tennis ball. The formula is: momentum = mass × velocity. The unit for momentum is kilogram metres per second (kg m/s). One of the most important laws in physics is the Principle of Conservation of Momentum. It states that for a 'closed system' (one with no external forces like friction), the total momentum before an event (like a collision or explosion) is equal to the total momentum after the event. This is incredibly useful for calculating velocities after collisions.

Newton's Second Law can also be expressed in terms of momentum. It states that the resultant force acting on an object is equal to the rate of change of its momentum. This gives us a powerful equation: Force = (change in momentum) / time. The change in momentum is 'final momentum (mv) - initial momentum (mu)'. This relationship is key to understanding impacts. The quantity 'Force × time' is called impulse, and it is equal to the change in momentum (Δp). To reduce the force experienced during an impact (like in a car crash), we need to increase the time over which the momentum changes. This is the principle behind safety features like airbags, crumple zones, and crash mats. They all increase the impact time to reduce the impact force.

When two or more forces act on an object at angles to each other, you cannot simply add their magnitudes. You must add them as vectors. For IGCSE, this is done using a scale diagram. The most common method is the 'parallelogram rule'.

1. Choose a suitable scale (e.g., 1 cm = 5 N).
2. Draw the first force vector as an arrow, with its length representing the magnitude and its direction matching the problem.
3. From the tail of the first vector, draw the second force vector, again to scale and in the correct direction.
4. Complete the parallelogram by drawing lines parallel to your two vectors.
5. The resultant force is the diagonal of the parallelogram starting from the common tail of the two original vectors. Measure the length of this diagonal and use your scale to find the magnitude of the resultant force. Use a protractor to measure its direction.