Note Throughout This Work Use G10 Ms For The Gravitational ✓ Solved
Note Throughout This Work Use G 10 Ms For The Gravitational Accel
This assignment covers fundamental concepts in physics, including Newton's laws, energy, thermodynamics, motion, projectile dynamics, circular motion, gravitational acceleration, elastic collisions, rotational motion, kinetic energy of gases, thermodynamic efficiency, electromagnetic waves, and electrostatics in conductors. The questions range from theoretical explanations to practical calculations involving kinematics, dynamics, energy, rotational motion, gravitation, thermodynamics, electromagnetism, and electrostatics. The task is to provide comprehensive answers, including relevant formulas, detailed steps, and accurate numerical computations, resulting in approximately 1000 words with credible references.
Sample Paper For Above instruction
1. Explanation of Key Physics Terms
Newton’s Three Laws of Motion
Newton’s laws describe the relationship between the motion of an object and the forces acting on it. The first law, the law of inertia, states that an object remains at rest or in uniform motion unless acted upon by a net external force. The second law establishes that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass, expressed as F = ma. The third law states that for every action, there is an equal and opposite reaction.
Potential Energy and Kinetic Energy
Potential energy (PE) is stored energy possessed by an object due to its position or state, such as gravitational PE which depends on height. Kinetic energy (KE) is the energy an object possesses because of its motion, given by KE = ½ mv². Both are scalar quantities contributing to the total mechanical energy in a system.
Conservation of Momentum
The principle states that in the absence of external forces, the total momentum of a system remains constant. Mathematically, the sum of initial momenta equals the sum of final momenta, expressed as m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂', crucial in analyzing collisions.
Absolute Temperature
The thermodynamic temperature measured on the Kelvin scale, starting from absolute zero (0 K), where particles possess minimum thermal energy. It relates directly to the average kinetic energy of molecules in a gas.
First and Second Laws of Thermodynamics
The first law states energy cannot be created or destroyed, only transformed. The second law introduces entropy, indicating that in any isolated system, entropy tends to increase, implying the irreversibility of real processes and the direction of natural heat flow from hot to cold objects.
2. Car Acceleration and Distance
A car initially at rest accelerates with a constant acceleration of 10 m/s² over 20 seconds. The final velocity (v) is calculated using v = u + at, where u is initial velocity (0 m/s):
v = 0 + (10)(20) = 200 m/s.
The displacement (s) during this time is given by s = ut + ½ at²:
s = 0 + ½ (10)(20)² = 5 * 400 = 2000 meters.
Hence, after 20 seconds, the car's velocity is 200 m/s, and it has traveled 2000 meters.
3. Motion of a Thrown Stone
Initial velocity u = 50 m/s upward. Using g = -10 m/s² (negative because it's directed downward).
At t = 1 s, 2 s, 3 s:
Position (height): h(t) = ut + ½ gt²
Velocity: v(t) = u + gt
- At t=1 s:
h = 50(1) + ½(-10)(1)² = 50 - 5 = 45 m
v = 50 + (-10)(1) = 40 m/s upward
- At t=2 s:
h = 50(2) + ½(-10)(4) = 100 - 20 = 80 m
v = 50 - 20 = 30 m/s
- At t=3 s:
h = 150 - 45 = 105 m
v = 50 - 30 = 20 m/s
The height increases to a maximum at the apex (when v=0), but at these times, the velocities are still positive, indicating upward motion.
4. Projectile Motion at 45° Launch
Initial speed u = 20√2 m/s ≈ 28.28 m/s.
Component velocities:
u_x = u cos 45° = 20√2 / √2 = 20 m/s
u_y = u sin 45° = 20 m/s
(1) Horizontal distance at highest point: Since horizontal velocity u_x is constant, and the time to reach the maximum height is t = u_y / g:
t = 20 / 10 = 2 s
Horizontal distance = u_x t = 20 2 = 40 meters.
(2) Time to reach the highest position: t = u_y / g = 2 seconds.
Total time of flight is double this, 4 seconds, but only asked for reaching the highest point.
5. Centripetal Force on the Child
Given values: rotational frequency = 10 rev/min = (10/60) rev/sec ≈ 0.167 rev/sec.
Centrifugal acceleration: a_c = (4π² r f²), where r = 2 m, f = 0.167 s⁻¹.
a_c = 4 π² 2 (0.167)² ≈ 4 9.8696 2 0.02789 ≈ 4.4 m/s².
Centripetal force: F_c = m a_c = 20 kg 4.4 m/s² = 88 N.
The force exerted on her is approximately 88 Newtons.
6. Gravity Acceleration on the Planet
Given: mass M = 3.0 × 10²³ kg, radius R = 2.0 × 10⁶ m, G = 6.674 × 10⁻¹¹ N·(m/kg)².
Formula: g = G * M / R²
g = (6.674 × 10⁻¹¹) * (3.0 × 10²³) / (2.0 × 10⁶)²
g = 2.0022 × 10¹³ / 4.0 × 10¹² = ~5.005 m/s².
The acceleration of gravity on this planet is approximately 5.0 m/s².
7. Velocity After Elastic Collision
Masses: m₁=3kg, m₂=4kg.
Initial velocities: v₁i=5 m/s, v₂i=0.
After collision, v₁f=2 m/s.
Using conservation of momentum:
m₁v₁i + m₂v₂i = m₁v₁f + m₂v₂f
(3)(5) + 0 = (3)(2) + 4(v₂f)
15 = 6 + 4v₂f
4v₂f = 9
v₂f = 2.25 m/s
The second ball’s velocity after the collision is 2.25 m/s in the same direction.
8. Rotational Inertia Change
Initial angular velocity ω₁=0.8 rev/sec, final ω₂=4 rev/sec.
Moment of inertia before: I₁=2.5 kg·m².
Using conservation of angular momentum: I₁ω₁=I₂ω₂
Since ω₁ is zero, initial angular momentum is zero, which is inconsistent; it suggests the question relates only to the relative change. Assuming the problem means the skater spins faster by pulling arms, we can relate initial and final inertia from angular momentum conservation.
If initial angular momentum L = I₁ω₁, and final L = I₂ω₂:
Assuming initial L is zero (not physically meaningful here), instead, use the principle that angular momentum is conserved during the pull-in, and the relation: I₁ω₁ = I₂ω₂.
Rearranged, I₂= I₁(ω₁/ω₂) = 2.5 (0.8/4) = 2.5 0.2 = 0.5 kg·m².
Her moment of inertia when pulling in arms is 0.5 kg·m².
9. Temperature for Double Kinetic Energy
Average kinetic energy per molecule: KE ∝ T.
At T = 0°C = 273 K, KE = (3/2)k_B T.
We want KE at T₂ to be twice that at 0°C:
2 (3/2)k_B 273 = (3/2)k_B T₂
T₂ = 2 * 273 = 546 K.
Convert back to Celsius: T_C = T_K - 273 = 546 - 273 = 273°C.
The temperature is 273°C.
10. Efficiency of Carnot Engine
Efficiency η = 1 - T_C / T_H, where temperatures in Kelvin.
Convert given temperatures: T_H = 400°C + 273 = 673 K.
T_C = 20°C + 273 = 293 K.
η = 1 - (293/673) ≈ 1 - 0.435 = 0.565 or 56.5%.
Maximum theoretical efficiency is approximately 56.5%.
11. Wavelength of Microwave
Frequency f = 15 GHz = 1.5 × 10¹⁰ Hz.
Speed of light c = 3.0 × 10⁸ m/s.
Wavelength λ = c / f = 3.0 × 10⁸ / 1.5 × 10¹⁰ = 0.02 m = 2 cm.
12. Why Charges in Conductors Are on Surface
In conductors, free charges tend to reside on the surface due to electrostatic repulsion and the conductor's property of expelling internal electric fields. When charges are placed inside a conductor, they induce rearrangements that cancel internal electric fields, resulting in excess charge moving to the surface. This distribution minimizes potential energy and leads to an equilibrium state where the electric field inside the conducting material is zero, confining electric charges to the surface (Griffiths, 2017; Serway & Jewett, 2018).
References
- Serway, R. A., & Jewett, J. W. (2018). Physics for Scientists and Engineers with Modern Physics. Cengage Learning.
- Griffiths, D. J. (2017). Introduction to Electrodynamics. Cambridge University Press.
- Tipler, P. A., & Mosca, G. (2008). Physics for Scientists and Engineers. W. H. Freeman and Company.
- Feynman, R. P., Leighton, R. B., & Sands, M. (2010). The Feynman Lectures on Physics. Pearson.
- Halliday, D., Resnick, R., & Walker, J. (2014). Fundamentals of Physics. Wiley.
- Young, H. D., & Freedman, R. A. (2019). University Physics. Pearson.
- Beiser, A. (2014). Concepts of Modern Physics. McGraw-Hill Education.
- Gibilisco, S., & Steiner, S. (2016). Physics Handbook. McGraw-Hill.
- Morin, D. (2013). Introduction to Classical Mechanics. Cambridge University Press.
- Resnick, R., Halliday, D., & Krane, K. S. (2008). Physics. Wiley.