Physics Take Home Exam Must Show All Work If A Calculation I ✓ Solved

Physics Take Home Exammust Show All Work If A Calculation Is Needed

Drawn from the provided instructions, the assignment requires completing a comprehensive physics exam covering topics such as motion, energy, sound, light, electricity, magnetism, conversions, and more. Students must show all work for calculations, answer conceptual questions, and include references where applicable.

Sample Paper For Above instruction

Introduction

Physics provides a framework for understanding the natural phenomena around us, from the motion of objects to the behavior of energy and waves. This paper addresses the key questions outlined in the assignment, demonstrating relevant calculations and conceptual explanations based on fundamental physics principles. Throughout, emphasis is placed on showing all work for calculations, providing clear reasoning, and applying scientific laws appropriately.

Motion and Kinematics

1. To determine the velocity of a rock accelerating at 10 m/sec² over 12 seconds, we use the first equation of motion: v = u + at, where initial velocity (u) is 0 (assuming drop from rest).

v = 0 + (10 m/sec²)(12 sec) = 120 m/sec.

Thus, the rock reaches a velocity of 120 m/sec after 12 seconds.

2. Considering a rollercoaster, if potential energy at the start exceeds kinetic energy at the end, energy is lost. This loss is typically attributed to non-conservative forces like friction and air resistance. These forces dissipate mechanical energy as heat and sound, aligning with the law of conservation of energy which states energy cannot be created or destroyed, only transformed.

3. To find the average speed:

Total distance = sum of speeds * time per segment; assuming equal durations of 1 hour each:

Average speed = (40 + 45 + 50) / 3 = 45 miles/hour.

For acceleration, since speeds change linearly over time:

Change in velocity = 50 - 40 = 10 miles/hour over 2 hours.

Acceleration = (final - initial)/time = (10 miles/hour) / 2 hours = 5 miles/hour².

4. The difference between average speed and instantaneous speed:

- Average speed is total distance divided by total time over a trip.

- Instantaneous speed is the speed at a specific moment.

For example, if you start at 0 mph, accelerate to 60 mph, then decelerate back to 0, your average speed is the total distance over total time, but your instantaneous speeds vary during the trip.

5. Traveling 30 miles/hour, then changing to 60 miles/hour in 3 hours involves calculating acceleration:

\[

a = \frac{\Delta v}{\Delta t} = \frac{60 - 30}{3} = 10 \text{ miles/hour}^2

\]

6. It is possible to accelerate at a constant rate even if your speed remains constant, provided your direction changes. For example, turning in a circular track involves centripetal acceleration without changing the magnitude of velocity.

7. Newton's statement indicates that the sensations of forces felt at rest (e.g., gravity) are equivalent to experienced forces during uniform motion, exemplifying the equivalence principle which states that inertial and gravitational mass are indistinguishable.

8. Dropping a baseball from a building on the moon would result in the ball falling faster than on Earth because the moon's gravitational acceleration (~1.6 m/sec²) is less than Earth's (~9.8 m/sec²). The smaller gravitational pull causes less resistance against the fall.

9. A golf ball hit with the same force on the moon would travel farther because of weaker gravity and less atmospheric drag, leading to a longer flight and greater distance coverage.

10. Experiencing 3.5G's means feeling a force 3.5 times your weight; on a rollercoaster, this occurs at rapid changes in acceleration, especially at turns or drops. Experienced at the bottom of drops, where inertia causes increased G-forces.

11. Objects fall faster in a vacuum because there is no air resistance. A feather and a hammer dropped simultaneously on the Moon would hit the surface at the same time, unlike on Earth, where air drastically slows the feather.

12. Constant speed means the object covers equal distances in equal times, with zero acceleration. Constant acceleration involves speed continuously increasing or decreasing, such as a car accelerating on a highway.

13. The larger mass (the man) reaches terminal velocity first due to greater gravitational force, but both eventually fall at their respective terminal velocities. In vacuum, both reach the same acceleration regardless of mass.

14. In space, with engines off, the spacecraft maintains its velocity due to Newton's First Law. Without external forces, it will continue in a straight line at constant speed.

15. To find horsepower:

\[

\text{Power} = \frac{\text{Work}}{\text{Time}}

\]

Work done = force × distance; force = weight = 200 lbs (convert to Newtons: 200 lbs × 4.4 N/lb = 880 N), distance = 100 meters (convert from miles: 1 mile = 1609 meters), so:

\[

\text{Work} = 880 N \times 100 m = 88,000 J

\]

Time = 9.97 s, so power in Watts:

\[

P = \frac{88,000}{9.97} \approx 8,828 \text{ Watts}

\]

Horsepower:

\[

\text{HP} = \frac{8,828}{745.7} \approx 11.82 \text{ HP}

\]

16. Turning a bolt with a wrench is easier because the longer handle provides greater torque due to increased lever arm, reducing the force needed compared to using a screwdriver.

17. Power expended:

Force on the barbell:

\[

F = \text{Weight} = 200 lbs \times 4.4 N/lb = 880 N

\]

Convert 4 feet to meters:

\[

4 \text{ ft} \times 0.3048 = 1.2192 \text{ m}

\]

Power:

\[

P = \frac{F \times d}{t} = \frac{880 N \times 1.2192 m}{1.5 s} \approx 715.5 \text{ Watts}

\]

18. Work cannot be calculated from pushing pedals without considering the force component in the direction of movement. Only torque, which relates to rotational force, directly calculates work on pedals.

19. Machines make work easier by providing mechanical advantage—reducing the force needed—even though the total work output remains the same, by distributing effort over a longer distance.

20. Engine power:

Force = weight in Newtons = 6400 lbs × 4.4 N/lb = 28,160 N

Distance = 0.5 miles = 804.672 meters

Time = 60 sec

Work:

\[

W = F \times d = 28,160 \times 804.672 \approx 22,684,872 \text{ Joules}

\]

Power (Watts):

\[

P = \frac{W}{t} \approx \frac{22,684,872}{60} \approx 378,081 \text{ Watts}

\]

Convert to horsepower:

\[

\frac{378,081}{745.7} \approx 506.5 \text{ HP}

\]

Heat and Energy

21. Internal combustion engines convert chemical energy from gasoline into mechanical energy. Energy transformations include chemical → thermal → mechanical. The efficiency (~35%) is limited by thermodynamic losses such as heat dissipation and friction.

22. An incandescent bulb gets hotter because electrical energy converts mainly into heat and light, whereas LED lights convert most electrical energy directly into light, making them more efficient.

23. Layered clothing traps layers of air, an insulator that reduces heat transfer via conduction and convection, keeping you warmer than a single thick jacket.

24. Thermal blankets use reflective surfaces to reflect body heat back to the body, reducing heat loss by radiation, making them more effective than regular blankets.

25. Metal conducts heat efficiently, so holding a metal spoon feels colder because it conducts heat away from your hand faster. Plastic is a poor conductor, so it retains heat, feeling warmer.

Sound

26. Time taken for sound to travel through iron tracks:

Speed of sound in steel ≈ 5000 m/sec; distance = 1600 m.

Time = distance / speed = 1600 m / 5000 m/sec = 0.32 sec.

Distance from source:

Using the time = 10 sec, distance = speed × time = 5000 m/sec × 10 sec = 50,000 m (or 31.07 miles).

27. Sound travel time in air:

Distance = 10,000 m; speed of sound in air ≈ 343 m/sec.

Time = 10,000 / 343 ≈ 29.15 sec.

Underwater, speed ≈ 1482 m/sec; time = 10,000 / 1482 ≈ 6.75 sec.

28. Resonance occurs when fibers in the ear vibrate at their natural frequency in response to a specific pitch, enabling the brain to interpret different pitches as distinct sounds.

29. Sound propagates around corners through diffraction, a wave property allowing waves to bend around obstacles, unlike light, which primarily relies on reflection and refraction.

30. Sonar uses sound waves to detect objects underwater; radar uses radio waves for detection in the atmosphere; applications include submarine navigation and aircraft weather monitoring.

31. A sonic boom results from the Doppler effect caused by an object exceeding sound speed, creating a sudden change in pressure waves that produce a loud noise and involves constructive interference of shock waves.

32. If the reflected wave has a longer wavelength, the object is moving away from the observer due to the Doppler effect, indicating a lower frequency and longer wavelength.

33. A sound system spanning 10–50,000 Hz covers the range of human hearing; older individuals may have diminished hearing, making such a range less necessary for them.

34. Voice sounds different on recordings because of the way sound waves interact with the recording device and microphone, capturing a different sound profile than in real life.

35. Your voice sounds different over the phone because the transmitted sound is processed and often compressed, altering tonal qualities; also, it lacks the full acoustic environment.

Light

36. To distinguish a diverging (concave) from a converging (convex) lens:

- Place an object and observe the image size; convex lenses magnify, while concave reduce.

- Use a screen: convex lenses project a real image; concave lenses produce virtual images.

37. The mirror in the funhouse that enlarges or inverts the image is a convex mirror if it enlarges or a concave mirror if it inverts and enlarges depending on position.

38. A mirror that makes you look smaller is typically a convex mirror, which diverges light rays, producing a diminished image.

39. To start a fire with a lens using sunlight, a converging (convex) lens is needed to focus sunlight to a point, increasing temperature through concentration.

40. Colorblind individuals often have deficiencies in cone cell sensitivity, especially the red or green cones, affecting their perception of shades.

41. More men are colorblind because the gene responsible is on the X chromosome; males (XY) have only one X, so if it carries the defective gene, they are affected.

42. Blueberries under colored lights:

- Magenta light: appears magenta (red + blue)

- Cyan light: appears cyan (blue + green)

- Yellow light: appears yellow (red + green)

- White light: appears white

43. Tomatoes under colored lights:

- Magenta: pinkish-red

- Cyan: darker red (less vibrant)

- Yellow: dull orange-red

- White: true red

Electromagnetism and Related Topics

44. Microwave heating involves resonance of water molecules: microwaves cause water molecules to vibrate at their natural frequency, generating heat directly.

45. Coherent light from lasers results from waves in phase, reinforcing each other and producing a high-intensity, narrow beam.

46. Glass lenses focus sunlight to a point; glasses contain multiple refractive elements. Ordinary glasses are not designed to focus sunlight enough to start fires physically.

47. Mixing magenta and cyan light yields white (the sum of red, green, blue). Paint mixing results in a darker, more absorptive color due to subtractive mixing.

48. Bifocals lead to near and far vision correction, indicating the eye's lens system has a problem with accommodation, affecting focus.

49. Nearsightedness (myopia) results from an eyeball too long or cornea too curved; corrected with diverging lenses. Farsightedness (hyperopia) results from a short eyeball or weak lens, corrected with converging lenses.

50. Suggestions for refracting elements in the eye: a) cornea, b) lens, c) aqueous humor. Problems include astigmatism and cataracts, affecting vision clarity.

Additional Physics Concepts

51. When red light illuminates a red rose, leaves absorb green and blue light and appear darker; under yellow light, they reflect green, so they appear red or darker depending on remaining illumination.

52. Under green light, petals appear black because they absorb green light and do not reflect it.

53. Under sunlight, yellow cloth appears yellow; under yellow light, it remains yellow; under blue light, it appears black since it reflects only blue light, which is absent.

Energy and Power in Practical Contexts

54. Microwave ovens heat food by exciting water molecules via resonance of the water's vibrational modes, resulting in rapid heating.

55. Laser coherence allows the photons to be in phase, resulting in constructive interference, intense focus, and minimal divergence, which is why laser beams are so powerful.

56. A "near-sighted" character aiming at the Sun with glasses can't start a fire because glasses do not focus sunlight; they only correct vision.

57. Mixing magenta and cyan light creates white (additive color mixing). Mixing magenta and cyan paint results in a darker shade—more subtractive.

58. Bifocals correct both distant and near vision by combining two different lens powers into one; the eye's accommodation is limited in some conditions.

59. If you can see far but not near (hyperopia), the eye's lens can't focus light on the retina; correct with converging lenses. The opposite (myopia) is corrected with diverging lenses.

60. The cornea, lens, and aqueous humor help focus light; defects in these (like astigmatism or cataracts) impair vision.

Conclusion

This comprehensive overview addresses the core conceptual and calculation-based questions from the exam prompts. It illustrates physics principles with detailed reasoning, emphasizing showing all work for clarity. The explorations reaffirm fundamental laws like conservation of energy, Newton's laws, wave properties, and electromagnetic phenomena, illustrating their real-world applications and significance.

References

• Halliday, D., Resnick, R., & Walker, J. (2014). Fundamentals of Physics (10th ed.). Wiley.
• Serway, R. A., & Jewett, J. W. (2014). Physics for Scientists and Engineers with Modern Physics. Brooks Cole.
• Giancoli, D. C. (2013). Physics for Scientists and Engineers. Pearson.
• Tipler, P. A., & Mosca, G. (2008). Physics for Scientists and Engineers. W. H. Freeman.
• NASA. (2020). Basic Principles of Space Physics. NASA.gov.
• Hecht, E. (2016). Optics (5th ed.). Pearson.
• Tipler, P. A., & Llewelyn, D. (2007). Modern Physics. W. H. Freeman.
• Young, H. D., & Freedman, R. A. (2014). University Physics with Modern Physics. Pearson.
• Marion, J. B., & Thornton, S. T. (2012). Classical Dynamics. Brooks Cole.
• Tipler, P. A., & Llewelyn, D. (2008). Physics for Scientists and Engineers: Extended Version. W. H. Freeman.