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# Work and Energy: Motion on a skateboard

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Your cousin Throckmorton skateboards down a curved playground ram. Treating Throcky and his skateboard as a particle, his center of mass moves through a quarter-circle with a radius R = 3.0 m (see figure below.) The total mass of Throcky and his skateboard is 25.0 kg. He starts from rest and there is no friction. (a) Find his speed at the bottom of the ramp. (b) Find the normal force that acts on him at the bottom of the ramp. (c) Suppose that the ramp is not frictionless and that Throcky's speed at the bottom is only 6.00 m / s. What work was done by the friction force acting on him?

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#### Solution Summary

Problem with work, energy and centripetal force is solved.

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## Natural Sciences Study Guide

1. Which of the following can be considered a definition of "theory?"
a. A theory can be an explanation of scientific laws.
b. A theory is an integrated explanation of numerous hypotheses, each supported by a large body of observations and experiments.
c. A theory is a condensation and simplification of much data that previously appeared unrelated.
d. All of the above.

2. What is the correct sequence of steps in the scientific method?
I. State a problem
II. Develop a hypothesis
III. Share results with other scientists
IV. Analyze and interpret data
V. Design and perform experiment to test hypothesis
a. 1-2-3-4-5
b. 5-3-2-1-4
c. 1-2-5-4-3
d. 5-1-2-4-3

3. Identify that type of radiation that has the highest energy.
b. Gamma rays
c. Ultraviolet waves
d. Microwaves

4. In Europe, alternating current vibrates to and fro 50 cycles in 1 second. The frequency of these vibrations is _______________.
a. 50 Hz
b. 1/50 Hz
c. 120 volts
d. 240 volts

5. When an atom forms an anion, it ___________.
a. Loses one or more electrons
b. Gains one or more electrons
c. Loses one or more protons
d. Gains one or more protons

6. When a liquid changes phase to a gas, it ___________.
a. Absorbs energy
b. Releases energy
c. Neither absorbs or releases energy
d. Freezes

7. The volume of a submerged body is equal to the ______of the fluid displaced.
a. Weight
b. Volume
c. Density
d. Buoyancy

8. The speed of a satellite in an elliptical orbit __________________.
a. Remains constant
b. Acts at right angles to its motion
c. Varies
d. All of these

9. _____ rocks form from existing rocks.
a. Igneous
b. Metamorphic
c. Sedimentary
d. All

10. Most of the Earth's fresh water is located in ________.
a. Polar icecaps and glaciers
b. The atmosphere
c. Rivers, lakes and streams
d. Groundwater

11. The following are entities or phenomena found in physics, chemistry, earth sciences and astronomy. Which is smallest in size?
a. Spiral galaxy
b. A hurricane
c. An atom
d. The solar system

12. Air is classified as ____________.
a. An element
b. A compound
c. A homogeneous mixture
d. A heterogeneous mixture

13. The following are entities or phenomena found in physics, chemistry, earth sciences, and astronomy. Which is largest in size?
a. A spiral galaxy
b. A hurricane
c. An atom
d. Jupiter

14. If an atom has 18 electrons 20 neutrons, and 19 protons, what is its mass number?
a. 19
b. 18
c. 39
d. 57

15. Identify the correct statement.
a. Heat flows from a lower temperature to a higher temperature.
b. Gases flow from high pressure to low pressure.
c. Electricity flows from a lower potential to a higher potential.
d. When there is air resistance, objects fall at an acceleration of 9.8m/s2

16. Condensation is a process that results in __________________.
a. Heating
b. Cooling
c. Convection
d. Conduction

17. The percentage of the Earth's surface that is covered by oceans is about ______.
a. 50%
b. 60%
c. 70%
d. 80%

18. What is the main source of energy driving our planet's hydrologic cycle?
a. The tides
b. The sun
c. The Earth's rotation
d. Strong equatorial winds

19. Ionic bonding would be found in which of the following compounds?
a. H2O
b. KCl
c. CO2
d. CH4

20. When fossil fuels are burned for energy, which of the following statements is correct?
a. The reaction is endothermic.
b. The reaction is exothermic.
c. The reaction depletes the atmosphere of carbon dioxide.
d. The reaction is classified as a chain reaction.

21. Periods on the periodic table list elements __________.
a. With similar chemical properties
b. With different chemical properties
c. With the same number of electrons
d. With the same number of neutrons

22. Which is not a specific branch of the physical sciences?
a. Astronomy
b. Geology
c. Astrology
d. Meteorology

23. If a sample of lead has a mass of 200 kg, and a large man has a mass of 200 kg, identify the correct statement.
a. The sample of lead and the large man will have the same volume.
b. The same of lead and the large man will have the same density.
c. The sample of lead and the large man will have different volumes.
d. The sample of lead and the large man may, or may not, have the same volume.

24. Identify the correct statement.
a. The Fahrenheit degree is 1.8 times as large as the Celsius degree.
b. The Fahrenheit degree is 9/5ths as large as the Celsius degree
c. The Celsius and the Fahrenheit degree are equal in size to one another.
d. The Celsius and the Kelvin degree are equal in size to one another.

25. When no air resistance acts on a fast-moving baseball, its acceleration is ________.
a. Zero
b. Downward, g
c. Opposite the force of gravity
d. Upward, g

26. Light waves and sound waves both consist of vibrations. However, _________.
a. Sound waves require no medium for transmission
b. Sound and light waves both require a medium for transmission.
c. Light waves require no medium for transmission.
d. Light waves require a medium for transmission.

27. Comets and asteroids orbit about the _______
a. Sun
b. Moon
c. Earth
d. All of the above

28. Scientists believe that the Earth is ________ of years old.
a. Trillions
b. Billions
c. Millions
d. Thousands

29. The colors we see when looking at an object depend on the ________
a. Density of the object
b. Amplitude of the light we see
c. Frequency of the light we see
d. Mass of the object we are looking at

30. The force of gravity between two bodies depends on their _______.
a. Masses and charges
b. Masses and distance apart
c. Charges and distance apart
d. Masses only

31. Identify the correct statement dealing with Newton's Second Law.
a. Force and mass are inversely proportional to one another.
b. Force and acceleration are inversely proportional to one another.
c. Mass and acceleration are inversely proportional to one another.
d. Mass and acceleration are directly proportional to one another.

32. A box is moved from the floor to the top of a table.
a. The work is done by the box.
b. Potential energy of the box increases.
c. Kinetic energy of the box is constant throughout the process.
d. Mass of the box changes.

33. What would be the path of the moon if all the gravitational forces on it vanished to zero?
a. A parabola
b. A straight line
c. A sine wave
d. An ellipse

34. The largest ocean is the __________.
a. Atlantic Ocean
b. Pacific Ocean
c. Southern Ocean
d. Indian Ocean

35. Volcanoes are especially present under ___________.
a. The Atlantic Ocean
b. The Pacific Ocean
c. The Southern Ocean
d. The Indian Ocean

36. If the distance between two stars is tripled, the force of gravity between them __________.
a. Is unchanged
b. Increases by a factor of 9
c. Decreases by a factor of 9
d. Decreases by a factor of 3

37. In a thunderstorm we _________.
a. See lightning before we hear the thunder
b. See lightning and hear the thunder at the same time
c. Hear thunder first and then see the lightning related to it
d. Sometimes see lightning first and then hear thunder and in other times, it is the reverse

38. Spectral lines are useful in __________.
a. Identifying atoms or molecules
b. Understanding how electrons are arranged in atoms
c. Both of the above
d. Neither of the above

39. Temperature is generally proportional to a substance's _______.
a. Chemical energy
b. Average translational kinetic energy
c. Rotational kinetic energy
d. Vibrational potential energy

40. Which of the following represents a chemical change?
a. Metal expanding when heated
b. Dry ice, solid carbon dioxide, undergoing sublimation
c. The burning of gasoline
d. Ice melting

41. The role of a catalyst is to _________.
a. Speed up a chemical reaction
b. Slow down a chemical reaction
c. Act as a reactant in a chemical reaction
d. Serve as a product in a chemical reaction

42. The family of elements that is highly nonreactive is called the _______.
a. Alkali Metals
b. Alkaline Earth Metals
c. Rare Gases
d. Transition Metals

43. The law of conservation of energy states that in the absence of external work input or output, __________.
a. Energy cannot be created or destroyed
b. Energy will be created and then destroyed
c. Momentum cannot be created
d. Mass cannot be created or destroyed

44. Which are the two most common elements in the Earth's core?
a. Silicon and oxygen
b. Iron and Nickel
c. Oxygen and Iron
d. Oxygen and Nickel

45. Fossils form in _________________.
a. Igneous rocks
b. Sedimentary rocks
c. Metamorphic rocks
d. All of the above

46. That mineral that is most prevalent on the Earth's landmasses is __________.
a. Basalt
b. Granite
c. Silicon
d. Oxygen

47. Which of the following laws is most closely related to current flow?
a. Boyle's law
b. Ohm's law
c. Archimedes' principle
d. Bernoulli's principle
48. The Himalayas and the Alps were created by the action of _________.
a. Converging plates
b. Diverging plates
c. Transform plates
d. Glaciers

49. In which layer of the atmosphere does weather occur?
a. Mesosphere
b. Troposphere
c. Thermosphere

50. Identify the science that is basic to all the physical sciences.
a. Chemistry
b. Physics
c. Meteorology
d. Astronomy

51. Explain the difference between fission and fusion. Describe in detail why both processes produce large amounts of energy. Which process was used in the Atomic Bomb? Which process is used in nuclear reactors? Which process can be harnessed for the production of electricity?

52. The ocean has a pH of approximately 8.9. Is the ocean acidic or basic? There is concern that the ocean's pH is becoming more acidic. Explain why this might be occurring. What would be the impact if the ocean's pH dropped significantly? How would you explain a logarithmic function?

53. Describe the similarity and differences between Newton's Law of Universal Gravitation and Coulomb's Law.

54. How would you explain the difference between kinetic energy and potential energy? Give an example from the real world where potential energy is converted into kinetic energy.

55. Answer the questions below given the following data for four elements:

Element Melting Pt. Boiling Pt. Density Moh's Rating
Sodium, Na 97.7oC 883oC 0.968g/cm3 N/a
Mercury, Hg -38.8oC 356.7oC 13.5 g/cm3 N/a
Gold, Au 1064oC Not given 19.3g/cm3 2.5
Carbon, C 3500oC 4827oC 3.515g/cm3 10 (diamond)
Density data are given at room temperature.
Which elements are metals? Which elements are solids at room temperature? Would any of these elements be able to float in water? Explain your answer. Which element is the most reactive in air?

Gold has a Moh's Scale Rating of 2.5. Diamond has a Moh's rating of 10.0. Explain what these ratings mean.

Show all work. Single answers will not be accepted.

56. A water wave oscillates up and down four times each second. The distance between wave crests is 2 meters.
a. What is its frequency?
b. What is its wavelength?
c. What is its wave speed?

57. Assume that a 6-volt energy source is in a circuit that has a resistance of 10 ohms. Determine the current and the power. Provide numerical values and units.

58. A 50 Newton horizontal force pushes on a 10 kg mass sitting on a horizontal surface. Additionally the horizontal surface exerts a 25 Newton frictional force on the mass. What is the acceleration of the mass?

59. A boy who has a mass of 100 kg is skateboarding at 9.0 m/s2 when he smacks into a brick walls. He immediately comes to a dead stop in 0.2 seconds.
a. Show that his deceleration is 45m/s2.
b. Show that the force of impact is very large - 4500 Newtons.

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