Chapter 6: Applications of Newton's Laws of Motion

Chapter Overview

• Introduces applications of Newton's laws of motion.

Newton’s Laws of Mechanics

1. 1st Law: An object in motion stays in motion at a constant velocity unless acted upon by a force.

   • Note: Constant velocity can be zero.

2. 2nd Law: The acceleration of an object is proportional to the total force acting on it (F = ma).

3. 3rd Law: For every action, there is an equal and opposite reaction.

   • If object A exerts a force on object B, then object B exerts an equal but opposite force on object A.

Example Problem: Spring and Block on Incline

• A 3.00 kg block at rest on a 30° ramp with spring constant 300 N/m and coefficient of static friction 0.30.

• Question: Calculate the maximum stretch of the spring while keeping the block at rest.

Tension in a Pulley System

• Setup: Two masses m1 and m2 over a massless ideal pulley (m1 > m2).

• Tensions:A. T1 < T2B. T1 > T2C. T1 = T2D. Not enough information to determine

Atwood Machine

• Definition: Two unequal masses (m1 < m2) over a frictionless pulley, used to measure acceleration due to gravity (g).

• Problem: Determine the magnitude of acceleration for mass 1 when m1 and m2 are known.

Sloped Atwood’s Machine

• Setup: A 5 kg mass hangs while a 10 kg mass rests on a frictionless 25° slope.

• Question: Calculate the acceleration of both blocks.

Circular Motion

• Concept: 2nd Law applied to circular motion (Uniform Circular Motion).

• Free Body Diagrams: Illustrate forces in both x and y directions.

• Centripetal Force: Net force causing circular motion; relates to tension, F = ma with centripetal acceleration.

Circular Motion Problem-Solving Strategies

1. Identify the circular motion and center.

2. Determine directions of acceleration and velocity.

3. Net force aligns with acceleration.

4. Analyze acting forces.

5. Define centripetal force from net force equation: F = mv²/r.

Newton’s Law of Gravitation

• Overview: Gravitational force between two masses works at all distances; attractive force.

• Formula: F = G(m1m2/r²)

  • Gravitational force is attractive.

• Weightlessness Explained: Astronauts in free fall create the appearance of weightlessness (g on ISS is ~8.7 m/s²).

Questions?

• Invite clarification on discussed topics.