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### Fall Final Exam Review

Almost there…….

Chapters Covered

- 1D Motion: 2 and 3
- 1D Forces: 4
- 2D Motion:6
- 2D Forces: 5 and 8
- Gravitational Forces: 7
- Energy and Work: parts of 10 and 11

Unit 1: 1D Motion

- v = (df-di)/(tf-ti)
- df= vt + di
- a = (vf-vi)/(tf-ti)
- vf = vi + a(tf-ti)
- df = di + vi(tf) + ½a(tf)2
- vf2=vi2 + 2a(df-di)

Unit 1: 1D Motion

- -Vectors and Scalars
- vectors are quantities that have both size (magnitude) and direction
- represented by arrows
- -scalars are quantities that are just numbers without direction, such as distance, time and temperature
- When drawing vectors the length of the vector should be proportional to the magnitude of the quantity being represented.
- -Resultant: the vector that represents the sum of the other vectors

Unit 1: 1D Motion

- Velocity
- -the rate of change of displacement with time
- -has magnitude AND direction
- -average velocity is calculated by dividing the change in distance (the displacement) by the change in time (the time interval)
- v = (df-di)/(tf-ti)
- -velocity can also be represented by the slope of the line on a position-time graph
- -Speed: the rate of change of distance with time
- -speed only has magnitude

Unit 1: 1D Motion

- Acceleration
- -the average acceleration of an object is the change in velocity during some measurable time interval divided by that time interval
- a = (vf-vi)/(tf-ti)
- -acceleration can be represented by the slope of the time on a velocity-time graph
- -acceleration can be both positive and negative
- -positive acceleration represents acceleration in the positive direction
- -negative acceleration represents acceleration in the negative direction

Unit 1: 1D Motion

- Position v Time Graphs
- Time goes on the X-axis and Position goes on the Y-axis
- -the slope represents the velocity
- horizontal lines= NO MOVEMENT
- -The steeper the line the faster the object is moving
- -lines with a negative slope are moving in the negative direction
- -lines with a positive slope are moving in the positive direction

Unit 1: 1D Motion

- Velocity v Time Graphs
- Time goes on the X-axis and Velocity goes on the Y-axis
- the slope represents acceleration
- horizontal lines= NO ACCELERATION
- positive slope implies an increase in velocity in the positive direction.
- negative slope implies an increase in velocity in the negative direction
- the "y" intercept equals the initial velocity

Unit 1: 1D Motion

- A high school athlete runs 100 m in 12.2 s. What is the velocity in m/s and mph? (8.20 m/s, 18.34 mph)
- A bus is moving at 25 m/s. The driver steps on the brakes, and the bus stops in 3.0 s.
- What is the average acceleration of the bus while braking? (-8.33 m/s/s)
- Suppose the bus took twice as long to stop. How would the acceleration compare to the acceleration you found above? (1/2 as much; -4.17 m/s/s)

Unit 1: 1D Motion

- During a baseball game, a batter hits a high pop-up. If the ball remains in the air for 6.0 s, how high does it rise(44.1m)
- A skateboarding student can slow from 20 m/s to rest in 2.5 s. How many meters before a wall must the skateboarder start to slow down in order to stop before the wall? (Hint: this is a two-part problem…)
- A man falls 1.0 m to the floor.
- How long does the fall take? (0.45 s)
- How fast is he going when he hits the floor? (-4.43 m/s)

Unit 1: 1D Motion

- Take a minute and look over Test 1…..any questions????

Unit 2: 1D Force

- Fnet=ma
- Fg=mg
- Ff=μFN
- Fnet=F1 + F2 +F3….
- T=2Π √(r3/GmE)
- Fgravitaion=G(m1m2/r2)
- CONSTANTS:
- G= 6.67 E -11 Nm2/kg2
- mE= 5.98 E 24 kg

Unit 2: 1D Force

- Force – the acceleration of an object with a certain mass.
- NewtonsSecond Law: the acceleration of an object is based on the sum of the forces acting on it, divided by the mass of the object!
- F=ma

- Newtons First Law: an object at rest will remain at rest, an object moving will remain moving… unless a force (or net forces) acts on it to change it.
- Inertia

- Newtons Third Law: For each action, there is an equal and opposite reaction.

Unit 2: 1D Force

- Free body diagram:. Draw an arrow for each for acting on an object, making the arrows big or small based on the size (magnitude) of the force, if all the arrows (positive for one direction, negative for one direction) add up to zero, an object is at equilibrium (all the forces are balanced).
- ALWAYS DRAW THE FREE BODY DIAGRAM!!!!!
- It helps….I PROMISE

Unit 2: 1D Force

- Friction force…..
- Friction opposes motion….negative force!

- Tensional force…..
- Tension force= force on a rope, string, chain, etc
- Opposes the force from gravity (aka the weight!)

Unit 2: 1D Forces

- Kepler’sLaws
- Kepler’sFirst Law: Planets orbit in Ellipses
- Kepler’s Second Law: Planets travel distances that cover equal amounts of area in the ellipse per month.
- Kepler’s Third Law: The ratio of two planets periods (squared) is equal to the ratios of distances of the two planets to the sun (cubed).

Unit 2: 1D Forces

- Newton’s Law of Universal Gravitation
- Gravitational Force is a field force that is based on an amount of mass two objects have which make them attract to each other.
FGravitation = G (m1m2/r2)

- G = 6.67E-11 Nm2/kg2
- m1 or m2 = mass of objects one and two
- r = distance between two centers of the two masses

Unit 2: 1D Forces

- Orbits
- Period of a Planet Orbiting the Sun or Satellite orbiting the earth:
T = 2π√(r3/Gm)

- G = 6.67E-11 Nm2/kg2
- M= mass of the sun for a planet orbiting the sun or mass of earth for a satellite orbiting the earth
- R = orbiting radius

Unit 2: 1D Force

- Together a bike and its rider have a mass of 275 Kg. The bike is slowed down with an acceleration of –4.5 m/s/s. What is the net force on the bike? Describe the direction of the force and the meaning of the negative sign. (1.24 E3 N; Fnet is opposite dxn of motion
- Suppose Joe, who weighs 600 N, stands on a bathroom scale calibrated in Newtons.
- What force would the scale exert on Joe? In what direction? (600 N, up)
- If Joe now holds a 50N cat in his arms, what force would the scale exert on him? (650 N, up)
- After Joe puts down the cat, his father comes up behind him and lifts upward on his elbows with a 100-N force. What force does the scale now exert on Joe? (500 N, up)

Unit 2: 1D Force

- A 52-N sled is pushed across a cement sidewalk at constant velocity. A horizontal pushing force of 36 N is exerted.
- What is the coefficient of sliding friction between the sidewalk and the metal runners of the sled? (0.69)
- Suppose the sled now runs on packed snow. The coefficient of friction is now only 0.12. If a person weighing 650 N now sits on the sled, what applied force is now needed to slide the sled across the snow at constant velocity? (84.24 N)

Unit 2: 1D Force

- A 7.0 E –5 Kg spider is moving down on its thread. There is 1.2 E-4N of tension in the thread. What is the acceleration of the spider? (-8.09 m/s/s)
- What lift force is necessary for a 5200 Kg helicopter to have an acceleration of 2.3 m/s/s? (6.29 E 4 N)
- The coefficient of sliding friction between rubber tires and wet pavement is 0.50. The brakes are applied to a 750-kg car traveling 30 m/s, and the car skids to a stop.
- What is the size and direction of the force of friction that the road exerts on the car? (3.68 E3 N, opp motion)
- What would be the size and direction of the acceleration of the car? (4.9 m/s/s, opp motion)
- How far would the car travel before stopping? (91.84 m

Unit 2: 1D Forces

- Superman (mass of 100kg) is orbiting earth at a distance of 5E6 m from the surface of the earth. How long does it take for him to make one orbit?

Unit 2: 1D Forces

- Take a minute and look over test 2……any questions?

Unit 3a: 2D Forces

- All of the equations are the same…..
- SOH CAH TOA

Unit 3a: 2D Forces

- Steps to solving 2D Forces Problems
- Draw the picture/scenario
- Draw the free body diagram
- Draw the triangle…and USE IT
- Find x and y components

- Use the GUESS method to solve

Unit 3a: 2D Forces

- Maggie is pushing on the handle of a stroller which has a mass of 15 kg with the baby in it. The handle makes a 34o angle with the horizontal. She wishes to accelerate the stroller from rest to 4.5 m/s in 3.5 s. What force must she apply to the handle if there is 13N of friction between the ground and the stroller?

Unit 3a: 2D Forces

- Rusty pulls his 35-kg backpack behind him at a constant speed by pulling on the strap that makes some angle with the horizontal. The frictional force between the suitcase and the ground is 15 N and Rusty exerts a 55-N force on the handle. What angle does the handle make with the horizontal?
- The weather has gone nuts and it snows like crazy turning the hill next to the softball field into the ideal sled zone. What is your acceleration sled down the hill, which makes a 35o angle with the horizontal if the force of friction between you (54kg) and the snow is 78N?

Unit 3a: 2D Forces

- Jason Bourne (80kg) is hanging from a rope. Where he hangs from the rope makes a 140 degree angle. What is the tension in the rope?

Unit 3a: 2D Forces

- Take a minute and look over test 3…..any questions?

Unit 3b : 2D Motion

- ac=v2/r
- ac= (4Π2r)/T2
- T=(2 Πr)/v

Unit 3b : 2D Motion

- Givens…..ALWAYS separate into x and y chart
- Acceleration in the x direction = 0
- Acceleration in the y direction = -9.8
- Initial Velocity in the y-direction = 0

Angry yellow bird is launched with a velocity of 5m/s.

How far away is the wooden structure he breaks?

What was his maximum height during his flight?

Unit 3b : 2D Motion

- Givens…..ALWAYS separate into x and y chart
- Acceleration in the x direction = 0
- Acceleration in the y direction = -9.8
- Velocity in y-direction at the highest point/peak=0
- USE TRIANGLES
- Helps you find the x and y components of the initial velocity

Unit 3b : 2D Motion

- Uniform circular motion
- motion of an object in a circle with a constant or uniform speed
- constant change in direction
- Centripetal force is the magnitude of the force required to maintain uniform circular motion.
- Always points toward center of circle. (Always changing direction!)

- Centripetal force is NOT a new “force”. It is simply a way of quantifying the magnitude of the force required to maintain a certain speed around a circular path of a certain radius.

Unit 3b : 2D Motion

- A football player throws the ball with an initial velocity of 15m/s at an angle of 54 degrees relative to the horizontal.
- How long was the ball in the air
- What was the max height of the ball?
- How far away was the receiver when he caught the ball?

Unit 3b : 2D Motion

- Ms. Shuler accidentally knocks the box of markers off the 1.75m high counter in the horizontal direction. How long does it take the markers to hit the ground?
- Becky Moye swings her arm with a 1.25m radius at a velocity of 17m/s to kill a volleyball on her helpless opponents. What centripetal acceleration is delivered to the ball?

Unit 3b: 2D Motion

- If you swing a rubber stopper attached to a 4.35m string above your head in a horizontal circular motion and it takes 2.63 seconds to complete one revolution. What is the acceleration of the stopper
- Mohammad decides to join the circus and gets awarded the honor of being launched out of a cannon as the big finale!!! If Mohammad is launched at a 53o angle with a velocity of 37 m/s how far away does the net that he lands on need to be placed?

Unit 3b: 2D Motion

- Take a minute and look over test 4…..any questions?

Unit 4: Work and Energy

- W=Fd
- KE=1/2mv2
- W=∆KE
- PE=mgh
- Esys=KE + PE
- KE1 + PE1= KE2 +PE2

Unit 4: Work and Energy

- Work is the transfer of energy by mechanical means
- In order for work to be done the object must move
- In order to do work two conditions MUST be met:
- 1. the applied force must make the object move
- 2. the movement must be in the same direction as the applied force

- When work is done energy is always transferred
- Work-energy theorem: when work is done on an object, the result is a change in kinetic energy

Unit 4: Work and Energy

- Clea is big into bungee jumping, so she puts her safety gear and bungee apparatus on and climbs to the highest point of a bridge, which is 34m above the water below. How much potential energy does she have before she jumps?
- On a recent trip to the water park, you notice there is a new slide that you ride down a steep hill, then it carries you back up another ramp and shoots you into a pool. All the kids around you are saying you leave the ramp, “at, like, 50m/s!!!!” If the initial height of the slide is 100m, and the ramp height is 10m do you really, “like”, get projected into the air at 50m/s?
- Your teachers do it to you again, each class has homework! BOOOO! You take all your books out of your locker and notice your bag weighs 150kgs! As you trudge up the stairs that are 30m high, how much work are you doing?

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