PHY1301 Chapter 5 — Further application of Newton’s laws: Friction and Drag

Chapter 5: Further Application of Newton’s Laws: Friction and Drag

Introductory Information

  • Prof. Wenqing Fan (wfan7@uh.edu)

  • Due time for Homework (HW) for Chapter 4: October 1st

  • Exam 1 dates: October 2-4 at CASA

  • Topics covered: Chapters 1-4

Topics Overview

  • Frictional Forces

  • Springs

  • Drag Forces

Frictional Forces

  • Definition: Friction is a force that opposes relative motion between surfaces in contact.

  • Unlike the normal force, which is perpendicular to the contact surface, friction acts parallel to the surface.

  • Microscopic Foundation: Friction arises when microscopic atoms from the object and atoms on the facing surface collide due to surface imperfections—no surface is perfectly smooth.

Types of Friction

  1. Kinetic Friction

    • Definition: Occurs when two surfaces are in contact and moving relative to one another.

    • Equation: fk = b{k}N where

      • $f_k$ is the kinetic friction force,

      • $b_{k}$ is the Coefficient of Kinetic Friction,

      • $N$ is the Normal Force.

  2. Static Friction

    • Definition: Acts when two surfaces are in contact and there is no relative motion between the objects.

    • Behavior: Adjusts itself to cancel the applied force parallel to the surfaces; can vary from 0 to a maximum value.

    • Equation: 0 <= fs <= f{s, ext{max}} where

      • $f{s, ext{max}} = b{s}N$

      • $b_{s}$ is the Coefficient of Static Friction.

Examples of Frictional Forces

  1. Static Friction Example:

    • Scenario: You want to move a 51 kg crate across a level floor. To start moving the crate requires pulling with a horizontal force of 230 N.

      • Question (a): What is the coefficient of static friction?

  2. Kinetic Friction Example:

    • Continuation: Once the crate starts moving, a force of 200 N is sufficient to keep it moving at constant velocity.

      • Question (b): What is the coefficient of kinetic friction?

  3. Rest Friction Question:

    • Additional Scenario: For the same crate, if a 50 N horizontal force is applied while it remains at rest.

      • Question (c): What is the friction force?

  4. Inclined Force Example:

    • A crate is pulled upward at a 30° angle above the horizontal while sliding across the floor with a coefficient of kinetic friction of 0.40.

    • What is the force required to maintain constant velocity?

  5. Sliding Crate on a Truck Bed:

    • A crate weighing 95.0 kg stays put on a tilted truck bed until the angle exceeds 23.3°.

      • Find the coefficient of static friction above this angle.

  6. Acceleration Calculation:

    • Once sliding begins, calculate the acceleration with a tilt angle of 23.3° and a coefficient of kinetic friction of 0.40.

  7. Toboggan Sliding:

    • A toboggan slides down a slope at angle α with coefficient of kinetic friction $b_k$. Find the angle's dependency to maintain constant velocity.

  8. Pulley System:

    • Analyze a system of a block with mass m1 = 4.00 kg and a ball with mass m2 = 7.00 kg connected by a light string. Determine the acceleration and the tension in the string with a coefficient of kinetic friction of 0.40.

  9. Kinetic vs Static Friction on Tires:

    • A car drives with freely rolling tires—determine if the friction is kinetic or static.

  10. Box and Force Application:

    • A box has a weight of 100 N on the floor with a static friction coefficient of 0.4, being pulled horizontally with a tension of 30 N. Determine the direction of the movement of the box.

Springs and Hooke's Law

  • Definition: Hooke's Law describes the force exerted by an ideal spring when compressed or stretched from its equilibrium position.

  • Equation: Fspring=kriangleLF_{spring} = k riangle L where:

    • $k$ is the Spring Constant (Force Constant),

    • $ riangle L$ is the distance the spring is displaced from its equilibrium position.

  • Directionality: The force exerted is directed towards the equilibrium position, opposite to the displacement.

  • Formal Equation: F=−kxF = -kx or Fextspring=−kriangleLF_{ ext{spring}} = -k riangle L

Examples of Springs

  1. Spring Stretching Example:

    • If a mass is gently hung on a spring with a spring constant of 250 N/m and stretches 0.10 m, calculate the mass.

  2. Compression Example:

    • A 2 kg block compresses a spring (spring constant = 500 N/m) on a floor where static friction coefficient = 0.8. Find the maximum compression before motion.

  3. Box on an Inclined Plane Example:

    • As a box rests on a board that is lifted, find out why it begins to slide when the angle increases.

Drag Forces

  • Definition: The Drag Force acts opposite to an object's motion through a fluid (air or water) often referred to as air resistance.

  • Importance: Relevant in both everyday scenarios (e.g., vehicles) and biological contexts (micro-organisms in water).

  • Factors Influencing Drag: The drag force's magnitude depends on the object's speed, mass, and the nature of the medium.

Drag Forces at High Speed

  • Equation: The drag force in high-speed motion is calculated as: FD=rac12ChoAv2F_D = rac{1}{2}C ho A v^2 where:

    • $C$ = drag coefficient,

    • $ ho$ = fluid density,

    • $A$ = cross-sectional area of the object facing the fluid,

    • $v$ = speed of the object.

  • Terminal Speed:

    • An object reaches terminal speed when the drag force equals the applied force.

Examples of Drag Force

  1. Skydiving Example:

    • A 75 kg skydiver and a 0.020 kg pet mouse are falling. Calculate their terminal speeds using the equation FD=rac12C<br>hoAv2F_D = rac{1}{2}C<br>ho A v^2 with

    • Drag Coefficient for cylinder 1.1, and air density 1.2 kg/m³.

  2. Low Speed Drag Forces:

    • At low speeds, the drag force is governed by Stokes' Law:
      FS=6racextπrhetavextfluiddensityF_S = 6 rac{ ext{π}r heta v}{ ext{fluid density}} where r is the object's radius and η is fluid viscosity. This shows relevance for small masses, such as:

    • Micro-organisms,

    • Pollen,

    • Dust particles,

    • Raindrops,

    • A slowly fallen ball in a viscous medium.

Concluding Notes

  • Understanding friction, drag forces, and Hooke's law is crucial for solving real-world physics problems related to motion and forces.

  • Ensure comprehension of the equations derived and their application in practical scenarios.