Newton's Laws and Resultant Forces
Newton’s First Law
Newton’s First Law states that an object remains at rest or continues to move at constant velocity unless acted upon by a resultant force. This means:
• If the resultant force is zero, a stationary object stays still and a moving object keeps moving at the same speed in the same direction.
• If there is a resultant force, the object accelerates — which means it speeds up, slows down, or changes direction.
A spacecraft drifting in deep space continues at the same velocity indefinitely because there is no friction or air resistance to produce a resultant force. A book on a table remains stationary because the normal contact force from the table (upward) exactly balances its weight (downward).
Objects do not need a force to keep moving at constant velocity. A resultant force is only needed to change the speed or direction of an object. Zero resultant force → no change in motion.
Newton’s Second Law: F = ma
Newton’s Second Law states that the resultant force on an object is equal to its mass multiplied by its acceleration:
$$F = m \times a$$
Where \(F\) is resultant force (N), \(m\) is mass (kg), and \(a\) is acceleration (m/s2). The equation shows that a larger force produces a larger acceleration for the same mass, and a larger mass requires a larger force for the same acceleration. Remember: \(F\) is always the resultant force, not just any single force acting on the object.
Question: A car engine provides 4 200 N of driving force. Friction and air resistance total 1 400 N. The car has a mass of 700 kg. Calculate its acceleration.
Step 1: Find the resultant force: \(F = 4200 - 1400 = 2800 \text{ N}\)
Step 2: Apply Newton’s Second Law: \(a = \frac{F}{m} = \frac{2800}{700} = 4 \text{ m/s}^2\)
You can investigate Newton’s Second Law using a trolley on a smooth track with a string passing over a pulley to a hanging mass. The hanging mass provides the driving force. Use light gates to measure acceleration. Keep the total mass of the system constant and vary the force by moving masses from the trolley to the hanger. Plot force against acceleration — a straight line through the origin confirms \(F \propto a\) at constant mass.
Weight, Mass and Gravitational Field Strength
Mass is the amount of matter in an object. It is measured in kg and does not change with location. Weight is the force of gravity acting on that mass, measured in newtons. The equation is:
$$W = m \times g$$
Where \(W\) is weight (N), \(m\) is mass (kg) and \(g\) is gravitational field strength (N/kg). At the Earth’s surface, \(g = 10 \text{ N/kg}\). A 70 kg person weighs 700 N on Earth but would weigh only about 112 N on the Moon, where \(g \approx 1.6 \text{ N/kg}\). Their mass stays at 70 kg in both locations. The numerical value of \(g\) at the Earth’s surface also equals the acceleration due to gravity in free fall (\(10 \text{ m/s}^2\)).
Inertial Mass
Inertial mass is defined as the ratio of the resultant force applied to an object to the acceleration it produces:
$$m = \frac{F}{a}$$
This is Newton’s Second Law rearranged. An object with greater inertial mass is harder to accelerate for the same applied force. Inertial mass and gravitational mass (the mass that determines how strongly gravity pulls an object) have the same value — this equivalence is a fundamental feature of physics and was central to Einstein’s thinking, though it is not required beyond GCSE level.
Newton’s Third Law
Newton’s Third Law states: for every action, there is an equal and opposite reaction. These action-reaction pairs always act on different objects and are always the same type of force. For example:
• When you push a wall, the wall pushes back on you with an equal force in the opposite direction (both are normal contact forces).
• When the Earth pulls you downwards by gravity (your weight), you pull the Earth upwards with an equal gravitational force.
• A swimmer pushes water backwards — the water pushes the swimmer forwards.
A common mistake is to treat weight and the normal contact force as a Third Law pair. They are not — both act on the same object. A true Third Law pair involves forces on different objects.
Newton’s Third Law pairs: equal in size, opposite in direction, same type of force, acting on different objects. If both forces act on the same object, they are NOT a Third Law pair.
Stopping Distance
Scope note: stopping distances are topic P8.1, examined on Physics Paper 2 (F2 / H4). They sit here because they follow on from forces and motion.
The total stopping distance of a vehicle is the sum of the thinking distance and the braking distance. Thinking distance is the distance covered from when the driver sees a hazard to when the brakes are applied. Braking distance is the distance covered while the brakes are applied and the vehicle slows to a stop.
• Factors increasing thinking distance: higher speed, tiredness, alcohol, drugs, distractions such as a mobile phone.
• Factors increasing braking distance: higher speed (braking distance is proportional to speed squared, so doubling speed quadruples braking distance), wet or icy roads, worn tyres, poorly maintained brakes, larger mass of vehicle.
• Speed affects both: at higher speed the vehicle covers more ground during the reaction time and also needs more braking distance to decelerate from a higher initial velocity.