Physics Final Exam Review

1. Physics Final Exam Review The following standards are derived from the State Content Standards for Physics

2. Motion and Forces 1. Newton's laws predict the motion of most objects. As a basis for understanding this concept:

3. The basic equation for any problem dealing with speed (velocity), time and distance isv = x/tor v = d/tAverage speed is determined by knowing two or more speed measures and dividing them by the number usedAvg v = vi + vf/2 • a. Students know how to solve problems that involve constant speed and average speed.

4. Acceleration only occurs when there is a changing velocity. a = Δv/t or a = (vf-vi)/t It should be noted that variables need to be consistent, thus in like units • b. Students know that when forces are balanced, no acceleration occurs; thus an object continues to move at a constant speed or stays at rest (Newton's first law) – Inertia.

5. c. Students know how to apply the law F = ma to solve one-dimensional motion problems that involve constant forces (Newton's second law). Force is a push or pull on an object of mass. The unit for force is Newton (N). The actual units are kg.m/s2 Any substitution can be used for determining acceleration, a. For example: F = m(Δv/t) or F = m[(vf-vi)/t] Keep in mind that units of mass must be kg and acceleration must be m/s2

6. Not much to be said here. Any loss of energy, momentum, speed, etc. has to be accounted for in some other object. • d. Students know that when one object exerts a force on a second object, the second object always exerts a force of equal magnitude and in the opposite direction (Newton's third law).

7. e. Students know the relationship between the universal law of gravitation and the effect of gravity on an object at the surface of Earth. Universal gravitation equation. The equation is Fg = G(m1m2)/r2 G is the gravitational constant. G = 6.67 x 10-11 N.m2/kg2 Mass is in kg and distance in meters

8. f. students know applying a force to an object perpendicular to the direction of its motion causes the object to change direction but not speed (e.g., Earth's gravitational force causes a satellite in a circular orbit to change direction but not speed) This has to do with rotational variables. An object at constant speed in circular motion, but with a changing direction, allows for a constant change in velocity, thus, constant acceleration. Variables include the radian of which there are pi radians in a half circle and 2 pi radians in a circle. Arc length, s, is the distance an object travels along an arc in a circular path. Angular velocity is the speed traveled on an circular path. Angular acceleration is the velocity/time.

9. g. Students know circular motion requires the application of a constant force directed toward the center of the circle Fc, centripetal force, is the force applied to keep an object in a circular path. Should an object lose its Fc, it will travel in a straight path. The “force” that makes you, a passenger in a car, push against the door in a sharp left turn, is really no force at all. Often called centrifugal force, a force that doesn’t really exist, the phenomenon is really Newton’s First Law in effect: an object in motion remains in motion, unless a force, Fc, acts against it, thus motion is in a straight line.

10. This concludes this StandardThe following questions are retired STAR questions given by the state in prior years. These questions are meant to be representative of the types of content/concepts you should know.

11. 1. How much time will it take for a person to walk the length of a football field (100 yards) at a constant speed of 5 ft/s? • A 20 seconds B 33 seconds • C 60 seconds D 166 seconds

12. 2. A ball is dropped from rest from a height 6.0 meters above the ground. The ball falls freely and reaches the ground 1.1 seconds later. What is the average speed of the ball? A 5.5 m/s B 6.1 m/s C 6.6 m/s D 11 m/s

13. 3. An object moves away from a motion detector with a constant speed. Which graph best represents the motion of the object?

14. 4. A 10-newton force and a 15-newton force are acting from a single point in opposite directions. What additional force must be added to produce equilibrium? A 5 N acting in the same direction as the 10-N force B 5 N acting in the same direction as the 15-N force C 10 N acting in the same direction as the 10-N force D 25 N acting in the same direction as the 15-N force

15. A student holds a book at rest in an outstretched hand. The force exerted on the book by the student is equal to the book’s • A mass. B weight. • C volume. D density.

16. Conservation of Energy and Momentum 2. The laws of conservation of energy and momentum provide a way to predict and describe the movement of objects. As a basis for understanding this concept:

17. a. Students know how to calculate kinetic energy by using the formula KE=(1/2)mv2 Kinetic energy is energy of motion. A mass or object that is moving has KE. A part of your understanding of energy began with your understanding of how “work” is measured: W = Fd Work units, and all energy units are measured in units called Joules, J. Energy is not created or destroyed, First Law of Thermodynamics, but it can change forms. Therefore, Work energy can be converted into Kinetic Energy. If W = KE, then Fd = (1/2)mv2 Remember: Velocity can be found by knowing distance and time.

18. b. Students know how to calculate changes in gravitational potential energy near Earth by using the formula PE =mgh (h is the change in the elevation). For an object to have PE in relation to gravity, it must be above a reference point. This is the height, h, of the equation. This can also be referenced as distance. When F = ma and W = Fd, it can be concluded that W = mad. When Force is measuring weight, acceleration, a, is substituted with gravitational acceleration, g, in the equation. Thus, F = mg. The same applies to Work, thus, W = mgd. Since d and h are really interchangeable, it can be concluded that W = PE or Fd = mgh. Further, if both d and h are the same, F = mg

19. c. Students know how to solve problems involving conservation of energy in simple systems, such as falling objects. KE=(1/2)mv2 = PE =mgh = Work = Fd This equality or derivation has been discussed earlier and does not need further discussion. However, you should remember that any energy lost in PE can be assumed as energy gained in KE. As a result, one can indirectly calculate KE when knowing mass and distance (height) of an object when asked to find KE at the end of an object’s fall.

20. d. Students know how to calculate momentum as the product of mass and velocity, p = mv. Somewhere, vaguely in you mind, you remember that this was the second time the variable, p, was introduced. The first introduction was with Power, P = W/t. (There is no mention in the standards how power is derived and/or measured. Power is mentioned as it relates to current, charge, and resistance later.

21. e. Students know momentum is a separately conserved quantity different from energy Momentum is a vector quantity because it involves velocity and velocity is a vector because it has magnitude and direction. The unit for momentum is kg.m/s

22. f. Students know an unbalanced force on an object produces a change in its momentum – this is known as impulse. Ft = mv Remember, F = ma? Remember, a = Δv/t? Using substitution, F = m (Δv/t) Further, clearing the right side of the equation of time, t, you get Ft = m Δv or more simply Ft = mv The unit for impulse is N.s An impulse will change momentum by increasing it or decreasing it

23. g. Students know how to solve problems involving elastic and inelastic collisions in one dimension by using the principles of conservation of momentum and energy Momentum can be transferred to another object(s). Any loss of momentum of one mass is found in another mass, therefore, the momentum before a collision must be accounted for after the collision. Original Finalm1v1 + m2v2 = m1’ v1’ + m2’ v2’ The general equation above reflects a collision that it elastic. In and inelastic collision, the masses combine after the collision and the equation is modified. Since the velocity of two combined masses is the same, the equation can be written as Original Finalm1v1 + m2v2 = (m1+ m2)v’

24. This concludes Standard 2, Conservation of Energy and Momentum The following questions are retired STAR questions given by the state in prior years. These questions are meant to be representative of the types of content/concepts you should know.

25. A 2.0-kilogram mass is moving with a speed of 3.0 m/s . What is the kinetic energy of the mass? • A 1.5 J B 6.0 J • C 9.0 J D 12.0 J

26. Three objects move with a velocity of 1. m/s • What is the total kinetic energy of the system? • A 1 J B 2 J • C 5 J D 10 J

27. A 50-kilogram firefighter is on a ladder 10 meters above the ground. When the firefighter descends to 5 meters above the ground, the firefighter’s gravitational potential energy will decrease by • A 0.194 joules. B 5.10 joules. • C 490 joules. D 2450 joules.

28. A high diver steps off a diving platform that is 10 meters above the water. If no air resistance is present, during the fall there will be a decrease in the diver’s • A gravitational potential energy. • B total mechanical energy. • C kinetic energy. • D momentum.

29. 10. A child is on a sled moving down a hill at 20 meters per second. The combined mass of the sled and child is 100 kilograms. The momentum of the child and sled is

30. Heat and Thermodynamics 3. Energy cannot be created or destroyed, although in many processes energy is transferred to the environment as heat. As a basis for understanding this concept

31. a. Students know heat flow and work are two forms of energy transfer between systems. There are many forms of energy, but one thing appears to be constant. Energy is often lost in the form of heat when energy is transformed/transferred from one place to another. The sun’s rays are only partially absorbed by plants during photosynthesis. Only part of the plant food or other foods we eat are converted to usable energy. The remaining energy is lost in heat and inefficiency. To that end, many forms of energy are converted to heat in order to measure the amount of energy in a system.

32. There is an equation to determine the “heat content” of an energy system. mΔtCp = Q m = mass in kg Δt = change in temperature in the system Cp = specific heat capacity (amount of heat energy required to raise one kg of the substance by one degree Celsius) Q = Energy content or heat gained or lost Units for Q are in Joules.

33. There is a graphical expression that reflects phase changes. It is shown below. The flat portions of the graph reflect time it takes to undergo a phase change. It takes considerable energy to move from one phase to another. It takes half the energy to change the temperature of a solid or a gas phase of water than to change the temperature of the liquid phase. That is why the slope is steeper for the solid and gas phases shown.

34. b. Students know that the work done by a heat engine that is working in a cycle is the difference between the heat flow into the engine at high temperature and the heat flow out at a lower temperature (first law of thermodynamics) and that this is an example of the law of conservation of energy. This means that energyin must be accounted for in energyout. This would make sense with the first law of thermodynamics – Energy is neither created or destroyed in a reaction or exchange.

35. c. Students know the internal energy of an object includes the energy of random motion of the object's atoms and molecules, often referred to as thermal energy. The greater the temperature of the object, the greater the energy of motion of the atoms and molecules that make up the object. Temperature is the measure of the average KE of a system. As the KE (movement) of molecules in an object increases, the temperature increases. At a temperature of absolute zero, the KE of all molecules ceases, therefore, there would be no temperature at all, hence, absolute zero. 0 Kelvin is -273 Celsius. The freezing point of water is 273 K or 0 C.

36. The different gas laws come into play here. Boyle’s Law P1V1 = P2V2 applies when there is no change in temperature and number of gas molecules Charles’ Law P1V1 /T1 = P2V2 /T2 addresses a change in temperature with gases but requires no change in gas molecules. The Ideal Gas Law PV = nRT addresses all aspects of gas behavior. In this law n is the number of moles of gas and R is a gas constant.

37. d. Students know that most processes tend to decrease the order of a system over time and that energy levels are eventually distributed uniformly. 2nd Law of Thermodynamics or Law of Increasing Entropy. Increasing Entropy can be viewed as increasing chaos or increasing disorder. Systems with energy will lose that energy over time, usually to inefficiencies such as heat loss during a time of work or energy transfer. Even a battery with stored energy will run down over time whether or not it is used. Nothing has been shown to violate the 2nd law of thermodynamics.

38. e. Students know that entropy is a quantity that measures the order or disorder of a system and that this quantity is larger for a more disordered system. Duh! Here is a thought. Heat always radiates from hot to cold, never the reverse. You feel cold because you are radiating heat away from you body. The ‘colder’ an object feels is an indirect way of measuring how fast heat is radiating to that object from you. The reverse of this is also true.

39. This concludes Standard 3, Heat and Thermodynamics The following questions are retired STAR questions given by the state in prior years. These questions are meant to be representative of the types of content/concepts you should know.

40. When a gas is heated in a closed container, the internal pressure increases. Which best describes the reason for the increase in pressure? A The average kinetic energy of the gas molecules decreases. B The potential energy of the gas increases. C The average kinetic energy of the gas molecules increases. D The potential energy of the gas decreases.

41. A container of cold water is dumped into a larger container of hot water. It is mixed and then left alone for a long time interval. The water temperature is found to • A randomly vary from region to region in the container. • B be uniform throughout the container. • C fluctuate at all positions in the container. • D be greater at the bottom of the container.

42. 13. A cup of water at 40 °C and a cup of water at 5 °C are left on a table. Which graph correctly shows the temperature of the two cups of water as time passes?

43. 14. An engine has an input of heat energy of 10,750 J and does 2420 J of work. Which of the following is the heat loss? A 0.225 J B 4.44 J C 8330 J D 13,170 J

44. 15. Entropy decreases when A wood burns. B water freezes. C a snowball melts. D an iron nail rusts.

45. Waves 4. Waves have characteristic properties that do not depend on the type of wave. As a basis for understanding this concept:

46. a. Students know waves carry energy from one place to another. Waves carry energy through some form of medium (matter). The only waves that can travel in a vacuum are EM waves of which light is an example. The energy of a wave is found in its amplitude. Think of an ocean wave. The taller the wave, the higher its amplitude. The taller wave carries more energy.

47. b. Students know how to identify transverse and longitudinal waves in mechanical media, such as springs and ropes, and on the earth (seismic waves). There are two basic wave types: transverse and longitudinal. Both require a medium through which to travel with the exception noted Waves can be easily demonstrated through springs and ropes. Less obvious waves EM waves and Seismic waves can be measured through the use of sophisticated instruments.

48. c. Students know how to solve problems involving wavelength, frequency, and wave speed. The basic equation for wavelength, frequency, and speed is V = fλ Frequency is measured in Hertz (Hz). It is the measure of how many waves travel a point per second. Wavelength is the physical measure of how long the distance from one point on a wave until it repeats. A wavelength can be measured at any point on a wave.

49. d. Students know sound is a longitudinal wave whose speed depends on the properties of the medium in which it propagates. Longitudinal waves compress and decompress matter as it moves through it. Since gas molecules are far apart, relatively speaking, longitudinal waves travel slower than in other forms of matter (liquids and solids). Sound travels fastest through solids than any other medium. Sound travels in some gases much faster than in air. That is why your voice is much higher when you breathe helium. The frequency increases, thus, a higher pitch.

50. e. Students know radio waves, light, and X-rays are different wavelength bands in the spectrum of electromagnetic waves whose speed in a vacuum is approximately 3 x 108 m/s (186,000 miles/second). As mentioned, EM waves do not require a medium through which to travel. All EM waves travel at the same speed in a vacuum. When waves travel into a different medium, its speed will slow down or speed up depending upon the original medium. Remember, fondly, the take home test that you did using Snell’s Law?