Motion Forces II Describing Motion Speed Velocity u

Motion & Forces II. Describing Motion Speed & Velocity u Acceleration u u

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

Motion

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

Reference Point

A. 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.

Motion You can describe the direction of an object in motion with a reference direction. north, south, east, west, up, or down

Distance Displacement

Distance – the length traveled by an object Practice – What is the distance? ◦ Liz walks 4 km North, then 3 km East ◦ Xavier runs 30 m East, then runs 40 meters West ◦ Aaron jogs 4 km East, 4 km North, 4 km West, and 4 km South ◦ Answers: 7 km ; 70 meters ; 16 km

Distance It is a scalar quantity Scalar quantities are fully described by a magnitude (or number value) alone. I travelled a distance of 100 miles. No direction needs to be stated.

Distance vs. Displacement Distance – length Displacement – distance AND direction of a movement from the starting point

Displacement vector quantity such as displacement is direction-aware When an object changes its direction of motion, displacement takes this direction change into account; heading the opposite direction effectively begins to cancel whatever displacement there once was.

Displacement If an object moves in a single direction, the displacement equals the distance + the direction 4 km start here total displacement = 4 km North

Displacement If an object moves in two opposing directions, the displacement is the difference between the two. total distance = 4 + 3 = 7 km 4 km start here 3 km Displacement can be positive or negative. A negative direction can be either the opposite of the original movement, or can follow the sign of a typical graph [North/East vs South/West] total displacement = 4 km North + -3 km South = 1 km North (of original starting point)

Practice problems Distance and displacement

Displacement – cont’d If an object moves in two directions, a triangle will be formed. If the angle is 90º , use a 2 + b 2 = c 2 to solve. 3 km 4 km start here displacem ent

Displacement – cont’d If an object moves in two directions, a triangle will be formed. If the angle is 90º , use a 2 + b 2 = c 2 to solve. 3 km displacement = 4 km 5 km 42 + 3 2 = c 2 = (16) + (9) = 25 start here c 2 = √(25) c = 5 km

Displacement – cont’d Displacement can be given in: ◦ units and direction example: 10 meters West A person jogs 30 meters East then turns around and jogs 40 meters West displacement = 10 meters West

Displacement Practice – What is the displacement? ◦ Liz walks 8 km North, then 3 km East ◦ 8. 5 km Northeast displacement ◦ Aaron jogs 4 km East, 4 km North, 4 km West, and 4 km South ◦ 0 meters displacement from the start

B. Speed & Velocity Speed ◦ rate of motion ◦ distance traveled per unit time d v t

B. Speed & Velocity Instantaneous Speed Average Speed ◦ speed at a given instant

B. 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!

B. Speed & Velocity ◦ speed in a given direction ◦ can change even when the speed is constant!

Practice Find the velocity in m/s of a swimmer who swims 110 m toward the shore in 72 s. v =d t v = 110 m = 1. 5 m/s toward 72 s shore

C. Acceleration vf - vi Acceleration ◦ the rate of change of velocity ◦ change in speed or direction a: v f: v i: t: a t acceleration final velocity initial velocity time

C. Acceleration Positive acceleration “speeding up” Negative acceleration “slowing down”

Other ways to accelerate Acceleration can also be a change in direction. You standing on Earth (changing direction). You are skiing down a hill and turning to avoid all the snowboarders falling in front of you. (velocity changed and you changed directions) You are slowing your car for a stop sign. (decreased in speed along the road – negative acceleration)

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

D. 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: WORK: l vi = 10 m/s t=3 s vf = 32 m/s vf - vi a=? a t a = ( v f - v i) ÷ t a = (32 m/s - 10 m/s) ÷ (3 s) a = 22 m/s ÷ 3 s a = 7. 3 m/s 2

D. 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: WORK: l v = 330 m/s t=d÷v d = 1 km = 1000 m t = (1000 m) ÷ (330 m/s) t=? t = 3. 03 s = 3 s d v t

D. Calculations How long will it take a car traveling 30 m/s to come to a stop if its acceleration is -3 m/s 2? GIVEN: WORK: l t=? vi = 30 m/s vf = 0 m/s a = -3 m/s 2 t = (vf - vi) ÷ a t = (0 m/s-30 m/s)÷(-3 m/s 2) vf - vi a t t = -30 m/s ÷ -3 m/s 2 t = 10 s

E. Graphing Motion Distance-Time Graph A B slope =speed steeper slope = faster speed straight line = constant speed flat line = no motion

E. Graphing Motion 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 = (2400 m) ÷ (30 min) A = 80 m/min ◦ B = (1200 m) ÷ (30 min) B = 40 m/min

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

E. Graphing Motion Velocity-Time Graph slope =acceleration § +v = speeds up § -v = slows down straight line = constant accel. flat line = no accel. (constant velocity)

E. Graphing Motion Specify the time period when the object was. . . slowing down ◦ 8 to 10 seconds speeding up ◦ 3 to 5 seconds moving at a constant speed ◦ 5 to 8 seconds

Motion & Forces III. Defining Force Newton’s First Law u Friction u u

Balanced and Unbalanced forces

A. Force ◦ Anything that changes the state of rest or motion of an object. It has a magnitude and a direction. ◦ What forces are being exerted on the football? Fkick Fgrav

Force Net force the combination of all the forces acting on an object

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

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

Balanced Forces Subtract opposite forces to find net force on an object. Since these two forces are of equal magnitude and in opposite directions, they balance each other. The book is said to be at equilibrium. There is no unbalanced force acting upon the book and thus the book maintains its state of motion.

The force of gravity pulling downward and the force of the table pushing upwards on the book are of equal magnitude and opposite directions. These two forces balance each other. Yet there is no force present to balance the force of friction. As the book moves to the right, friction acts to the left to slow the book down.

Free body diagrams Free-body diagrams are diagrams used to show the relative magnitude (strength) and direction of all forces acting upon an object in a given situation. The size of the arrow in a free-body diagram is shows the magnitude of the force. The direction of the arrow reveals the direction in which the force acts.

Free body diagrams It is customary in a free-body diagram to represent the object by a box or a small circle and to draw the force arrow from the center of the box or circle in an outward direction.

Free body diagrams F = force Ffrict = friction Fgrav = gravity Ftens = tension Fnorm = normal force Fapp = applied force Fair = air resistance

Example Object lies motionless on a surface.

Example A rightward force is applied to a book in order to move it across a desk at a constant velocity. Consider frictional forces. Neglect air resistance.

Example Object slows due to friction (rough surface).

Example An object is suspended from the ceiling. A new force is tension.

Example A flying squirrel is gliding (no wing flaps) from a tree to the ground at constant velocity. Consider air resistance. A new force is air resistance. It pushes an object up.

http: //www. mrwaynesclass. com/freebodies/r eading/index 01. html Free body diagrams with movement

Resultant forces A stationary object remains stationary if the sum of the forces acting upon it - resultant force is zero. A moving object with a zero resultant force keeps moving at the same speed and in the same direction.

Resultant forces If the resultant force acting on an object is not zero, a stationary object begins to accelerate in the same direction as the force. A moving object speeds up, slows down or changes direction.

Resultant forces Add forces going in the same direction. Subtract forces going in opposite directions.

Resultant Forces http: //physicsnet. co. uk/gcse-physics/the-effects-offorces-resultant-force-and-motion/

Concep. Test 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.

https: //www. youtube. com/watch? v=Vut. Ax 3 R DFb. I

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

Friction is greater when - a surface is rough (not smooth) - an object moves faster

Friction Static Friction: friction between surfaces that are stationary Kinetic Friction: friction between moving surfaces The force necessary to make a stationary object start moving is usually greater than the force needed to keep it moving.

Kinetic Friction How can a car minimize its fluid friction? smooth surface – wax car surface shape of the car -streamlining

http: //www. mrwaynesclass. com/freebodies/r eading/index 01. html Free body diagrams with movement

Chapter 11 Newton’s Laws

B. Newton’s First Law of Motion ◦ An object at rest will remain at rest and an object in motion will continue moving at a constant velocity unless acted upon by a net force.

B. Newton’s First Law of Motion ◦ “Law of Inertia” Inertia ◦ tendency of an object to resist any change in its motion ◦ increase mass increase inertia ◦ Think of the paper and book activity.

Concep. Test 2 You are a passenger in a car and not wearing your seat belt. Without increasing or decreasing its speed, the car makes a sharp left turn, and you find yourself colliding with the right-hand door. Which is the correct analysis of the situation? . . .

Concep. Test 2 1. Before and after the collision, there is a rightward force pushing you into the door. 2. Starting at the time of collision, the door exerts a leftward force on you. 3. both of the above 4. neither of the above 2. Starting at the time of collision, the door exerts a leftward force on you.

To Summarize Newton’s First Law describes when the net force acting on an object is zero. Think of a car crash; the coin, index card, and cup experiment

Motion & Forces IV. Force & Acceleration u Newton’s Second Law u Gravity u Air Resistance u Calculations

A. Newton’s Second Law of Motion Describes the effect of an unbalanced force on the motion of an object. The unbalanced force acting on an object equals the object’s mass times its acceleration.

A. Newton’s Second Law F m F = ma F m a F: force (N) m: mass (kg) a: accel (m/s 2) 1 N = 1 kg ·m/s 2

Newton Force is measured in Newtons (N). A Newton is equal to 1 kg x m/s 2 A mass x acceleration.

Practice Newton’s Second Law A baseball accelerates downward at 9. 8 m/s 2. If the gravitational force is the only force acting on the baseball and it is 1. 4 N, what is the baseball’s mass?

Newton’s Second Law F= m= a= First set up problem and rearrange equation m = F/a Put in numbers and solve.

Summary of Newton’s Second Law of Motion deals with unbalanced forces. Unbalanced forces on an object cause two things: 1. Change in motion 2. Causes acceleration

B. Gravity ◦ force of attraction between any two objects in the universe ◦ increases as. . . mass increases distance decreases

B. Gravity Who experiences more gravity the astronaut or the politician? l Which exerts more gravity the Earth or the moon? less distance more mass

Gravity Can gravity occur in space? Yes. Gravity does NOT require air. Does gravity continue acting on a fallen object after it hits Earth’s surface? Yes. Gravity keeps objects on Earth’s surface.

B. Gravity Weight ◦ the force of gravity on an object W = mg W: weight (N) m: mass (kg) g: acceleration due to gravity (m/s 2) MASS WEIGHT always the same (kg) depends on gravity (N)

B. Gravity Would you weigh more on Earth or Jupiter? § Jupiter because. . . greater mass greater gravity greater weight

you tube video on newton's 2 nd law https: //www. youtube. com/watch? v=iw. P 4 he. W Dhvw

B. Gravity Accel. due to gravity (g) § In the absence of air resistance, all falling objects have the same acceleration! § On Earth: g = 9. 8 m/s 2 elephant feather Animation from “Multimedia Physics Studios. ”

Free fall The motion of a body when only gravity is acting on it. (No air resistance. )

With air resistance Without air resistance

physics classroom

http: //www. animations. physics. unsw. edu. au/jw/Newton. htm#Newton 2 Go to the astronaut’s, David Scott, demonstration

C. 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

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

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

C. 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. ”

D. Calculations l What force would be required to accelerate a 40 kg mass by 4 m/s 2? GIVEN: F=? m = 40 kg a = 4 m/s 2 F m a WORK: F = ma F = (40 kg)(4 m/s 2) F = 160 N

D. Calculations l. A 4. 0 kg shotput is thrown with 30 N of force. What is its acceleration? GIVEN: WORK: m = 4. 0 kg F = 30 N a=? a=F÷m F m a a = (30 N) ÷ (4. 0 kg) a = 7. 5 m/s 2

D. Calculations l Mrs. J. weighs 557 N. What is her mass? GIVEN: WORK: F(W) = 557 N m=? a(g) = 9. 8 m/s 2 m=F÷a F m a m = (557 N) ÷ (9. 8 m/s 2) m = 56. 8 kg m = 57 kg

Concep. Test Is the following statement true or false? ◦ An astronaut has less mass on the moon since the moon exerts a weaker gravitational force. § False! Mass does not depend on gravity, weight does. The astronaut has less weight on the moon.

Motion & Forces VI. Action and Reaction u Newton’s Third Law u Momentum u Conservation of Momentum

A. Newton’s Third Law of Motion ◦ When one object exerts a force on a second object, the second object exerts an equal but opposite force on the first.

A. Newton’s Third Law Problem: § How can a horse pull a cart if the cart is pulling back on the horse with an equal but opposite force? § Aren’t these “balanced forces” resulting in no acceleration? NO!!!

A. Newton’s Third Law l Explanation: ◦ forces are equal and opposite but act on different objects ◦ they are not “balanced forces” ◦ the movement of the horse depends on the forces acting on the horse

3 rd Law of Motion

A. Newton’s Third Law Action-Reaction Pairs l The hammer exerts a force on the nail to the right. l The nail exerts an equal but opposite force on the hammer to the left.

A. Newton’s Third Law Action-Reaction Pairs The rocket exerts a downward force on the exhaust gases. l The gases exert an equal but opposite upward force on the rocket. l FG FR

A. Newton’s Third Law Action-Reaction Pairs l Both objects accelerate. l The amount of acceleration depends on the mass of the object. F m l Small mass more acceleration l Large mass less acceleration

Momentum Mass in motion Since all objects have mass, if an object is moving it has momentum The amount of momentum depends on two variables: mass velocity

Momentum = mass x velocity p = mv Momentum units are mass units times velocity units: kg m/s is the standard but can have a other unit combinations

Momentum Example Two football players of equal mass are traveling towards each other, one is moving at 5 m/sec and the other at 8 m/sec. The one moving with the faster velocity has a greater momentum and will knock the other one backwards.

Momentum Example A four-wheeler moving at a relatively fast velocity has a smaller momentum than the semi-truck because of its small mass and will stop much faster.

Momentum practice problem A 1000 kg car moving at 15 m/sec has what amount of momentum? 15, 000 kg • m/sec as a result of multiplying the mass and the velocity.

http: //www. physicsclassroom. com/Class/mo mentum/u 4 l 1 a. cfmphysics classroom examples

Motion & Forces I. Newton’s Laws of Motion “If I have seen far, it is because I have stood on the shoulders of giants. ” - Sir Isaac Newton (referring to Galileo)

A. Newton’s First Law of Motion ◦ An object at rest will remain at rest and an object in motion will continue moving at a constant velocity unless acted upon by a net force.

B. Newton’s Second Law of Motion ◦ The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. F = ma

C. Newton’s Third Law of Motion ◦ When one object exerts a force on a second object, the second object exerts an equal but opposite force on the first.