Applying Newton’s Laws

Overview

This chapter focuses on the application of Newton’s laws of motion to a variety of physical situations, including equilibrium (statics), accelerating bodies (dynamics), frictional forces, fluid resistance, and circular motion. Mastery of these concepts is essential for solving real-world physics problems involving forces and motion.

Statics: Newton’s First Law and Equilibrium

Conditions for Equilibrium

• Equilibrium occurs when a body is at rest or moves with constant velocity in an inertial frame of reference.

• All forces acting on the body must sum to zero: .

• Common forces include: normal force, friction, tension, contact forces, and weight (gravity).

Steps for Solving Equilibrium Problems

• Visualize the situation and choose a coordinate system.

• Draw a free-body diagram (FBD) showing all forces acting on the object.

• Break forces into components along the chosen axes.

• Apply Newton’s laws to each component: , .

Worked Example: Engine Suspended by Chains

• Given: Engine weight suspended by three chains at angles.

• Solution involves resolving tensions and applying equilibrium conditions.

Worked Example: Car on a Ramp

• Forces: weight , normal force , tension .

• Weight is resolved into components parallel and perpendicular to the ramp.

• Equilibrium equations:

Worked Example: Traffic Light at Rest

• Traffic light suspended by cables at angles; find tensions and check if cables will break.

Dynamics: Newton’s Second Law

Newton’s Second Law for Accelerating Bodies

• When the net force on a body is not zero, it accelerates: .

• Free-body diagrams should include only real forces, not (which is the result of the net force).

Worked Example: Iceboat on Frictionless Surface

• Given: Iceboat of mass 200 kg, wind force, and acceleration over time.

• Find the force exerted by the wind.

• Use to find acceleration, then .

• Result:

Worked Example: Iceboat with Friction

• Now include a friction force opposing motion.

• Apply Newton’s second law:

• Result:

Worked Example: Apparent Weight in an Elevator

• When an elevator accelerates, the normal force (apparent weight) changes.

• Apply

• For upward acceleration:

• For downward acceleration:

Frictional Forces

Types of Friction

• Static friction (): Acts when there is no relative motion; .

• Kinetic friction (): Acts when a body slides; .

• Friction always acts parallel to the surface and opposes relative motion.

Fluid Resistance and Terminal Speed

Fluid Resistance

• A fluid is a gas or liquid that can flow.

• Fluid resistance (drag) acts opposite to the velocity of a body moving through a fluid.

• Drag force can depend on speed () or speed squared ():

  • (linear drag)

  • (quadratic drag)

• Terminal speed is reached when drag force equals weight:

  • For :

  • For :

Circular Motion

Dynamics of Circular Motion

• For uniform circular motion, the net force and acceleration are directed toward the center of the circle (centripetal).

• Magnitude of net force:

• If the inward force ceases (e.g., string breaks), the object moves tangentially to the circle.

• There is no real “centrifugal force” in an inertial frame; it is a fictitious force.

Summary Table: Types of Forces in Newtonian Mechanics

Key Equations

• Newton’s First Law (Equilibrium):

• Newton’s Second Law:

• Kinetic Friction:

• Static Friction:

• Drag Force (linear):

• Drag Force (quadratic):

• Centripetal Force:

Applications and Examples

• Free-body diagrams are essential for analyzing forces in all problems.

• Friction and drag must be considered in real-world applications such as vehicles, sports, and engineering.

• Apparent weight changes in accelerating systems (e.g., elevators).

• Circular motion analysis is crucial for understanding orbits, amusement park rides, and rotating machinery.