How do I calculate force?

Use F = ma. Multiply mass by acceleration. For example, a 10 kg object accelerating at 3 m/s² experiences a net force of 30 N. Enter mass and acceleration in the Newton's Second Law tab to see the step-by-step working.

What is the difference between mass and weight?

Mass is the amount of matter in an object, measured in kilograms (kg) — it does not change with location. Weight is the gravitational force acting on that mass, measured in Newtons (N), and it varies depending on the strength of gravity at that location.

How does the car crash calculator work?

It applies the impulse-momentum theorem: F × t = m × Δv. Enter the vehicle mass, initial speed, and stopping time to find the average impact force. A shorter stopping time produces a much larger force, which is why crumple zones save lives by extending the collision duration.

What are Newton's three laws of motion?

First law: an object stays at rest or in uniform motion unless acted on by a net force. Second law: F = ma — net force equals mass times acceleration. Third law: for every action there is an equal and opposite reaction. All three laws are applied across the tabs in this dynamics solver.

How do I use Hooke's Law to find spring force?

Hooke's Law states F = kx, where k is the spring constant in N/m and x is the extension or compression in metres. Enter the spring constant and displacement in the Hooke's Law tab and the solver calculates the restoring force instantly with full working shown.

How is gravitational force calculated between two objects?

Use Newton's Law of Universal Gravitation: F = G × m1 × m2 / r², where G = 6.674 × 10⁻¹¹ N m² kg⁻². Enter both masses and the distance between them in the Gravitation tab.

What is the banking angle formula and when do I use it?

The ideal banking angle is θ = arctan(v² / (r × g)), where v is the vehicle speed, r is the radius of the curve, and g is gravitational acceleration. Use the Banking Angle tab for road design, circular motion on banked tracks, or AP Physics mechanics problems.

Can I use this solver for AP Physics 1 and IB Physics?

Yes. The topics covered — Newton's second law, gravitational force, Hooke's law, impulse-momentum, and banking angles — appear in AP Physics 1, AP Physics C Mechanics, IB Physics SL and HL, and A-Level Physics.

What is the difference between static and kinetic friction?

Static friction acts on a stationary object and prevents it from moving, adjusting up to a maximum of μs × N. Kinetic friction acts on a moving object with a constant value of μk × N. Static friction is always greater than or equal to kinetic friction for the same surface pair.

How do I solve problems involving inclined planes?

Resolve forces along and perpendicular to the slope. The component of gravity along the slope is mg sin(θ) and perpendicular is mg cos(θ). Net force along the slope equals mg sin(θ) minus friction. Enter the known values in the Newton's Second Law tab to calculate acceleration on the incline.

Dynamics Solver

Dynamics Solver F=ma · Gravity · Tension · Banking

Result

—

Mass

Acceleration

Quick Examples

Formula Reference

Newton's 2nd: F = ma

Weight: W = mg (g=9.8)

Gravity: F = GmM/r²

Hooke's Law: F = kx

Normal (Inclined): F_n = mg cos(θ)

Impulse: FΔt = mΔv

Results are calculated using standard gravity g = 9.80665 m/s² and gravitational constant G = 6.67430 × 10⁻¹¹ N·m²/kg².

Dynamics Solver: Solve Newton's Laws and Forces Step-by-Step

A comprehensive tool to calculate force, acceleration, tension, gravity, and other dynamics problems for students and engineers.

How to Use the Dynamics Solver

Select Tool

Choose the specific dynamics problem you want to solve from the top tabs (e.g., F=ma, Hooke's Law, or Tension).

Enter Values

Input your known numbers. Use the unit dropdowns to select kg, lb, m/s, mph, etc. The tool converts units automatically.

Automatic Conversion

If you change a unit dropdown after typing a number, the value will automatically update to match the new unit.

Get Solutions

Click Calculate to see the step-by-step physics formulas and the final result in standard SI units.

Physics Dynamics by Student Level

Middle School

Topics: Basic F=ma, weight vs mass, and simple net force addition. Focus is on understanding that forces cause motion.

How to use: Use the F=ma tab. Enter your mass and acceleration to see how they multiply to give force.

High School (AP/IB/GCSE)

Topics: Friction, normal force on inclines, tension in pulleys, and Hooke's law for springs.

How to use: Use the Normal Force or Tension tabs. Switch units to match your textbook (like lb to kg).

College Level

Topics: Universal gravitation, impulse-momentum in crashes, and banking angles in civil engineering.

How to use: Use the Car Crash tab for impact simulations. Use the Gravitation tab for celestial mechanics.

Using This Tool for Physics Assignments

Homework Problems

Solve your problem sets by hand first, then use this solver to verify your result. Our unit conversion feature ensures you never fail because of a metric vs imperial mix-up.

Physics Case Studies

For projects on road safety or car engineering, use the Crash and Stopping Distance tools. These provide the scientific basis for analyzing impact forces.

Core Concepts in Dynamics

What is Dynamics in Physics?

Dynamics is the branch of mechanics that deals with the motion of bodies under the action of forces. Unlike kinematics, which describes how things move, dynamics explains why they move by looking at the forces involved.

Explain Newton's Second Law

Newton's Second Law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. F = ma is the core formula.

What is Normal Force?

Normal force is the support force exerted upon an object that is in contact with another stable object. On an incline, it is reduced by the cosine of the angle.

Common Dynamics Questions and Simple Answers

1. Why do I need to use kilograms for mass?
Newtons are defined using kg, meters, and seconds. If you use grams, your force value will be 1000 times too large.

2. Does gravity change on different planets?
Yes, gravity depends on the planet's mass and radius. Our gravity solver allows you to enter any planet's mass.

3. What happens if net force is zero?
The object will either stay still or keep moving at a constant speed in a straight line.

4. Is tension the same everywhere in a rope?
In basic physics, we assume the rope is massless, so tension is constant.

5. Why is banking road useful?
It uses a component of the normal force to provide centripetal force for safer turns.

6. How do I solve for acceleration?
Rearrange F = ma to get a = F / m.

7. What is the spring constant k?
It represents the stiffness of a spring. Higher k means a stiffer spring.

8. Why is the reaction force negative?
It indicates opposite direction according to Newton's 3rd law.

9. How do I find friction if it is not given?
Friction equals mu times Normal force.

10. What is impulse?
Impulse is the change in momentum (Force times time).

11. Why do heavy cars take longer to stop?
They have more kinetic energy and momentum.

12. Does Hooke's Law work for all materials?
Only within the elastic limit.

13. Can a normal force be horizontal?
Yes, when pushing against a wall.

14. What is G?
The Universal Gravitational Constant (6.674e-11).

15. How do I calculate weight on the moon?
Multiply mass by 1.6 m/s².

16. What is centripetal force?
The net force keeping an object in circular motion.

17. Does air affect stopping distance?
Yes, but it's often ignored in basic physics.

18. How do I find the resultant force?
Sum all vector components.

19. Why does mass not affect falling speed?
Because force and mass scale together in gravity.

20. What is a free body diagram?
A sketch of all forces on an object.

Frequently Asked Questions

1. How do I calculate force?: Use F = ma. Multiply mass by acceleration. For example, a 10 kg object accelerating at 3 m/s² experiences a net force of 30 N. Enter mass and acceleration in the Newton's Second Law tab to see the step-by-step working.
2. What is the difference between mass and weight?: Mass is the amount of matter in an object, measured in kilograms (kg) — it does not change with location. Weight is the gravitational force acting on that mass, measured in Newtons (N), and it varies depending on the strength of gravity at that location.
3. How does the car crash calculator work?: It applies the impulse-momentum theorem: F × t = m × Δv. Enter the vehicle mass, initial speed, and stopping time to find the average impact force. A shorter stopping time produces a much larger force, which is why crumple zones save lives by extending the collision duration.
4. What are Newton's three laws of motion?: First law: an object stays at rest or in uniform motion unless acted on by a net force. Second law: F = ma — net force equals mass times acceleration. Third law: for every action there is an equal and opposite reaction. All three laws are applied across the tabs in this dynamics solver.
5. How do I use Hooke's Law to find spring force?: Hooke's Law states F = kx, where k is the spring constant in N/m and x is the extension or compression in metres. Enter the spring constant and displacement in the Hooke's Law tab and the solver calculates the restoring force instantly with full working shown.
6. How is gravitational force calculated between two objects?: Use Newton's Law of Universal Gravitation: F = G × m&sub1; × m&sub2; / r², where G = 6.674 × 10²¹¹ N m² kg²². Enter both masses and the distance between them in the Gravitation tab. This formula applies to planets, moons, and any two masses in the universe.
7. What is the banking angle formula and when do I use it?: The ideal banking angle for a curved road is θ = arctan(v² / (r × g)), where v is the vehicle speed, r is the radius of the curve, and g is gravitational acceleration. Use the Banking Angle tab when solving problems about road design, circular motion on banked tracks, or AP Physics mechanics questions.
8. Can I use this solver for AP Physics 1 and IB Physics?: Yes. The topics covered here — Newton's second law, gravitational force, Hooke's law, impulse-momentum, and banking angles — appear directly in AP Physics 1, AP Physics C Mechanics, IB Physics SL and HL, and A-Level Physics. Use the solver to verify hand-worked answers and review step-by-step methods before exams.
9. What is the difference between static and kinetic friction?: Static friction acts on a stationary object and prevents it from moving — it adjusts up to a maximum value of μ⊂s × N. Kinetic friction acts on a moving object and has a constant value of μ⊂k × N. Static friction is always greater than or equal to kinetic friction for the same surface pair.
10. How do I solve problems involving inclined planes?: Resolve forces along and perpendicular to the slope. The component of gravity along the slope is mg sin(θ) and perpendicular to it is mg cos(θ). The normal force equals mg cos(θ) on a frictionless surface. Net force along the slope equals mg sin(θ) minus friction (if any). Enter the known values in the Newton's Second Law tab to calculate acceleration on the incline.