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Newton's Laws and Forces

24 min Physics Math

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

Example 1

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

$a = F/m = 50/10 = 5$ 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)

Normal force $N = mg = 50$ N.

Friction: $f = \mu N = 0.3 \times 50 = 15$ N.

$a = f/m = 15/5 = 3$ 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.

Net force: $(5-3)g = 2(10) = 20$ N.

Total mass: $3 + 5 = 8$ kg.

$a = 20/8 = 2.5$ 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