Newton's Second Law explains how an object's motion changes when a net force acts on it. It connects three central ideas in mechanics: force, mass, and acceleration. This law matters because it lets us predict how carts, cars, rockets, athletes, and falling objects speed up, slow down, or change direction.
The compact equation Fnet = ma is one of the most useful tools in physics.
Understanding Newton's Second Law
Acceleration is a change in velocity, not simply a change in speed. Velocity includes direction. A bicycle turning around a corner can accelerate even when its speedometer reading stays the same.
The acceleration points in the direction that the velocity is changing. This is why a force that acts sideways bends an object's path.
A ball on a string moves in a circle because the string pulls it inward. Its motion is constantly changing direction, so it has acceleration toward the centre of the circle.
To use the law well, start by choosing one object to study. Draw that object by itself, then draw every external force acting on it as an arrow. This is called a free body diagram.
Arrow length can show relative size, while arrow direction shows the direction of each force. Forces along the same straight line can be combined by taking account of their directions. For forces at right angles, treat the horizontal and vertical directions separately.
A book resting on a table has gravity pulling downward and the table pushing upward. These forces cancel, so the book does not begin moving vertically.
Mass measures resistance to changes in motion. A full shopping trolley needs more push than an empty one because the loaded trolley has more mass. The same push gives the empty trolley a greater acceleration.
Weight is different from mass. Weight is the gravitational force on an object, so it depends on the local strength of gravity. On Earth, weight equals mass times gravitational field strength.
An astronaut has nearly the same mass on the Moon, yet weighs less there. This distinction prevents a common mistake when solving problems involving scales, lifts, or falling objects.
Real situations usually involve several forces, including friction, air resistance, tension, support forces, and pushes from motors or people. Friction often acts opposite to sliding motion. Air resistance usually grows as an object moves faster, which can reduce its acceleration.
In a car, the engine provides a forward force through the tyres, while resistive forces act backward. When the forward force is larger, the car speeds up. When braking forces are larger, it slows down.
Pay close attention to the chosen direction and use a consistent sign for every force. Many errors come from adding forces that point opposite ways, or from using weight when the question asks for mass.
Key Facts
- Newton's Second Law: Fnet = ma.
- Acceleration is directly proportional to net force when mass is constant: a = Fnet/m.
- Acceleration is inversely proportional to mass when net force is constant: a decreases as m increases.
- The SI unit of force is the newton: 1 N = 1 kg·m/s^2.
- Net force is the vector sum of all forces acting on an object.
- If Fnet = 0, then a = 0, so the object keeps a constant velocity.
Vocabulary
- Net force
- The net force is the combined total of all forces on an object, including their directions.
- Mass
- Mass is a measure of how much matter an object has and how strongly it resists acceleration.
- Acceleration
- Acceleration is the rate at which an object's velocity changes over time.
- Newton
- A newton is the SI unit of force, equal to the force needed to accelerate 1 kg at 1 m/s^2.
- Free-body diagram
- A free-body diagram is a simplified drawing that shows all forces acting on a single object.
Common Mistakes to Avoid
- Using the applied force instead of the net force. This is wrong because friction, gravity, normal force, and other forces may change the total force that causes acceleration.
- Forgetting that force and acceleration are vectors. This is wrong because direction matters, so forces in opposite directions must be subtracted.
- Thinking a heavier object always has more force on it. This is wrong because force depends on both mass and acceleration, and the same mass can experience different net forces.
- Using grams instead of kilograms in Fnet = ma. This is wrong because the standard SI units are newtons, kilograms, and meters per second squared.
Practice Questions
- 1 A 4.0 kg cart is pushed with a net force of 12 N to the right. What is its acceleration?
- 2 A 10 kg box accelerates at 1.5 m/s^2 to the left. What is the net force on the box, including direction?
- 3 Two carts are pushed with the same net force. Cart A has a mass of 2 kg and Cart B has a mass of 6 kg. Explain which cart has the greater acceleration and why.