Newton's second law of motion is the foundation of classical mechanics. It links the force acting on a body with its mass and acceleration. Thanks to it, you can calculate how hard you have to push an object to give it a certain acceleration. In this article we discuss the formula, the units, and we show the calculations using an example.
The statement of the second law of motion
Newton's second law states that the acceleration of a body is directly proportional to the net force acting on it and inversely proportional to its mass. We write it as a formula:
- F = m × a — force equals mass times acceleration
- a = F / m — acceleration equals force divided by mass
- m = F / a — mass equals force divided by acceleration
The symbol F stands for the net force, m for mass, and a for acceleration.
SI units
In the SI system these quantities have the following units:
- Force F — newton (N), where 1 N = 1 kg·m/s²
- Mass m — kilogram (kg)
- Acceleration a — metre per second squared (m/s²)
One newton is the force that gives a body of mass 1 kg an acceleration of 1 m/s².
Worked example
A force of F = 20 N acts on a cart with a mass of m = 5 kg. We calculate the acceleration.
- We apply the formula a = F / m.
- We substitute: a = 20 N / 5 kg.
- We calculate: a = 4 m/s².
The cart moves with an acceleration of 4 m/s², which means its speed increases by 4 m/s every second.
Calculating the force needed to accelerate
We often look for the force when we know the mass and the desired acceleration. To give a body of mass 1200 kg an acceleration of 2 m/s², we need: F = m × a = 1200 × 2 = 2400 N. This is exactly how the driving force of vehicles is estimated.
The force of gravity as a special case
We calculate the force of gravity from the second law by substituting the acceleration due to gravity g ≈ 9.81 m/s²:
- F = m × g
A body with a mass of 10 kg therefore weighs: F = 10 × 9.81 = 98.1 N. This shows the difference between mass (kilograms) and weight (newtons).
Second example: calculating the mass
A force of F = 60 N acts on a body, giving it an acceleration of a = 3 m/s². We calculate the mass of the body.
- We apply the formula m = F / a.
- We substitute: m = 60 N / 3 m/s².
- We calculate: m = 20 kg.
The body has a mass of 20 kg. This shows that the same formula lets you find any of the three quantities.
Where does resistance to motion come from?
In real situations only one force rarely acts on a body. It is opposed by friction, air resistance, and sometimes an elastic force. For a body to accelerate, the driving force must exceed the sum of the resisting forces. Only this surplus, that is the net force, determines the acceleration according to the formula F = m × a. When the driving force balances the resistance, the body moves at a constant speed and its acceleration is zero.
The three laws of motion in brief
The second law works together with the other two:
- First law (of inertia): a body with no net force acting on it stays at rest or moves with uniform motion.
- Second law: the net force gives the body an acceleration according to the formula F = m × a.
- Third law (action and reaction): every force is accompanied by a force equal in magnitude but opposite in direction.
Most common mistakes
- Confusing mass with weight — mass is in kg, while the force of gravity is in newtons.
- Ignoring the net force — in the formula what counts is the sum of all forces, not just one of them.
- Wrong units of acceleration — we give acceleration in m/s².
- Ignoring friction — in real problems the net force is the driving force minus the friction force.
Frequently asked questions
- What is the net force? It is the vector sum of all the forces acting on a body. Only it produces acceleration.
- Can a body accelerate without a force? No. The absence of a net force means zero acceleration, in accordance with the first law of motion.
- What is the acceleration due to gravity? About 9.81 m/s², which is why a freely falling body increases its speed by almost 10 m/s every second.
Summary
Newton's second law F = m × a links force, mass and acceleration. Knowing two of these quantities, you can find the third. Remember that force is expressed in newtons, and that the formula refers to the net force acting on the body.
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