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Follow the book at Note: Throughout this exam, use g = -10 m/s for the gravitational acceleration of the earth. The unit has to be m/s² (meter per sec squared). Ignore air resistance or friction between surfaces.

1. Briefly explain the following terms: (1) Newton’s three laws of motion (2) Potential energy and Kinetic energy (3) Conservation of momentum (4) Absolute temperature (5) First and Second law of thermodynamics

2. Suppose a car was at rest and then started accelerating at constant rate of 10 m/s². What is the car’s velocity after 20 seconds? How far has it travelled during that time?

3. A stone is thrown straight up with the initial velocity of 50 m/s. Calculate the position and velocity of the stone at t = 1 sec, 2 sec and 3 sec after it is thrown.

4. A baseball is thrown at angle of 45º above the horizontal with initial speed of 20√2 m/s. (1) How far has it travelled horizontally when it is at the highest position? (2) How long does it take for the ball to reach the highest position?

5. A child is riding a merry-go-round that is rotating at 10.0 rev/min. How much is the centripetal force exerted on her if her mass is 20 kg and she is 2 m from the center?

6. A planet has mass 3.0 × 10²³ kg and radius 2.0 × 10⁶ m. Calculate its acceleration of gravity. Use G = 6.67 × 10^-11 N·kg^-2·m².

7. A ball of mass 3 kg was moving at constant velocity 5 m/s before colliding with a second ball at rest whose mass is 4 kg. After the collision, the first ball moves at 2 m/s to the same direction as the initial movement. Assuming the collision was elastic, calculate the velocity of the second ball.

8. A skater was rotating at 0.8 rev/s with her arms extended, and is rotating at 4 rev/s when she pulls in her arms. Her moment of inertia was 2.5 kg·m² when her arms were extended. What is her moment of inertia when she pulled in her arms?

9. At which temperature will the average kinetic energy of gas molecules be twice as much as that at temperature 0ºC? Answer in Celsius.

10. A Carnot engine operates between temperatures 400ºC and 20ºC. What is its theoretical maximum efficiency?

11. A particular microwave has frequency 15 GHz (that is, 1.5 × 10¹⁰ vibrations per second). Using the speed of light c = 3.0 × 10⁸ m/s, calculate its wavelength.

12. Explain why free charges in static distribution inside conductors are located at the surface.

Sample Paper For Above instruction

Introduction

The principles of physics form the foundation for understanding the natural world, spanning across mechanics, thermodynamics, electromagnetism, and quantum physics. These fundamental concepts explain how objects move, how energy is conserved and transformed, and the nature of forces at play within the universe. This paper provides comprehensive explanations of essential physics terms and applies these principles to various practical problems involving motion, energy, gravitational forces, rotational dynamics, and thermodynamics, supported by relevant equations and theoretical insights.

Section 1: Definitions of Fundamental Physics Terms

Newton’s Three Laws of Motion

Newton's three laws of motion are fundamental principles that describe how objects behave in response to forces. The first law, also known as the law of inertia, states that an object remains at rest or moves uniformly in a straight line unless acted upon by an external force. The second law quantifies the relationship between force, mass, and acceleration: F = ma. It states that the acceleration of an object is directly proportional to the applied force and inversely proportional to its mass. The third law states that for every action, there is an equal and opposite reaction, emphasizing the mutual forces between interacting objects.

Potential Energy and Kinetic Energy

Potential energy is the stored energy possessed by an object due to its position or configuration, such as an object held at height in a gravitational field. Kinetic energy is the energy an object possesses due to its motion, given by KE = ½ mv². The conversion between potential and kinetic energy underpins many physical processes and conservation of energy in isolated systems.

Conservation of Momentum

The principle of conservation of momentum states that in a closed system with no external forces, the total momentum before an interaction equals the total momentum after. Mathematically, ∑p_initial = ∑p_final. This principle is crucial in analyzing collisions and explosions, ensuring the system's total momentum remains constant over time.

Absolute Temperature

Absolute temperature is a measure of thermal energy based on the absolute scale Kelvin (K), where 0 K corresponds to absolute zero, the lowest temperature possible. It is directly proportional to the average kinetic energy of molecules in a substance, allowing a precise quantification of thermal states.

First and Second Laws of Thermodynamics

The first law states that energy cannot be created or destroyed, only transformed from one form to another. The second law introduces the concept of entropy, asserting that in an isolated system, entropy tends to increase, dictating the direction of thermodynamic processes and the irreversibility of natural processes.

Section 2: Kinematic Calculations for Accelerating Cars

A car initially at rest accelerates at 10 m/s². After 20 seconds, its velocity (v) can be found using v = u + at, where u = 0: v = 0 + (10)(20) = 200 m/s. The distance traveled (s) is given by s = ut + ½ at² = 0 + ½ (10)(20)² = 0 + ½ (10)(400) = 2000 meters. These calculations exemplify basic kinematic equations that describe linear motion under constant acceleration.

Section 3: Motion of a Thrown Stone

The initial velocity of the stone is 50 m/s vertically upward. Its position after t seconds is given by y(t) = v_initial t + ½ g t², with g = -10 m/s². At t=1 s: y(1) = 50(1) + ½(-10)(1)² = 50 - 5 = 45 m. Velocity at that time: v = v_initial + g t = 50 - 10(1) = 40 m/s upward. Similarly, at t=2 s: y(2) = 50(2) + ½ (-10)(4) = 100 - 20 = 80 m; v = 50 - 20 = 30 m/s. At t=3 s: y(3) = 150 - 45 = 105 m; v = 20 m/s upward. The analysis illustrates the parabolic trajectory characteristic of projectile motion.

Section 4: Horizontal Range and Time to Peak for Projectile

The baseball's initial speed is 20√2 m/s at 45°, so the horizontal component is v_x = v_initial cos 45° = 20√2 × (1/√2) = 20 m/s. The time to reach maximum height: t_up = v_initial sin 45° / g = (20√2)(1/√2) / 10 = 20 / 10 = 2 s. The horizontal distance traveled to the highest point: v_x × t_up = 20 × 2 = 40 m.

Section 5: Centripetal Force on a Child

The centripetal force is calculated by F_c = m v_t² / r, where v_t is the tangential velocity. First, convert rotation speed: 10 rev/min = (10/60) rev/sec ≈ 0.1667 rev/sec. The circumference: C = 2π r = 2π(2) ≈ 12.566 m. The tangential velocity v_t = C × frequency = 12.566 × 0.1667 ≈ 2.094 m/s. Therefore, F_c = 20 × (2.094)² / 2 ≈ 20 × 4.386 / 2 ≈ 43.86 N.

Section 6: Gravitational Acceleration of a Planet

Using g = GM / R², where G = 6.67 × 10^-11 N·kg^-2·m², M = 3.0 × 10²³ kg, R = 2.0 × 10⁶ m, g = (6.67 × 10^-11) × (3.0 × 10²³) / (2.0 × 10⁶)² ≈ (2.001 × 10¹³) / 4 × 10¹² ≈ 5.00 m/s².

Section 7: Elastic Collisions and Velocity Calculations

In an elastic collision, both momentum and kinetic energy are conserved. Total initial momentum: p_initial = m₁ v₁ + m₂ v₂ = 3 × 5 + 4 × 0 = 15 kg·m/s. Final velocity of ball 1: v_1f = 2 m/s. Using conservation of momentum: 3 × 2 + 4 × v_2f = 15, so 6 + 4 v_2f = 15, v_2f = (15 - 6)/4 = 2.25 m/s.

Section 8: Conservation of Angular Momentum

The initial angular velocity ω_i = 0.8 rev/s; final ω_f = 4 rev/s. The moment of inertia I_i = 2.5 kg·m². Angular momentum L = Iω. Therefore, I_f = L / ω_f = (I_i ω_i) / ω_f = (2.5 × 0.8) / 4 = 2 / 4 = 0.5 kg·m².

Section 9: Temperature and Kinetic Energy of Gas Molecules

Since kinetic energy KE ∝ T, to double the KE, T must double. Therefore, if KE at 0°C (273 K), then KE at T: 2 KE at 273 K, so T = 2 × 273 = 546 K. Converting back to Celsius: T - 273 = 273 ºC, so T = 273 + (546 - 273) = 546 - 273 = 273ºC.

Section 10: Efficiency of Carnot Engine

The maximum efficiency η = 1 - T_C/T_H, with temperatures in Kelvin. T_H = 400 + 273 = 673 K; T_C = 20 + 273 = 293 K. η = 1 - 293/673 ≈ 1 - 0.435 = 0.565 or 56.5%.

Section 11: Wavelength of Microwave

Wavelength λ = c / f = (3.0 × 10⁸ m/s) / (1.5 × 10¹⁰ Hz) = 0.02 m or 2 cm.

Section 12: Charges in Conductors

Inside a conductor, free charges move under the influence of electric fields until they reach a state where the internal electric field cancels any further movement. This equilibrium results in charges accumulating on the surface, establishing an electric field outside that neutralizes the interior. This phenomenon ensures that the electric field within a static conductor is zero, and charge distribution occurs exclusively on the surface, minimizing potential energy.

Conclusion

The exploration of core physics concepts and their application to practical scenarios illustrates the interconnectedness of classical mechanics, thermodynamics, electromagnetism, and wave physics. These principles provide the tools necessary to analyze and predict physical phenomena, enhancing our understanding of the natural world and enabling technological advancements.

References

• Serway, R. A., & Jewett, J. W. (2018). Physics for Scientists and Engineers. Cengage Learning.
• OpenStax College. (2013). College Physics. OpenStax CNX. https://openstax.org/books/college-physics
• Young, H. D., & Freedman, R. A. (2019). University Physics with Modern Physics. Pearson.
• Tipler, P. A., & Mosca, G. (2008). Physics for Scientists and Engineers. W. H. Freeman.
• Halliday, D., Resnick, R., & Walker, J. (2014). Fundamentals of Physics. Wiley.