End-of-the-Year Project Vectors and Forces in Two Dimensions.

Slides:



Advertisements
Similar presentations
Chapter 3: Two Dimensional Motion and Vectors
Advertisements

CH. 4 Vector Addition Milbank High School. Sec. 4.1 and 4.2 Objectives –Determine graphically the sum of two of more vectors –Solve problems of relative.
Forces in Two Dimensions Trig Review: Sin, Cos, and Tan only work in a RIGHT TRIANGLE. SOHCAHTOA,an ancient Hawaiian word.
Kinematics Chapters 2 & 3.
Graphical Analytical Component Method
Vector addition, subtraction Fundamentals of 2-D vector addition, subtraction.
Chapter 5 Forces in Two Dimensions Vectors Again! How do we find the resultant in multiple dimensions? 1. Pythagorean Theorem- if the two vectors are at.
Vectors. Vectors and Direction Vectors are quantities that have a size and a direction. Vectors are quantities that have a size and a direction. A quantity.
Vectors - Fundamentals and Operations A vector quantity is a quantity which is fully described by both magnitude and direction.
Physics: Chapter 3 Vector & Scalar Quantities
Method #2: Resolution into Components. Solving Vector Problems using the Component Method  Each vector is replaced by two perpendicular vectors called.
Scalar & Vector Quantities. SCALAR QUANTITIES Described by a single number and unit of measurement. Gives the magnitude (size) Examples Mass = 20 g Time.
Unit 1 – Physics Math Algebra, Geometry and Trig..
Vector Mathematics Physics 1.
Kinematics in Two or Three Dimensions; Vectors
Forces in 2D Chapter Vectors Both magnitude (size) and direction Magnitude always positive Can’t have a negative speed But can have a negative.
Vectors Chapter 3, Sections 1 and 2. Vectors and Scalars Measured quantities can be of two types Scalar quantities: only require magnitude (and proper.
Chapter 2 Mechanical Equilibrium I. Force (2.1) A. force– is a push or pull 1. A force is needed to change an object’s state of motion 2. State of motion.
CHAPTER 5 FORCES IN TWO DIMENSIONS
Chapter 3 Kinematics in Two Dimensions; Vectors. Units of Chapter 3 Vectors and Scalars Addition of Vectors – Graphical Methods Subtraction of Vectors,
Vectors. Vector and Scalar quantities Scalar quantities have size or magnitude, but a direction is not specified. (temperature, mass, speed, etc.) Vector.
Vector & Scalar Quantities
Scalars and Vectors A scalar quantity is one that can be described by a single number: temperature, speed, mass A vector quantity deals inherently with.
VectorsVectors. What is a vector quantity? Vectors Vectors are quantities that possess magnitude and direction. »Force »Velocity »Acceleration.
Vector Basics. OBJECTIVES CONTENT OBJECTIVE: TSWBAT read and discuss in groups the meanings and differences between Vectors and Scalars LANGUAGE OBJECTIVE:
Physics Quantities Scalars and Vectors.
Chapter 3 Projectile Motion. What does this quote mean? “Pictures are worth a thousand words.”
Laws of Motion and Force Diagrams Many of the following slides are from the online physics site:
Projectile Motion. Vectors and Scalars A Vector is a measurement that has both a magnitude and a direction. Ex. Velocity, Force, Pressure, Weight A Scalar.
Physics: Problem Solving Chapter 4 Vectors. Physics: Problem Solving Chapter 4 Vectors.
Vector components and motion. There are many different variables that are important in physics. These variables are either vectors or scalars. What makes.
Vectors. A vector is a quantity and direction of a variable, such as; displacement, velocity, acceleration and force. A vector is represented graphically.
Chapter 4 Vectors The Cardinal Directions. Vectors An arrow-tipped line segment used to represent different quantities. Length represents magnitude. Arrow.
Kinematics in Two Dimensions. Section 1: Adding Vectors Graphically.
Vectors.
Vectors- Motion in Two Dimensions Magnitudethe amount or size of something Scalara measurement that involves magnitude only, not direction EX: mass, time,
Chapter 3 Kinematics in Two Dimensions; Vectors 1.
CP Vector Components Scalars and Vectors A quantity is something that you measure. Scalar quantities have only size, or amounts. Ex: mass, temperature,
Vector & Scalar Quantities. Characteristics of a Scalar Quantity  Only has magnitude  Requires 2 things: 1. A value 2. Appropriate units Ex. Mass: 5kg.
Vectors Physics Book Sections Two Types of Quantities SCALAR Number with Units (MAGNITUDE or size) Quantities such as time, mass, temperature.
Physics I Unit 4 VECTORS & Motion in TWO Dimensions astr.gsu.edu/hbase/vect.html#vec1 Web Sites.
Scalars and Vectors Physical Quantities: Anything that can be measured. Ex. Speed, distance, time, weight, etc. Scalar Quantity: Needs only a number and.
Physics and Physical Measurement Topic 1.3 Scalars and Vectors.
Component Vectors Vectors have two parts (components) –X component – along the x axis –Y component – along the y axis.
Vectors Chapter 4. Vectors and Scalars What is a vector? –A vector is a quantity that has both magnitude (size, quantity, value, etc.) and direction.
Chapter 4: How do we describe Vectors, Force and Motion? Objectives 4 To note that energy is often associated with matter in motion and that motion is.
Vector Basics Characteristics, Properties & Mathematical Functions.
Chapter 1-Part II Vectors
VECTORS ARE QUANTITIES THAT HAVE MAGNITUDE AND DIRECTION
Characteristics, Properties & Mathematical Functions
Basic Trigonometry We will be covering Trigonometry only as it pertains to the right triangle: Basic Trig functions:  Hypotenuse (H) Opposite (O) Adjacent.
Question 3 A car of mass 800kg is capable of reaching a speed of 20m/s from rest in 36s. Work out the force needed to produce this acceleration. m = 800kg v.
3.1 Two Dimensions in Motion and Vectors
Vectors Unit 4.
Calculate the Resultant Force in each case… Extension: Calculate the acceleration if the planes mass is 4500kg. C) B) 1.2 X 103 Thrust A) 1.2 X 103 Thrust.
Introduction to Vectors
Vectors- Motion in Two Dimensions
Vectors.
7.1 Vectors and Direction 1.
Chapter 3 Projectile Motion
Chapter 3.
VECTORS Level 1 Physics.
Forces in Two Dimensions
Vectors.
VECTORS ARE QUANTITIES THAT HAVE MAGNITUDE AND DIRECTION
Vectors.
Math Review.
Vectors.
VECTORS Level 1 Physics.
Introduction to Vectors
Presentation transcript:

End-of-the-Year Project Vectors and Forces in Two Dimensions

Definitions Vector: a quantity possessing both magnitude and direction, represented by an arrow the direction of which indicates the direction of the quantity and the length of which is proportional to the magnitude Force: a dynamic influence that changes a body from a state of rest to one of motion or changes its rate of motion. The magnitude of the force is equal to the product of the mass of the body and its acceleration

One Dimension In one dimension, vectors can be easily added. 10m 6m + = 1m + 8m = Not drawn to scale

What's the use? It may look like just lines, but really it's more than that. Vectors aren't just for distances, but anything with direction and magnitude. For example, there are force vectors and velocity vectors These can be used to represent forces on an object. 20N15N Not drawn to scale

It's simple in one dimension... Vector addition is very simple in one dimension, basically just an addition problem. In two dimensions, it gets more complicated. In two dimensions, there are a few ways to add vectors  Head-to-tail method  Pythagorean theorem  Trigonometry

Head-to-Tail Method When vectors are drawn perfectly in proportion and you have a ruler, an easy way to add vectors is head-to-tail. (note: this works for any number of vectors at any angle)‏ Scale: 1cm=1m

Pythagorean Theorem The Pythagorean theorem is something we've known for years and has many applications. It can be used to add two vectors that are at right angles to each other Not drawn to scale 15N 13N a²+b²=c² c=√(a²+b²)‏

Trig Trig is fun! Remember SOH CAH TOA We can determine the direction of the resultant with trig

Trig examples 27N Not drawn to scale 13N Θ Tan Θ=opp/adj Θ=tan^(-1) (opp/adj)‏ Θ=tan^(-1) (27/13)=

Components Components make up vectors that are at angles. This is basically the opposite of adding vectors to find a resultant 7N 40° SOHCAHTOA Not drawn to scale

Inclined planes One of the uses of finding components is figuring out forces on an object on an inclined plane

Inclined planes example F w =mg g=9.8m/s² Mass is 85kg F w =(9.8)(85)=833N F parallel =F w (sin Θ)‏ F perpendicular =F w (cos Θ)‏ 34° Not drawn to scale F parallel =(833)(sin 34°)=440.7 F perpendicular =(833)(cos 34°)=-706.9

In conclusion... We always ask “how does this apply to life?” about math... solving seemingly endless triangles in the math book may seem useless...well it is unless you realize what it actually means and what its connection is to the study of motion and forces.