Chapter 5: Applying Newton’s Laws

Overview

This chapter focuses on using Newton’s laws to solve equilibrium and dynamics problems. It covers the identification and analysis of forces, the use of free-body diagrams, and the application of Newton’s laws to various physical situations, including friction, drag, ropes, pulleys, and interacting objects.

Equilibrium

Static and Dynamic Equilibrium

Equilibrium occurs when the net force acting on an object is zero. There are two types:

• Static Equilibrium: Object at rest; net force is zero.

• Dynamic Equilibrium: Object moving at constant velocity; net force is zero.

In equilibrium, the sums of the x and y components of the force are zero:

Example: An orangutan weighing 500 N hangs from a rope. The tension in the rope equals the weight: .

Problem-Solving Approach for Equilibrium

• Check if the object is in equilibrium (at rest or constant velocity).

• Identify all forces and draw a free-body diagram.

• Write Newton’s second law in component form and solve for unknowns.

• Assess the result for reasonableness and correct units.

Dynamics and Newton’s Second Law

Newton’s Second Law

Newton’s second law relates the forces acting on an object to its acceleration:

• Component form: ,

Use kinematics to find position and velocity if acceleration is known.

Problem-Solving Approach for Dynamics

• Identify known quantities and what needs to be found.

• Draw force identification and free-body diagrams.

• Write Newton’s second law in component form.

• Solve for acceleration or unknown forces.

• Use kinematics as needed.

Mass and Weight

Definitions

• Mass: Measure of inertia; does not change with location.

• Weight: Gravitational force on an object; varies with planet.

• Weight formula:

Example: A 90 lb gymnast has a mass of about 41 kg and a weight of .

Apparent Weight

• Apparent weight is the contact force supporting an object.

• In an accelerating elevator, apparent weight differs from true weight.

• Formula: (if accelerating upward)

Normal Forces

Definition and Properties

• Normal force is perpendicular to the surface of contact.

• Adjusts to keep the object on the surface.

• On an incline, normal force is less than weight:

Example: A book pressed down with extra force has a normal force greater than its weight.

Friction

Types of Friction

• Static Friction: Prevents slipping; adjusts up to a maximum value.

• Kinetic Friction: Opposes motion; constant magnitude.

• Rolling Friction: For rolling objects; usually less than kinetic friction.

Formulas:

• Static friction:

• Kinetic friction:

Example: Carol pushes a sofa at constant speed; the force equals kinetic friction.

Drag

Drag Force and Reynolds Number

• Drag opposes motion through a fluid.

• High Reynolds number: Drag proportional to .

• Low Reynolds number: Drag proportional to (Stokes' law).

High Reynolds number drag formula:

Low Reynolds number drag formula (Stokes' law):

Example: Terminal speed is reached when drag equals weight: .

Interacting Objects

Newton’s Third Law

• Every force is part of an action/reaction pair.

• Pairs act on different objects, equal in magnitude, opposite in direction.

Objects in contact have the same acceleration; analyze each with separate free-body diagrams.

Ropes and Pulleys

Tension in Ropes and Strings

• Tension is the same throughout a massless rope.

• Passing over a massless, frictionless pulley does not change tension.

• For two objects connected by a rope, tension is equal at both ends.

Example: A stage set and stagehand connected by a rope; their accelerations are related and tension is the same for both.

Summary of Strategies and Concepts

• Use free-body diagrams to identify forces.

• Apply Newton’s laws in component form.

• Assess results for physical reasonableness.

• Apparent weight differs from true weight when accelerating.

• Terminal speed occurs when drag equals weight.

• Tension in ropes and pulleys is constant for massless, frictionless systems.