Forces Calculator F = ma
Calculate force, mass, acceleration, weight, and friction with step-by-step solutions. Perfect for GCSE and A-Level Physics.
Force = Mass × Acceleration
Solve for:
Quick Examples
Newton's First Law (Inertia)
A book on a table stays at rest because forces are balanced.
Newton's Second Law
Pushing a shopping trolley: more force = more acceleration.
Newton's Third Law
When you push a wall, the wall pushes back on you with equal force.
What is Force?
Force is a push or pull acting on an object. It is a vector quantity, meaning it has both magnitude (size) and direction. Forces can cause objects to start moving, stop moving, change speed, or change direction.
Newton's Second Law (F = ma)
Force (N) = Mass (kg) × Acceleration (m/s²)
The SI unit of force is the Newton (N), which equals 1 kg·m/s². One Newton is the force needed to accelerate a 1 kg mass at 1 m/s².
Example: A 5 kg object accelerating at 2 m/s²
F = 5 × 2 = 10 N
Contact Forces
- • Friction - opposes sliding motion
- • Normal force - perpendicular to surface
- • Tension - pulling through rope/string
- • Air resistance - drag force
Non-Contact Forces
- • Gravity - attraction between masses
- • Magnetic force - between magnets
- • Electrostatic - between charges
- • Nuclear forces - within atoms
Newton's Three Laws of Motion
First Law (Law of Inertia)
An object at rest stays at rest, and an object in motion stays in motion with constant velocity, unless acted upon by an unbalanced net force.
Example: A book on a table stays still because gravity pulling down is balanced by the normal force pushing up. A hockey puck slides across ice for a long distance because friction is very small.
Second Law (F = ma)
The acceleration of an object is directly proportional to the net force and inversely proportional to its mass. This gives us the famous equation F = ma.
Example: Pushing a shopping trolley with twice the force gives twice the acceleration. A heavier trolley (more mass) needs more force for the same acceleration.
Third Law (Action-Reaction)
For every action force, there is an equal and opposite reaction force. These forces act on different objects.
Example: When you push against a wall, the wall pushes back on you with equal force. When a rocket expels gas downward, the gas pushes the rocket upward.
⚠️ Common mistake: Action-reaction pairs act on DIFFERENT objects. They don't cancel out because they're not acting on the same object.
Weight vs Mass
One of the most common confusions in physics is between weight and mass. They are NOT the same thing!
Mass (m)
- • Amount of matter in an object
- • Measured in kilograms (kg)
- • Constant everywhere
- • Scalar quantity (no direction)
- • Measured with a balance
Weight (W)
- • Force of gravity on an object
- • Measured in Newtons (N)
- • Changes with location
- • Vector quantity (has direction)
- • Measured with a spring scale
Weight Formula
Weight (N) = Mass (kg) × Gravitational field strength (m/s²)
| Location | g (m/s²) | 70 kg person weighs |
|---|---|---|
| 🌍 Earth | 9.81 | 687 N |
| 🌙 Moon | 1.62 | 113 N |
| 🔴 Mars | 3.71 | 260 N |
| 🟠 Jupiter | 24.79 | 1735 N |
Note: The person's mass is always 70 kg regardless of location. Only weight changes.
Types of Friction
Friction is a force that opposes the relative motion between two surfaces in contact. It acts parallel to the contact surface.
Friction Formula
Friction Force (N) = Coefficient of friction × Normal Force (N)
Static Friction (μₛ)
- • Prevents motion from starting
- • Acts when object is stationary
- • Greater than kinetic friction
- • Maximum value: Fₛ,max = μₛN
Kinetic Friction (μₖ)
- • Opposes motion in progress
- • Acts when object is moving
- • Less than static friction
- • Constant value: Fₖ = μₖN
Common Friction Coefficients
| Surfaces | μₛ (static) | μₖ (kinetic) |
|---|---|---|
| Rubber on dry concrete | 1 | 0.8 |
| Rubber on wet concrete | 0.7 | 0.5 |
| Steel on steel (dry) | 0.74 | 0.57 |
| Ice on ice | 0.1 | 0.03 |
| Wood on wood | 0.5 | 0.3 |
Common Mistakes in Force Problems
Avoid these frequent errors when solving forces questions in GCSE and A-Level Physics exams:
Confusing mass and weight
Mass (kg) is amount of matter; weight (N) is gravitational force. A 70 kg person has mass 70 kg everywhere, but weighs 687 N on Earth and only 113 N on the Moon.
Always check units: if it's in kg, it's mass. If in Newtons, it's weight.
Wrong units for F = ma
F = ma only works with SI units: Force in Newtons (N), mass in kilograms (kg), acceleration in m/s². Using grams or km/h² gives wrong answers.
Convert all values to SI units before calculating. 1 N = 1 kg·m/s².
Forgetting direction of friction
Friction always opposes the direction of motion (or intended motion). If a box slides right, friction acts left.
Ask: "Which way is the object moving (or trying to move)?" Friction acts opposite to that.
Wrong normal force on inclines
On a horizontal surface, N = mg. But on an inclined plane, N = mg cos θ (perpendicular to surface, not vertical).
Normal force is always PERPENDICULAR to the surface, not just "upward".
Using wrong friction coefficient
Static friction (μₛ) is for objects at rest; kinetic friction (μₖ) is for moving objects. μₛ > μₖ always.
Check if the object is moving or stationary. Use static for "about to move" problems.
Mixing up Newton's Third Law pairs
Action-reaction pairs act on DIFFERENT objects. The book pushes down on the table; the table pushes up on the book. These are the pair.
Third Law pairs: same type of force, same magnitude, opposite direction, DIFFERENT objects.
Worked Examples
Practice with these GCSE and A-Level style force problems:
Example 1: Finding Force
A 1500 kg car accelerates at 2.5 m/s². Calculate the driving force needed.
Solution:
Given: m = 1500 kg, a = 2.5 m/s², F = ?
Formula: F = ma
F = 1500 × 2.5
F = 3750 N
Example 2: Weight on the Moon
An astronaut has a mass of 80 kg. Calculate their weight on the Moon where g = 1.62 m/s².
Solution:
Given: m = 80 kg, g = 1.62 m/s², W = ?
Formula: W = mg
W = 80 × 1.62
W = 129.6 N
(Compare: On Earth they would weigh 80 × 9.81 = 784.8 N)
Example 3: Friction Force
A 25 kg crate sits on a floor. The coefficient of static friction is 0.4. What force is needed to start it moving?
Solution:
Step 1: Find normal force (on flat ground, N = W = mg)
N = 25 × 9.81 = 245.25 N
Step 2: Find maximum static friction
F = μₛN = 0.4 × 245.25
F = 98.1 N
You need to push with more than 98.1 N to start it moving.
Example 4: Resultant of Two Forces at Right Angles
A 30 N force acts horizontally and a 40 N force acts vertically on an object. Find the resultant force.
Solution:
Given: F₁ = 30 N (horizontal), F₂ = 40 N (vertical)
Use Pythagoras: R = √(F₁² + F₂²)
R = √(30² + 40²) = √(900 + 1600) = √2500
R = 50 N
Direction: θ = tan⁻¹(40/30) = 53.1° from horizontal
Frequently Asked Questions
What is the formula for force?
The formula for force is F = ma (Newton's Second Law), where F is force in Newtons (N), m is mass in kilograms (kg), and a is acceleration in m/s².
What is the difference between mass and weight?
Mass (kg) is the amount of matter and stays constant. Weight (N) is the gravitational force on that mass and changes with location. W = mg.
What are Newton's three laws?
1st: Objects stay at rest/in motion unless acted on by unbalanced force. 2nd: F = ma. 3rd: Every action has an equal and opposite reaction.
How do I calculate friction force?
Use F = μN, where μ is the coefficient of friction and N is the normal force. On flat ground, N = mg (the weight).
What is the normal force?
The normal force is the support force from a surface, acting perpendicular to it. On horizontal surfaces, N = mg. On inclines, N = mg cos θ.
Why is static friction greater than kinetic?
It takes more force to start motion than to maintain it. Once moving, surfaces have less time to 'interlock', reducing friction.
How do I resolve forces into components?
For a force F at angle θ: Horizontal Fx = F cos θ, Vertical Fy = F sin θ. These components are perpendicular.
Is this calculator suitable for GCSE and A-Level?
Yes! It covers all force topics including Newton's laws, weight, friction, and force components with step-by-step solutions.
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