Chapter 10: Motion

Motion Problem: We need a reference point... Is your desk moving? nonmoving point from which motion is measured

Motion Reference point Motion Motion Change in position in relation to a reference point. Reference point Motion

You have mistakenly set yourself as the reference point. Motion Problem: You are a passenger in a car stopped at a stop sign. Out of the corner of your eye, you notice a tree on the side of the road begin to move forward. You have mistakenly set yourself as the reference point.

Displacement Displacement: the change in position (location) of an object Differences between distance and displacement Distance can be a straight line but doesn’t have to be Displacement MUST be a straight line Displacement must be in a particular direction

v d t Speed & Velocity Speed rate of motion distance traveled per unit time SI Unit: m/s

Speed & Velocity Instantaneous Speed Average Speed speed at a given instant Average Speed

Speed can be measured at a certain point in time. Instantaneous Speed Speed can be measured at a certain point in time. For instance, if you are driving, your speedometer may read 30 mi/hr. You don’t have to drive for an hour for your car to know this – your speed is instantaneous.

It depends on the storm’s direction! Speed & Velocity Problem: A storm is 10 km away and is moving at a speed of 60 km/h. Should you be worried? It depends on the storm’s direction!

Speed & Velocity Velocity speed in a given direction can change even when the speed is constant! = DISPLACEMENT / TIME

velocity = displacement ÷ time Velocity is a measure of an object’s SPEED and DIRECTION. Velocity is measured by: velocity = displacement ÷ time v = d/t

Velocity & Displacement If you run around a circular track and end up in the same position you started, your displacement is 0. So is your velocity: v = 0/time, so v=0

Acceleration is the rate of change of velocity Acceleration occurs when an object: Speeds up Slows down Changes direction Acceleration is the rate of change of velocity

t a a: acceleration vf: final velocity vi: initial velocity t: time vf - vi t Acceleration Acceleration the rate of change of velocity change in speed or direction SI UNIT: m/s2 a: acceleration vf: final velocity vi: initial velocity t: time

Positive acceleration “speeding up” Negative acceleration “slowing down”

t d v d = 100 m v = d ÷ t t = 20 s v = (100 m) ÷ (20 s) v = ? Calculations Your neighbor skates at a speed of 4 m/s. You can skate 100 m in 20 s. Who skates faster? GIVEN: d = 100 m t = 20 s v = ? WORK: v = d ÷ t v = (100 m) ÷ (20 s) v = 5 m/s You skate faster! v d t

t a a = (vf - vi) ÷ t t = 3 s a = (32m/s - 10m/s) ÷ (3s) vf = 32 m/s Calculations A roller coaster starts down a hill at 10 m/s. Three seconds later, its speed is 32 m/s. What is the roller coaster’s acceleration? GIVEN: vi = 10 m/s t = 3 s vf = 32 m/s a = ? WORK: a = (vf - vi) ÷ t a = (32m/s - 10m/s) ÷ (3s) a = 22 m/s ÷ 3 s a = 7.3 m/s2 a vf - vi t

t d v v = 330 m/s t = d ÷ v d = 1km = 1000m t = (1000 m) ÷ (330 m/s) Calculations Sound travels 330 m/s. If a lightning bolt strikes the ground 1 km away from you, how long will it take for you to hear it? GIVEN: v = 330 m/s d = 1km = 1000m t = ? WORK: t = d ÷ v t = (1000 m) ÷ (330 m/s) t = 3.03 s v d t

t a t = ? t = (vf - vi) ÷ a t = (0m/s-30m/s)÷(-3m/s2) vf = 0 m/s Calculations How long will it take a car traveling 30 m/s to come to a stop if its acceleration is -3 m/s2? GIVEN: t = ? vi = 30 m/s vf = 0 m/s a = -3 m/s2 WORK: t = (vf - vi) ÷ a t = (0m/s-30m/s)÷(-3m/s2) t = -30 m/s ÷ -3m/s2 t = 10 s a vf - vi t

Distance and Time are variables! Graphing Speed Distance and Time are variables! Independent Variable: time Dependent Variable: distance

Graphing Constant Speed

Graphing Changing Speed

Graphing Changing Speed

Graphing Changing Speed

slope = speed steeper slope = straight line = faster speed flat line = * 07/16/96 Graphing Motion Distance-Time Graph A B slope = steeper slope = straight line = flat line = speed faster speed constant speed no motion *

Graphing Motion Who started out faster? A (steeper slope) Distance-Time Graph A B Who started out faster? A (steeper slope) Who had a constant speed? A Describe B from 10-20 min. B stopped moving Find their average speeds. A = (2400m) ÷ (30min) A = 80 m/min B = (1200m) ÷ (30min) B = 40 m/min

Acceleration is indicated by a curve on a Distance-Time graph. Graphing Motion Distance-Time Graph Acceleration is indicated by a curve on a Distance-Time graph. Changing slope = changing velocity

no accel. (constant velocity) Graphing Motion Speed-Time Graph slope = straight line = flat line = acceleration +ve = speeds up -ve = slows down constant accel. no accel. (constant velocity)

Graphing Motion Specify the time period when the object was... Speed-Time Graph Specify the time period when the object was... slowing down 5 to 10 seconds speeding up 0 to 3 seconds moving at a constant speed 3 to 5 seconds not moving 0 & 10 seconds

Fkick Fgrav Force Force a push or pull that one body exerts on another What forces are being exerted on the football? Fkick Fgrav

Fnet Ffriction Fpull N W Force Net Force unbalanced forces that are not opposite and equal velocity changes (object accelerates) Fnet Ffriction Fpull N W

Net Force The net force on an object is the sum of all the forces on the object Net force = F1 + F2 + F3 + … When gravity acts on an object, but the object does not fall, there is a normal force pushing up on the object Fnormal + Fgravity = 0

Force Balanced Forces forces acting on an object that are opposite in direction and equal in size no change in velocity

Balanced Forces If an object is not accelerating, either: 1. no forces are acting on it, or 2. all the forces on it balance 2 forces are balanced if they have equal sizes but opposite directions

Taken from “The Physics Classroom” © Tom Henderson, 1996-2001. ConcepTest 1 TRUE or FALSE? The object shown in the diagram must be at rest since there is no net force acting on it. FALSE! A net force does not cause motion. A net force causes a change in motion, or acceleration. Taken from “The Physics Classroom” © Tom Henderson, 1996-2001.

Forces Remember – an object can be moving with CONSTANT VELOCITY and the net force would equal 0. The object must ACCELERATE, or CHANGE VELOCITY when a net force is applied

Unbalanced Forces If an object is being pushed or pulled, the changing motion is caused by forces The forces are unbalanced They may have different sizes, or be in the same direction

Force Diagrams Force diagrams use arrows to represent the sizes, directions, and types of forces on an object The object is usually represented by a box

force that opposes motion between 2 surfaces depends on the: Friction Friction force that opposes motion between 2 surfaces depends on the: types of surfaces force between the surfaces

between rough surfaces Friction Friction is greater... between rough surfaces when there’s a greater force between the surfaces (e.g. more weight) Pros and Cons?

Static vs Kinetic Friction Static Friction: The force that resists the initiation of sliding motion between two surfaces that are in contact and at rest Friction between stationary (non-moving) surfaces The force that prevents a car wheel from slipping as it rolls on the ground. Even though the wheel is in motion, the patch of the tire in contact with the ground is stationary relative to the ground Kinetic Friction: The force that opposes the movement of two surfaces that are in contact and are sliding over each other Friction between moving surfaces

Types of Kinetic Friction Sliding Friction Rolling Friction When objects slide past each other Examples: Sliding glass or screen door If a round object rolls over a flat surface Usually less than sliding friction

Fluid Friction Any object moving through a fluid like air Example: when air slides past a car; can be minimized by smooth surfaces Air resistance opposes motion Air resistance to the car’s motion increases as the car travels faster because more of air must be moved each second

Friction Ways to Reduce Ways to Increase Ways to Reduce Harmful/ Unwanted Friction Ways to Increase Helpful Friction Ways to Reduce Use of lubricants (oil, wax, and grease) Motor oil on engine parts Replacing sliding friction with rolling friction Ball bearing in between wheels and axels of bikes Make Surfaces Smoother Ways to Increase Make surfaces rougher Sand on ice Increase the force between surfaces Pressing down on sponge to clean dishes

a.k.a. “fluid friction” or “drag” Air Resistance Air Resistance a.k.a. “fluid friction” or “drag” force that air exerts on a moving object to oppose its motion depends on: speed surface area shape density of fluid

Fair Fgrav Terminal Velocity Air Resistance Terminal Velocity maximum velocity reached by a falling object reached when… Fgrav = Fair Fair no net force  no acceleration  constant velocity Fgrav

Animation from “Multimedia Physics Studios.” Air Resistance Terminal Velocity increasing speed  increasing air resistance until… Fair = Fgrav Animation from “Multimedia Physics Studios.”

Animation from “Multimedia Physics Studios.” Air Resistance Falling with air resistance heavier objects fall faster because they accelerate to higher speeds before reaching terminal velocity Fgrav = Fair larger Fgrav  need larger Fair  need higher speed Animation from “Multimedia Physics Studios.”

Without air resistance, everything would fall at the same speed! A bowling ball would hit the same time as a ping pong ball; a car and a skateboard; etc

follows a parabolic path called a trajectory Projectile Motion Projectile any object thrown in the air acted upon only by gravity follows a parabolic path called a trajectory has horizontal and vertical velocities PROJECTILE MINI-LAB

Projectile Velocities Projectile Motion Projectile Velocities Horizontal and vertical velocities are independent of each other!

Projectile Motion Horizontal Velocity depends on inertia remains constant Vertical Velocity depends on gravity accelerates downward at 9.8 m/s2

Animation from “Multimedia Physics Studios.” ConcepTest A moving truck launches a ball vertically (relative to the truck). If the truck maintains a constant horizontal velocity after the launch, where will the ball land (ignore air resistance)? A) In front of the truck B) Behind the truck C) In the truck C) In the truck. The horizontal velocity of the ball remains constant and is unaffected by its vertical motion. Animation from “Multimedia Physics Studios.”