Physics Lecture 3

Announcements : 

Announcements Homework for tomorrow… (Ch. 3, Probs 13, 23, & 25) Office hours… MTWRF 11-noon

Review : 

Review Displacement Average Velocity Average Acceleration Instantaneous velocity (acceleration) is the slope of the line tangent to the curve of the position (velocity) -time graph For constant acceleration… For constant gravitational acceleration…

Chapter 3 : 

Chapter 3 Vectors & Motion in 2D

Section 3.1:Vectors and their Properties : 

Section 3.1:Vectors and their Properties Vector Magnitude & Direction i.e. - instantaneous velocity - instantaneous acceleration Scalar Magnitude only

Equality of Two Vectors : 

Equality of Two Vectors Two vectors are equal if they have the same magnitude & direction Are the vectors here equal?

Vector Addition : 

Vector Addition Given two vectors , what is ?

Graphical Techniques of Vector Addition : 

Graphical Techniques of Vector Addition “Tip-to-Tail Method” Two vectors can be added by placing the tail of the 2nd on the tip of the 1st

Multiplying a Vector by a Scalar : 

Multiplying a Vector by a Scalar Given , what is ?

Graphical Techniques of Vector Addition : 

Graphical Techniques of Vector Addition What about subtraction?

Quiz Question 1 : 

Quiz Question 1 The vector c in the diagram is equal to 1. 2. 3. 4. 5. None of these

Quiz Question 2 : 

Quiz Question 2 The magnitudes of two vectors are 12 units and 8 units, respectively. What are the largest and smallest possible values for the magnitude of the resultant vector ? 14.4 and 4 12 and 8 20 and 4 None of these

Section 3.2:Components of a Vector : 

Section 3.2:Components of a Vector where and are the components of the vector

Components of a Vector : 

Components of a Vector Notice also that…

Quiz Question 3 : 

Quiz Question 3 The angle between where and the positive x axis is: 29° 61° 151° 209° 241°

Section 3.3: Displacement, Velocity, and Acceleration in 2D : 

Section 3.3: Displacement, Velocity, and Acceleration in 2D The displacement of an object is defined as the change in its position

Velocity : 

Velocity Average velocity is the ratio of the displacement to the time interval for that displacement Velocity is tangent to the path, pointing in the direction of motion

Acceleration : 

Acceleration Average Acceleration is the ratio of the change in velocity divided by the time interval for that change in velocity is in the direction of not

Ways an Object Might Accelerate… : 

Ways an Object Might Accelerate… The magnitude of the velocity can change The direction of the velocity can change Even though the magnitude is constant Both can change

Quiz Question 4 : 

Quiz Question 4 Which of the following objects can’t be accelerating? an object moving with a constant speed an object moving with a constant velocity an object moving along a curve

Section 3.4:Motion in 2D : 

Section 3.4:Motion in 2D Projectile Motion The object moves in both the x and y directions simultaneously Object will follow the path of a parabola!

Projectile Motion continued… : 

Projectile Motion continued… The x- and y-directions of motion are completely independent of each other! Motion in the x-direction is uniform motion Motion in the y-direction is 1D free fall

Quiz Question 5 : 

Quiz Question 5 Suppose you are carrying a ball and running at constant speed, and wish to throw the ball and catch it as is comes back down. Should you: throw the ball at an angle of about 45° above the horizontal and maintain the same speed. throw the ball straight up in the air and slow down to catch it throw the ball straight up in the air and maintain the same speed?

Projectile Motion continued.. : 

Projectile Motion continued.. The Kinematic Equations are…

Serway: Prob 22 : 

Serway: Prob 22 One of the fastest recorded pitches in major-league baseball, thrown by Billy Wagner in 2003, was clocked at 101.0 mi/h. If a pitch were thrown horizontally with this velocity, how far would the ball fall vertically by the time it reached home plate, 60.5 ft away?

Projectile Motion at Various Initial Angles : 

Projectile Motion at Various Initial Angles Complementary values of the initial angle result in the same range The heights will be different The maximum range occurs at a projection angle of 45o

Velocity of the Projectile : 

Velocity of the Projectile The velocity of the projectile at any point of its motion is the vector sum of its x and y components at that point with

Quiz Question 6 : 

Quiz Question 6 As a projectile moves in its parabolic path, the velocity and acceleration vectors are perpendicular to each other everywhere along the projectile’s path at the peak of its path nowhere along its path not enough information is given

Quiz Question 7 : 

Quiz Question 7 A hunter aims his gun directly at a monkey hanging in a tree. However, as soon as the monkey sees the flash of the gun he lets go and falls to avoid the bullet. From this information we can say that: the bullet will pass over the monkey the bullet will pass below the monkey the bullet will hit the monkey people shouldn’t shoot monkeys

Demo : 

Demo Drop the rings attached to a string..

From the MCAT… : 

From the MCAT… Which of the following extremes is reached when a projectile launched at a 60 deg angle is at the highest point of its path: minimum vertical speed minimum horizontal speed maximum vertical speed maximum horizontal speed

From the MCAT… : 

From the MCAT… Two projectiles are propelled with the same initial vertical speed but with different initial horizontal speeds. If air resistance is negligible, how will their time in the air and horizontal flight distance compare? they will remain in the air different amounts of time but travel the same distance they will remain in the air different amounts of time and travel different distances they will remain in the air the same amount of time and travel the same distance they will remain in the air the same amount of time but travel different distances

Typical Projectile Motion Problem… : 

Typical Projectile Motion Problem… Approach: 1. Break problem into x & y components 1 (2D) problem -> 2 (1D) problems 2. Use 1D Kinematic Equations

Serway: Problem 26 : 

Serway: Problem 26 Tom the cat is chasing Jerry the mouse across the surface of a table 1.5 m above the floor. Jerry steps out of the way at the last second, and Tom slides off the edge of the table at a speed of 5.0 m/s. Where will Tom strike the floor, and what velocity components will he have just before he hits?

Serway: Problem 28 : 

Serway: Problem 28 An artillery shell is fired with an initial velocity of 300 m/s at 55.0º above the horizontal. To clear an avalanche, it explodes on a mountainside 42.0 s after firing. What are the x- and y-coordinates of the shell where it explodes, relative to the firing point?