Training Physics Math Newton's Laws and Forces
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Newton's Laws and Forces

24 min Physics Math

Newton’s three laws of motion provide the foundation for understanding how forces affect the movement of objects. The first law introduces inertia, the second law relates net force to mass and acceleration (F = ma), and the third law establishes that every action has an equal and opposite reaction. These principles govern everything from the tension in a cable to the normal force on a ramp. Learning to draw free-body diagrams and apply Newton’s second law systematically is the single most important skill in introductory mechanics.

Newton's Laws and Forces

Forces and motion are governed by simple linear equations — Newton's second law is just $F = ma$.

Newton's Second Law

$$\Sigma F = ma$$

The net force equals mass times acceleration. This is a linear equation.

Common Forces
  • Weight: $W = mg$
  • Normal force: perpendicular to surface
  • Friction: $f = \mu N$
  • Tension: force through a rope
Example 1

A 10 kg box is pushed with 50 N of force on a frictionless surface. Find acceleration.

  1. $a = F/m = 50/10 = 5$ m/s².
Example 2

A 5 kg block slides on a surface with $\mu = 0.3$. Find the friction force and acceleration. ($g = 10$ m/s²)

  1. Normal force $N = mg = 50$ N.
  2. Friction:
  3. $f = \mu N = 0.3 \times 50 = 15$ N.
  4. $a = f/m = 15/5 = 3$ m/s² (deceleration).
Example 3

Two blocks (3 kg and 5 kg) are connected by a rope over a frictionless pulley (Atwood machine). Find acceleration.

  1. Net force:
  2. $(5-3)g = 2(10) = 20$ N.
  3. Total mass: $3 + 5 = 8$ kg.
  4. $a = 20/8 = 2.5$ m/s².

Practice Problems

1. What force accelerates a 20 kg object at 4 m/s²?
2. A 1500 kg car brakes with 6000 N force. Find deceleration.
3. Find the weight of a 70 kg person. ($g = 9.8$ m/s²)
4. A 2 kg book on a table with $\mu = 0.4$. Find friction force.
5. Atwood machine: masses 4 kg and 6 kg. Find acceleration.
6. Two forces, 30 N right and 10 N left, act on a 5 kg box. Find acceleration.
Show Answer Key

1. $F = 20 \times 4 = 80$ N

2. $a = 6000/1500 = 4$ m/s²

3. $W = 70 \times 9.8 = 686$ N

4. $f = 0.4 \times 2 \times 9.8 = 7.84$ N

5. $a = (6-4)(10)/(6+4) = 2$ m/s²

6. $a = (30-10)/5 = 4$ m/s² to the right

⚖ Newton's Second Law Calculator
Weight (mg)
Normal force
Friction force
Net force along incline
Acceleration
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