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Chapter 8 Yes, you’re taking notes, didn’t I just give you an outline? Motion What is motion? If I threw a ball from here to there, can you tell me when the ball is in motion and when it isn't? Motion = ∆ location • In math, ∆ means "change in" • What could affect the motion of the ball? –How hard I throw the ball… I can change the speed. • Change in speed: – Faster means it has to go the same distance in a shorter time. – Slower means it has to go the same distance in a longer time. • Think about when you're running to class: Gym - - - - - - - - - - - - - - - - - - - - - -Classroom – When you are late to class… you run through the halls – When you are early… you strut down the halls Speed Speed = ∆ Distance ∆ Time Various speeds: To be measured Turtle Miles per hour 0.25 Mile per second 0.00006 Feet per second 0.3 Rifle bullet 2045 0.57 3,000 Columbia shuttle Earth's orbit 12,000 3.3 17,598 40,000 11.1 58,666 • These are all different numbers that have the same values… they have different units of measure. • Note: Always pay close attention to units of measure, your units should always agree with what's asked for in a question. • Speed = how fast something is moving – on average = over time = AVERAGE SPEED –at an exact moment = INSTANTANEOUS SPEED Average speed = Total Distance traveled Time taken to travel Distance • Average speed = The average overall speed on a trip –Example: 2 hours in the car to travel a distance of 100 miles –Equation 100 miles = 50 MPH 2 hours • Instantaneous speed = The speed you are traveling at that exact moment –Example: During a 2 hour trip over 100 miles • stop at a red light = 0 MPH • speed at 75 MPH on the highway • slowly driving at 25 MPH past a school Image for remembering equations for speed math problems Velocity Velocity = Speed and direction –Measured by a speedometer and a compass • Velocity = ∆ Distance + direction of movement ∆ Time • In this class we will use the terms interchangeably… and imply the direction. • However: CONSTANT SPEED ≠ CONSTANT VELOCITY The car can be traveling at the same speed, but has changes in direction • Changes in velocity can have different causes: – ∆ V = same speed + ∆ direction – ∆ V = ∆ speed + same direction – ∆ V = ∆ speed + ∆ direction Mathematical – Graphic Representations of Velocity • If we know the average speed, we can plot the time and distance along a trip: Distances Traveled (miles) Time (hours) Car A at 15 MPH Car B at 30 MPH Car C at 60 MPH 0.5 7.5 15 30 1 15 30 60 1.5 22.5 45 90 2 30 60 120 Car Speed 140 120 Dist. miles 100 80 Car A Car B Car C 60 40 20 0 0 0.5 1 1.5 Time (hours) 2 2.5 • What do you notice about the 3 lines on the Car Speed graph? –Steepness of line = greater the slope of the line –the greater the slope, the faster the speed of the car – slope = ∆ Y or rise ∆X run – If distance is placed on the y-axis and time is placed on the x-axis, Velocity = ∆ D = ∆ Y = Slope of line ∆T ∆X • So, Velocity = Slope of line Car A Slow Gradual line Car B Medium Medium Car C Fast Steep line Graphing Velocity (Average Speed) What can you tell from different graphs? • 3 Different objects moving at 3 different speeds D T • Stopped Object: Time passes but distance does not change • No movement D T D T • Backward moving object… • The distance is decreasing, so there is movement towards the source • Circular Motion: Time passes as the same distances are revisited: like a race track D T • Series of motions D T • Rest-forward-restbackward-rest • Note: does not represent the profile of the terrain Velocity Graphs and Profiles of Terrain 3 1 D 4 2 5 T • What do we know about movement? • 1 – rest • 2 – gradual movement forward • 3 – rest • 4 – backward movement • 5 – rest Velocity Graphs and Profiles of Terrain 3 1 D 4 2 5 T • What could be a possible explanation: pulling a wagon uphill? • 1 – You are halfway up a hill, at rest holding a wagon. • 2 – You start moving uphill • 3 – You take a rest • 4 – The wagon handle slips out of you hand and travels backward down the hill. • 5 – The wagon stops moving at the bottom of the hill. Dimensional Analysis – Unit Analysis In your head, you can probably convert… … inches to feet sure, 12 in = 1 ft … inches to yards okay, 3 ft in 1 yd = 36 in … inches to miles um, probably not • FAQ: When I convert from inches to yards or yards to inches, when do I multiply and when do I divide? • The easiest way to approach these unit conversions is by using dimensional analysis. There are 4 rules: 1. If you use only one unit to start, put it over a 1. 2. Determine the conversion factors. (Ex: 12 inches = 1 ft) and put into a fraction. 3. Properly place the conversion factors in an equation. 4. Check cancellations of units so that you are left with the unit you were looking for on the top of a division bar. The units that are canceled should be on opposite sides of the division bar. Example 1: How many feet in 13 in? 1 1/12 or 1.083 ft Step 1… starting with 13, so… 13 inches 1 Step 2… conversion factors: 1 foot or 12 inches 12 inches 1 foot Step 3… place factors: 13 inches 1 x 1 foot 12 inches Step 4… check cancellations: 13 inches 1 13 inches = 1.083 ft x 1 foot 12 inches Example 2: Convert 13 inches into yards. Step 1… starting with 13, so… 13 in 1 Step 2… conversion factors: 1 ft 12 in 1 yd 3 ft Step 3… place factors: 13 in x 1 ft x 1 yd = 1 12 in 3 ft Step 4… check cancellations: 13 in x 1 ft x 1 yd 1 12 in 3 ft 13 in = 0.36 yd Example 3: Convert 2 years into seconds. 2 yrs x 365 days x 24 h x 60 min x 60 sec 1 1 yr 1 day 1h 1 min 2 yrs = 63,072,000 sec Example 4: Convert 4 decades into minutes. 4 dec x 10 yrs x 365 days x 24 h x 60 min 1 1 dec 1 yr 1 day 1h 4 decades = 21,024,000 m Example 5: I am 5’ 3” or (5 x 12) + 3 = 63 inches tall. How many cm tall am I? 63 in x 2.56 cm = 1 1 in 63 in = 160.1 cm Dimensional Analysis Worksheet 1. In New Jersey, students in public schools go to school for 4 years. How many minutes are students enrolled in high school? 4 years x 365 days x 24 h x 60 min 1 1 yr 1 day 1h 4 yrs = 2,102,400 min 2. Alayna’s dog is 3 ft tall. What is the dog’s height in mm? 3 ft x 12 in x 2.54 cm x 10 mm 1 1 ft 1 in 1 cm 3 ft = 914.4 mm 3. Brian and Jesse were on a bus trip going 50 MPH. For some extra fun, they decided to convert the bus’s speed into km/h. What should their answer be? 50 miles x 1.61 km 1 hr 1 mile 50 MPH = 80.5 km/h 4. Driving home from practice, Alex’s mother was driving at a speed of 30 m/s. What was their speed in km/h? 30 m x 1 km x 60 s x 60 min 1 s 1000 m 1 min 1h 30 m/s = 108 km/h 5. Saskia was riding her bike down the road at a speed of 5 km/h. What was her speed in m/s? 5 km x 1000 m x 1 hr x 1 min 1h 1 km 60 min 60 s 5 km/h = 1.39 m/s Class experiment: 1. Determine how tall you are in inches. 2. Using the conversion factor: 1 mile = 1.61 km, determine how tall you are in cm. 3. Check your answer with a meter stick. Acceleration When you accelerate, what are you doing? Speeding up… accelerating When you slow down, what are you doing? Decelerating In physics, we use the same term, “acceleration” for both speeding up and slowing down. We distinguish between the two by assigning positive or negative values. + acceleration as in speeding up positive - acceleration as in slowing down negative Acceleration = the change in velocity over time - measured in m/s or m/s2 s Acceleration = ∆ Velocity ∆ Time Acceleration = ∆ Distance + Direction ∆ Time ∆ Time Given an object moving in a circle - ∆ velocity due to a ∆ direction - if ∆ velocity, the ∆ acceleration as well - circular motion = ∆ D = ∆ V = ∆ A Graphing Acceleration A = ∆ V and slope = ∆ Y ∆T ∆X Acceleration = ∆ V = ∆ Y = Slope of line ∆T ∆X So, Acceleration = Slope of line Steep slope = fast movement Gradual slope = slow movement V V T Acceleration T Deceleration Steepness of the line indicates the degree of acceleration V T Comparing Velocity and Acceleration Velocity = ∆ Distance ∆ Time D Acceleration = ∆ Velocity ∆ Time V T T These two lines indicate the exact same thing the same rate of acceleration • Acceleration = + slope • Deceleration = - slope - slope V + slope T When object is a rest Velocity is zero If ∆ Distance = 0, then ∆ Velocity… so Acceleration = 0 V D 0 T T When acceleration equals zero A= ∆ V no change in velocity ∆ T Time will always pass No change in velocity - no velocity – V = 0 then object is at rest - constant velocity - ∆ V = Vfinal – Vinitial Vf = 50 miles/h and Vi = 50 miles/h Then ∆ V = 0 If acceleration = zero, you are either stopped or on cruise control To determine which, you must find if there is a change in distance. How it all fits together From Motion Acceleration only one variable is added at a time 1. Motion = ∆ Distance 2. Speed = ∆ Distance ∆ Time 3. Velocity = ∆ Distance + Direction ∆ Time 4. Acceleration = ∆ Distance + Direction ∆ Time ∆ Time Momentum When an object is in motion, we think velocity. However, we must not forget Momentum – which is also acting on the object. Momentum = a quantity defined as the product of an object’s mass and its velocity. - In a formula, P = momentum. - momentum moves in the same direction as the velocity P = Mass x Velocity - Measured in kg·m/s Momentum and ∆ Velocity - large momentum, difficult to change velocity - small momentum, easier to change velocity Class Experiment: Red light, green light Stationary objects have momentum of zero Why? No motion = no speed = no velocity = no momentum Momentum is directly proportional to mass… momentum increases as mass increases. P Mass (kg) Force Force = the cause of acceleration or a change in velocity - force is measured in units called Newtons Net force = the combination of all the forces acting upon an object. • The size of the arrow represents the amount of force… • The arrows are the same so there is no movement. Friction Friction = the force between two objects in contact that opposes the motion of either object. Pretend you are in a helicopter looking down on a ski slope in early spring…. The ice is melting…. Patches of dirt and gravel begin to show… ********** How much friction? Skis + snow = little friction… skis move over snow Skis + dirt = a lot of friction… skis do not move over dirt Air resistance is a type of friction. Gravity Gravity = Force of attraction between 2 objects due to their masses. The force of gravity is different on different planets, moons etc. On earth: g = 9.8m/s2 Gravity depends upon the masses as well as the distance between objects. Newton’s Laws of Motion Newton’s 1st Law- the law of inertia An object at rest remains at rest and an object in motion remains in motion unless it experiences an unbalanced force. • Example 1: Whiplash – Person B is stopped at a traffic light. Person A is not paying attention, and rear-ends Person B. • Result: Person B moves forward suddenly… Their head snaps back as it attempts to “remain at rest.” Their body, attached to the seat moves forward… their head snaps forward to catch up with the body resulting in whiplash. Example 2: Bus ride - The bus driver does not like children. Every time, they get too loud, he slams on the breaks. Why does he do this? Inertia = The tendency of an object to remain at rest or in motion with a constant velocity. All objects have inertia because they resist changes in motion. Trivia: If two people on a space ship (in space) get into a physical fight, which will win? Person A Person B Even though they are weightless… there is no gravity Person A has a greater mass, therefore, a greater inertia. Newton’s 2nd law of Motion- the law of acceleration • The unbalanced force acting on an object equals the object’s mass times its acceleration. • Force = Mass x Acceleration Example: pushing a cart The greater the mass, the more force needed to cause acceleration. Bumper cars Newton’s 3rd law of Motion- the law of interaction • For every action, there is an opposite and equal reaction force. • Forces occur in pairs Example: Holding up a wall