EOC Review

1. EOC Review This review should remind you of important concepts, definitions and equations we have used through out the year. It also contains example problems for you to try. The answers to the examples are given so that you can check your work as you go along.

2. Units • Know the units of measurement. • Length/distance = meters (m) • Time = seconds (s) • Mass = kilograms (kg) • These are the basic units of measurement. Everything is built off of them.

3. Conversions • Remember to convert to your basic units. • Kilo = 1000 (1000 g in 1 kg) • Centi = 1/100 (100 cm in 1 m) • Milli = 1/1000 (1000 mm in 1 m) • Just multiply by the number above to get the answer in your base unit.

4. Scientific Notation • Extremely big numbers and extremely small numbers are often put in scientific notation. • When putting these numbers in your calculator, it is important to use the “EE” key and parentheses. • Example: (1.2x104)/(3.2x 105)

5. Kinematics • Also called one dimensional motion. • 4 major quantities in kinematics – time, distance, velocity, and acceleration • Time is always positive. • Distance is always positive. Displacement is distance with a direction so it can be positive or negative. • Velocity is speed with a direction so it can be positive or negative. • Acceleration is the change in velocity so it can be positive or negative. • It all depends on the frame of reference. • Remember that you can pick your frame of reference

6. Kinematics Example 1 : A ball is rolling to a stop from an initial velocity of 5 m/s. It takes 8 s for the ball to completely stop. How far does it roll? Hints: Hidden info: stopping means vf = 0 m/s This is a 2 step problem. Find acceleration, then displacement. Answer: a = -0.625 m/s2, d = 20 m

7. Distance/Displacement • Formula for distance/displacement is: • Unit is: m Example: A ball is rolling to a stop from an initial velocity of 5 m/s. It takes 8 s for the ball to completely stop. How far does it roll?

8. Velocity • Formula for velocity is: • Unit is: m/s

9. Acceleration • Formula for acceleration is: • Or : • Unit is: m/s2

10. Free Fall • When an object is falling through the air, you use the same equations but realize that the acceleration is now gravity. • Gravity = 9.8 m/s2

11. Free Fall Example 2: How long before a falling flower pot hits the ground if it falls from a height of 50 m? Hints: Hidden info: dropping means vf = 0 m/s a = g = -9.8 m/s2 Answer: t = 3.2 s

12. Forces • Forces cause objects to move, to stop moving, or to change directions. • Forces are summative. This means that you will need to add forces that are going in the same direction and subtract forces that are going in opposite directions. • We can see how forces act on an object using force diagrams. • Force diagrams will allow you to find the net force. • If the net force is zero, there is no acceleration • Unit is: Newton (N)

13. Forces • There are 3 Laws for Forces. • 1st law is the Law of Inertia. It says that an object in motion/at rest will stay in motion/at rest unless acted upon by an outside force. • 2nd Law is: • 3rd law says that for every action there is equal but opposite reaction. • Weight is the force of gravity on your mass. • W=mg (mass times acceleration due to gravity) and the unit is still Newtons.

14. Forces Example 3: A 50 N box sitting on a carpeted floor was pushed with a force of 35 N. The carpet provided a frictional force of 10 N. What is the acceleration of the box? Hints: This is a multi step problem. You will need the mass of the box. g = -9.8 m/s2 Answer: Fnet = 25 N, a = 4.9 m/s2

15. Vectors • A vector quantity has both a magnitude (number) and direction. • Ex: acceleration • A scalar quantity has only a magnitude. • Ex: time • When adding vectors, you can only add vectors that are in the same directions (x-direction or y-direction). • If you have one vector in the x direction and one vector in the y direction, you have to use the Pythagorean theorem to get the resultant vector.

16. Vectors Example 4: A toy sailboat floats 5 m south across a pond in 30 s. Right before it gets to shore a cross breeze blows the sailboat 3 m east in 10 s. What is the magnitude of the average velocity of the sailboat? Hints: This is a multi step problem. Magnitude means amount or size Answer: d= 5.8 m SE, v = 0.15 m/s

17. Projectiles • Projectiles are free fall with a horizontal velocity. • Consider each direction separately. • The formula is: • It simplifies to: x=vit and y=1/2 at2

18. Projectiles Example 5: A cannon ball is fired from the top of a 75 m cliff with an initial horizontal velocity of 120 m/s. How far from the cliff with the cannon ball land? Hints: This is a multi step problem. a = g = 9.8 m/s2 Find the time in the air first hidden information – initial vertical velocity is 0 m/s Answer: t = 3.9 s, x = 469 m

19. Gravitation • Every object experiences an attractive force towards every other object. • Formula is: • Remember that as the distance increases, the force will decrease. They are inversely proportional.

20. Circular Motion • When an object travels in a circle, it experiences a force directed toward the center of the circle. This is called the centripetal force. • Remember that F=ma • In a circle: • Force is still in Newtons.

21. Circular Motion Example 6: In an experiment to explore centripetal motion a student attached a tennis ball to a string. The student then swung the ball in a horizontal circle over his head. The student measured the tangential speed of the ball to be 6 m/s. The string was 0.75 m long, the mass of the tennis ball was 0.3 kg. What is the centripetal force acting on the tennis ball? Hint: This is a multi step problem. Answer: ac= 48 m/s2, Fc= 14.4 N radially inward

22. Work • Work is a form of energy. • Formula is: • Unit is: Joule (J) • Work is also equal to the change in the KE as well. (We will talk about that shortly) • No work is done when moving in a circle. • Just carrying an object around does no work either. • When a force is applied at an angle, only the parallel component does work.

23. Energy • There are two forms of mechanical energy: kinetic energy and potential energy. • Formula for KE: • Formula for PE: • Unit for both forms: Joule (J) • KE is the energy of motion. • PE is stored energy. • There are two forms of PE. • Elastic PE is related to the spring constant k and gravitational potential energy is related to gravity.

24. Work-Kinetic Energy Theorem • Remember that work is a form of energy so if you change speed, you are doing work. • The formula is: • Remember the Δ means change in or final minus initial.

25. Work-Kinetic Energy Theorem Example 7: Friction slows a 0.4 kg moving ball from 5 m/s to a stop in 8 s. How much work is done if the ball travels 15 m before stopping? Hint: This is a multi step problem. Find acceleration, then force, then work. Answer: a= -0.625 m/s2, F= -0.25 N, W=3.75 m

26. Conservation of Energy • Energy is conserved which means whatever energy you start out with, you end up with. • The equation is: • KE + PE = KE + PE

27. Conservation of Energy Example 8: A 0.8 kg book falls from the top shelf of the library. The shelf 1s 1.5 m high. How fast is it going right before it hits the ground? Hint: This is a 2-step problem. Find GPE at the top of the shelf, use conservation of energy, then find speed. g = 9.8 m/s2 Answer: GPE = 11.8 J, v = 5.4 m/s

28. Power • Power is a form of energy usage. • The formula is: • The unit is: Watts (W)

29. Heat • The formula is: • The unit is: Joule (J) • When heat is added, the Q is positive. • When heat is given off, the Q is negative. • When two objects touch, they will come to equilibrium which means that their temperatures are the same and no more heat is exchanged.

30. Momentum • The formula is: • The unit is: kgm/s • Momentum is a vector quantity which means that it has a direction.

31. Conservation of Momentum • Whenever two objects collide, their total momentum will be conserved. • There are two types of collisions – elastic and inelastic. • In an elastic collision, both momentum and energy are conserved. • In an inelastic collision, only momentum is conserved. Some of the energy is lost to change the shape of the object. • The formula is: p1,i + p2,i = p1,f + p2,f OR m1v1,i + m2v2,i = m1v1,f + m2v2,f

32. Conservation of Momentum Example 9: Two cars collide and stick together. The west-bound car has a mass of 1500kg and was moving with a velocity of 14 m/s. The east-bound car has a mass of 1250 kg an was moving at 10 m/s. What is the velocity of the cars after the collision? Hint: be sure to assign +/- to velocity based on direction of travel Answer: v = 3.1 m/s west

33. Impulse • Whenever you change the momentum, you have to apply a force over time. • Force over time is called impulse. • The formula is: • The unit is: Ns or kgm/s

34. Waves • Waves are periodic in nature. • There are two types of waves – transverse and longitudinal. • Transverse waves have movement that is perpendicular. • Longitudinal waves have movement that is parallel. • Review the parts of the waves.

35. Waves • The formula is: • Unit for speed is: m/s • Unit for frequency is: Hz • Unit for wavelength is : m

36. Wave Behaviors • There are 6 ways waves can behave: • Interference • Reflection • Refraction • Diffraction • Resonance • Doppler Effect

37. Wave Behaviors • Interference happens when two waves overlap. • It can be constructive (add) or destructive (subtract). • In reflection, a wave hits a boundary and bounces back. • The angle it bounces back is the same angle at which it hits.

38. Wave Behaviors • Refraction occurs when the wave goes from one medium into another and the speed changes. • When the speed changes, the wave bends. • When it bends towards the normal, the speed decreases. • When it bends away from the normal, the speed increases.

39. Wave Behaviors • Diffraction occurs when a wave hits a barrier and goes around it. • Resonance occurs when the object oscillates at its natural frequency. • Doppler effect is the apparent shift in frequency when the source of the wave is moving. As the wave approaches, the frequency appears higher (pitch is higher) and as it moves away, the frequency appears lower (pitch is lower).

40. Light • All light moves at the speed of light which is 3.0 x 108 m/s. • We use the same formula as waves: • The velocity is now the speed of light. • Objects appear the color that they reflect.

41. Lenses • When light goes through a lens, it will bend (refract). • Converging makes all of the light rays converge(meet) at one spot. • The formula is: • Where f is the focal length measured in meters, di is the distance to the image in meters, and do is the distance to the object in meters.

42. Light Example 10: An object is placed 20 cm in front of a lens with a 15 cm focal length. How far away from the lens will the image be found? What type of image is it? Answer: di = 8.6 cm behind the lens, real and inverted.

43. Electrostatics • If you have two charged objects, they will experience a force that pulls them together or forces them apart. • The formula is: • When the charges are opposites, they attract. • When the charges are the same, they repel. • Remember that the force and the distance are inverses. • As you get further away, the force decreases.

44. Circuits • There are two types of circuits- series and parallel. • Ohm’s Law V = IR. Current and resistance are inversely proportional.

45. Circuits A parallel circuit is constructed using a 6 V battery, a 5 ohm resistor, a 10 ohm resistor and a 15 ohm resistor. What is the total current in the circuit? Hint: this is a 2 step problem. Answer: Rt = 2.8 ohms, I = 2.1 A