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# Physics 0110 Video Module 3 Notes PHYS 0110

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This 5 page Class Notes was uploaded by Tripsupstairs on Saturday September 17, 2016. The Class Notes belongs to PHYS 0110 at University of Pittsburgh taught by Matteo Broccio in Fall 2016. Since its upload, it has received 10 views. For similar materials see Introduction to Physics 1 in Physics at University of Pittsburgh.

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Date Created: 09/17/16

Video Module 3 Notes Until now, we have been dealing with motion in mostly one dimension, and some in two dimensions. 3.1 Motion in two dimensions 3.1.1 Constant velocity in 2 dimensions (1:41) • In two dimensions velocity is broken into two components which can be expressed using the same equation for constant velocity in one dimension • The velocity vector is represented by: v = vx^ + v y^ (1) • Where motion in the x and y dimensions can be written respectively as: x(t) = x0+ v x and y(t) = y +0v t y (2) • see 3:18 in video 3.1 for the bug example 3.1.2 Constant Acceleration (6:00 3.1) n two dimensions acceleration is also broken into two components which can be expressed using familiar equations. • The acceleration vector is represented by ~a = ax^ + a y^ (3) • Velocity in two dimensions is written again by using two separate one-dimensional equations vx(t) = vx + axt and vy(t) = v0y + ayt (4) 3.2 Projectile Motion A projectile is any object thrown. Any object thrown near the earth’s surface will feel the pull of gravity 1 3.2.1 Motion of a projectile If we neglect air resistance, the motion of a projectile is represented through the superposition of the following independent motions 1. horizontal motion with constant velocity, which is the initial horizonal velocity v , 0x where ▯ 0s the angle formed between the initial velocity vector, v and0(in most cases) the ground. v0 = v 0os▯ 0 (5) x 2. A vertical motion with intital vertical velocity v , 0y v0y = v 0in▯ 0 (6) and a constant downward acceleration due to gravity. ay= ▯g (7) where a iy the acceleration in the y direction, and ▯g represents the constant down- 2 ward acceleration towards the earth due to gravity, ▯9:8m=s 3.2.2 Writing Equations Projectile motion can be represented through two separate one-dimensional equations (3.2a 2:00) The horizontal component of motion takes the equation relating position and constant velocity as a function of time . x(t) = x + (v cos▯ ) ▯t (8) |{z} |{z} | 0 {z 0} horiz. posn. at time titial horiz. posn. initial horiz. 0x).(v Where the position on the x axis at time t, x(t) is equal to the initial position on the x axis x 0lus the x-component of the initial velocity vector v (v co0x ) 0ultip0ied by time. The vertical component of motion is also a simple modi▯cation of the equation relating position, velocity, and constant acceleration as a function of time. 1 2 y(t) = |{z} + (v0sin▯ 0 ▯t ▯ gt (9) |{z} | {z } 2 vert. posn. at time tnitial vert. poinitial vert. ye).(v Where the position on the y axis at time t, y(t) is equal to the initial y-position y 0 plus the y-component of the initial velocity vector v ;(v0yin▯ 0 mult0plied by time, 1 plus 2times the acceleration due to gravity in the negative y-direction, ▯g times time squared t . an example can be found at 2:39 of video 3.2a 2 3.2.3 Time of Flight • The time of ight, t fs the total time the projectile spends in the air • It is determined only by the vertical component of initial velocity, v (0:100yvideo 3.2b) • Since the vertical position of the object when it hits the ground is 0, then the y- component of motion at the time an object hits the ground can be written as 1 2 | ={z(tf} = (| 0i{z )0} |{z} ▯ gtf (10) 2 ▯nal vert. posn. at landing 0y ▯nal time Where both initial vertical position and ▯nal position are equal to 0, assuming the projectile started and landed on the ground. 3.2.4 Horizontal Range of Motion • A projectile will move with a constant hotizontal velocity v ,0xeglecting air resistance • R represents the horizontal range of motion and is equal to the horizontal position of the projectile when it returns to the ground at t f 2v 0y R = x(t )f= v t 0x f = v 0x▯ (11) g Or, without the variable of time, 2 R = 2v0sin▯ 0os▯ 0 (12) g Which can be simpli▯ed with trig using: 2sin▯ cos▯ = sin2▯ v2 sin2▯ R = 0 0 (13) g THIS ENDS THE MATERIAL THAT WILL BE COVERED ON EXAM 1 3.3 Newton’s First Law Newton’s First Law: An object at rest will remain at rest, and an object in motion will remain in motion at a constant velocity (at the same speed and direction), unless acted upon by an external net force. (3:53) • an object at rest is a special case of an object at constant velocity, where the velocity is 0. 3 • External forces include friction, gravity, and air resistence (really, friction from the air), so this law is best observed in a vaccum (like outer space). Inertia: The natural tendency for an object to remain at rest, or continue in a straight line at a constant velocity (5:07) Mass: the quantitative measure of an object’s inertia (SI unit is kilograms, kg.) 3.3.1 Frames of Reference Frame of Reference: The coordinate system from which we measure position, velocity, and acceleration of moving objects; the point of observation (6:17) Intertal Frame of Referece: a coordinate system in which Newton’s ▯rst laws are valid (6:39) • For example, your room is an inertal frame of reference because things in your room obey Newton’s ▯rst law Accelerating Frame of Reference: A frame of reverence where the Newton’s ▯rst law is violated (8:05) 3.4 Newton’s Second Law Newton’s Second Law states that the net force needed to change an object’s velocity is proportional to the object’s mass (or inertial mass) and its desired acceleration. F = m ▯ a = m ▯ ▯v~ (14) |{z} |{z} |{z} ▯t force mass acceleration Newton (N): The unit for force, F, which is kg ▯=s2. Because mass is a positive scalar, force F is always parallel to acceleration a Principle of Lineaear Superposition: If several forces are acting on an object simulta- neously, the net force netis the vector sum of each individual force. (4:35, 3.4a) Xn Fi= F~net (15) i=1 F net F 1 F +2F ::3F ~n (16) Mechanical Equilibrium: Occurs when the sum of the forces acting simultaneously on an object is equal to zera = 0 (7:23, 3.4a). Xn Fi= F~net= 0 (17) i=1 4 3.5 Newton’s Third Law Newton’s third law states that if an object exerts a force on another object, the second object will exert an equal and opposite force on the ▯rst object.(0:35 3.5) • For every action, there is an equal and opposite reaction. HOWEVER, action and reaction act on two separate objects, so they cannot balance each other • If two objects push against each other, the force felt by each object is equal, regardless of a di▯erence in mass (Ice skater example at 3:06) • see 2:34 in video 3.5 for an example 5

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