Section 2.1: Newton's Laws of Motion

Newton's Laws describe the relationship between the motion of an object and the forces acting upon it. Understanding these laws is fundamental to physics.

Newton's First Law (Law of Inertia):

An object at rest stays at rest, and an object in motion continues in a straight line at constant speed unless acted upon by a net external force.

Mass is a measure of an object's inertia.

Newton's Second Law:

The net force acting on an object is equal to its mass multiplied by its acceleration:

\( F_{\text{net}} = m a \)

Where \( F_{\text{net}} \) is the net force in Newtons (N), \( m \) is mass in kilograms (kg), and \( a \) is acceleration in meters per second squared (m/s²).

Newton's Third Law:

For every action, there is an equal and opposite reaction.

Example: When you push on a wall, the wall pushes back with equal force in the opposite direction.

Common Forces

  • Gravity: \( F_g = mg \), where g = 9.8 m/s²
  • Normal force: Perpendicular support force from a surface
  • Friction: Static or kinetic, opposes motion
  • Tension: Force along a string, rope, or cable
  • Applied force: Any external push or pull

Example 1

A 5 kg block is pushed with a force of 20 N on a frictionless surface. Find its acceleration.

\( a = \frac{F_{\text{net}}}{m} = \frac{20}{5} = 4 \text{ m/s²} \)

Example 2

A 10 kg box is at rest on a horizontal surface. A 40 N force acts to the right, and friction of 10 N opposes it. Find the acceleration.

\( F_{\text{net}} = 40 - 10 = 30 \text{ N} \)

\( a = \frac{F_{\text{net}}}{m} = \frac{30}{10} = 3 \text{ m/s²} \)

Practice Problems

  1. A 15 kg sled is pulled with a 60 N force across a frictionless surface. Find the acceleration.
  2. A 12 kg block on a horizontal surface experiences 30 N forward and 8 N friction. Determine net acceleration.
  3. A book of mass 2 kg rests on a table. Find the weight of the book.
  4. A 5 kg box is pushed with 25 N while friction is 5 N. Find acceleration.
  5. A 1000 kg car accelerates from 0 to 20 m/s in 5 s. Calculate the net force applied.
  6. A 50 kg crate is at rest. A 100 N horizontal force is applied, friction = 20 N. Determine acceleration.
  7. A person jumps off a 70 kg boat. Describe the boat’s motion using Newton’s third law.
  8. A 2 kg object falls freely under gravity. Find its acceleration and weight.
  9. A 10 kg box is pushed with a 50 N force on a surface with 15 N friction. Find net acceleration.
  10. Two blocks, 3 kg and 5 kg, connected by a rope on a frictionless surface. Force applied = 16 N. Find acceleration of the system.
  11. A block slides down a frictionless incline at 30°; mass = 10 kg. Find acceleration along incline.
  12. A 20 N force acts on a 4 kg object, while friction = 6 N. Find acceleration.
  13. A 1.5 kg box is at rest; a 10 N horizontal force is applied. Find acceleration.
  14. A 7 kg box experiences 28 N force to the right, friction = 14 N. Compute acceleration.
  15. A car weighs 1200 kg, accelerates at 2 m/s². Find net force.
  16. A 3 kg object experiences two forces: 10 N right, 4 N left. Find net acceleration.
  17. A 6 kg object on a frictionless surface experiences 18 N. Find acceleration.
  18. A 9 kg object is pushed with 36 N; friction = 9 N. Find acceleration.
  19. A 50 kg box is pulled with 200 N; friction = 50 N. Determine acceleration.
  20. A 1 kg book falls freely. Find the force of gravity acting on it.
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