Physics Review: Equations of Motion, Conservation Laws, and Thermodynamics, Exams of Physics

Download Physics Review: Equations of Motion, Conservation Laws, and Thermodynamics and more Exams Physics in PDF only on Docsity! PHYS 161LG Advanced Principles of Physics Review Exam Q & A 2024 1. What is the definition of linear momentum of a system of particles? a) The sum of the masses of the particles b) The sum of the velocities of the particles c) The sum of the products of mass and velocity of the particles d) The sum of the forces acting on the particles Answer: c) The sum of the products of mass and velocity of the particles Rationale: Linear momentum is defined as mass times velocity, and for a system of particles, it is the sum of the linear momentum of each particle. 2. What is the condition for conservation of angular momentum about a fixed point O for a system of particles? a) The net external force acting on the system is zero b) The net external moment acting on the system is zero c) The net internal force acting on the system is zero d) The net internal moment acting on the system is zero Answer: b) The net external moment acting on the system is zero Rationale: Angular momentum is conserved when the time derivative of angular momentum is zero, which implies that the net external moment acting on the system is zero. 3. What is the difference between kinematics and kinetics of motion? a) Kinematics deals with geometry and kinetics deals with forces b) Kinematics deals with forces and kinetics deals with geometry c) Kinematics deals with position and kinetics deals with velocity d) Kinematics deals with velocity and kinetics deals with acceleration Answer: a) Kinematics deals with geometry and kinetics deals with forces Rationale: Kinematics describes the motion of bodies without considering the causes of motion, while kinetics analyzes the forces that cause or change the motion. 4. What is the equation of motion for a particle in 2D plane under a constant force F? a) r ̈ = F/m b) r ̈ = F/mg c) r ̈ = mg/F d) r ̈ = F/mr Answer: a) r ̈ = F/m 11. What is a heat engine? a) A device that converts heat into mechanical work b) A device that converts mechanical work into heat c) A device that converts heat into electrical energy d) A device that converts electrical energy into heat Answer: a) A device that converts heat into mechanical work Rationale: A heat engine is a device that operates on a thermodynamic cycle, in which it takes in heat from a high-temperature source, performs some mechanical work, and rejects some heat to a low-temperature sink. The net work done by the engine is equal to the difference between the heat input and the heat output. 12. What is the efficiency of a heat engine? a) The ratio of the net work done by the engine to the heat input b) The ratio of the net work done by the engine to the heat output c) The ratio of the heat input to the net work done by the engine d) The ratio of the heat output to the net work done by the engine Answer: a) The ratio of the net work done by the engine to the heat input Rationale: The efficiency of a heat engine is a measure of how well it converts heat into mechanical work. It is defined as the ratio of the net work done by the engine to the heat input from the high-temperature source. It is always less than one, since some heat is always lost to the low-temperature sink. 13. What is entropy? a) A measure of energy in a system b) A measure of disorder in a system c) A measure of temperature in a system d) A measure of pressure in a system Answer: b) A measure of disorder in a system Rationale: Entropy is a thermodynamic property that quantifies the degree of randomness or chaos in a system. It is related to the number of microscopic states or configurations that are compatible with the macroscopic state or condition of the system. A higher entropy means more possible microscopic states and more disorder. 14. What is the relation between entropy and temperature? a) Entropy increases with increasing temperature b) Entropy decreases with increasing temperature c) Entropy is independent of temperature d) Entropy is inversely proportional to temperature Answer: a) Entropy increases with increasing temperature Rationale: Entropy is related to temperature by the Clausius inequality, which states that for any reversible process, dS = δQ/T, where dS is the change in entropy, δQ is the infinitesimal amount of heat transferred, and T is the absolute temperature. This implies that for any process involving heat transfer, entropy increases with increasing temperature, since more heat means more disorder. 1. A particle of mass 2 kg is moving in a straight line with a velocity of 4 m/s. If a force of 8 N acts on the particle in the direction of its motion, what will be its acceleration? A) 2 m/s^2 B) 4 m/s^2 C) 8 m/s^2 D) 16 m/s^2 Answer: A) 2 m/s^2 Rationale: Using Newton's second law, F = ma, we can rearrange to find a = F/m. Substituting the given values, a = 8 N / 2 kg = 4 m/s^2. 2. A rigid body is rotating about a fixed axis with an angular velocity of 6 rad/s. If the moment of inertia of the body is 3 kg*m^2, what is the rotational kinetic energy of the body? A) 18 J B) 36 J C) 54 J D) 72 J Answer: B) 36 J Rationale: The rotational kinetic energy of a body is given by KE = (1/2)Iω^2. Substituting the given values, KE = (1/2) * 3 kg*m^2 * (6 rad/s)^2 = 36 J. 3. A wave of frequency 500 Hz has a wavelength of 0.6 m. What is the speed of the wave? A) 300 m/s B) 450 m/s C) 600 m/s D) 750 m/s Answer: A) 300 m/s Rationale: The speed of a wave is given by v = fλ. Substituting the given values, v = 500 Hz * 0.6 m = 300 m/s. 4. A heat engine operates between two reservoirs at temperatures of 500 K and 300 K. If the engine has an efficiency of 40%, what is the maximum possible efficiency of a heat engine operating between these two reservoirs? A) 40% B) 60% C) 66.7% D) 75% Answer: C) 66.7% Rationale: The maximum possible efficiency of a heat engine operating between two reservoirs is given by 1 - (Tc/Th), where Tc is the temperature of the cold reservoir and Th is the temperature of the hot reservoir. Substituting the given values, efficiency = 1 - (300/500) = 0.667 or 66.7%. 5. A system absorbs 200 J of heat at 300 K and releases 100 J of heat at 200 K. What is the change in entropy of the system? A) 0.2 J/K B) 0.4 J/K C) 0.6 J/K D) 0.8 J/K A) 0.2 m B) 0.4 m C) 0.6 m D) 0.8 m Answer: B) 0.4 m Rationale: The wavelength of a wave is given by λ = v/f. Substituting the given values, λ = 600 m/s / 300 Hz = 0.4 m. 12. A heat engine operates at a temperature of 500 K and has an efficiency of 30%. If the engine absorbs 6000 J of heat, what is the maximum possible work output of the engine? A) 900 J B) 1800 J C) 2700 J D) 3600 J Answer: B) 1800 J Rationale: The maximum work output of an engine is given by efficiency * heat input. Substituting the given values, work output = 0.3 * 6000 J = 1800 J. 13. A system absorbs 400 J of heat at 200 K and releases 200 J of heat at 100 K. What is the change in entropy of the system? A) 0.5 J/K B) 1 J/K C) 1.5 J/K D) 2 J/K Answer: B) 1 J/K Rationale: The change in entropy of a system is given by ΔS = Q/T. Substituting the given values, ΔS = (400 J/200 K) - (200 J/100 K) = 2 J/K - 2 J/K = 1 J/K. 14. A car engine operates at a temperature of 600 K and has an efficiency of 20%. If the engine absorbs 5000 J of heat, what is the maximum possible work output of the engine? A) 800 J B) 1000 J C) 1200 J D) 1400 J Answer: B) 1000 J Rationale: The maximum work output of an engine is given by efficiency * heat input. Substituting the given values, work output = 0.2 * 5000 J = 1000 J. 15. A particle is moving in a circular path with a radius of 3 m and an angular velocity of 4 rad/s. What is the magnitude of the particle's acceleration? A) 6 m/s^2 B) 8 m/s^2 C) 12 m/s^2 D) 16 m/s^2 Answer: C) 12 m/s^2 Rationale: The acceleration of a particle moving in a circular path is given by a = rω^2. Substituting the given values, a = 3 m * (4 rad/s)^2 = 12 m/s^2. Dynamics of Particles and Rigid Bodies Question: A particle of mass 2 kg moves along the x-axis according to the equation of motion, x = 2t^3 - 3t^2 + 2t + 5. What is the net force acting on the particle at t = 2 seconds? a) 15 N b) 23 N c) 31 N d) 39 N Answer: c) 31 N Rationale: The net force acting on a particle can be determined using the equation F = ma, where a is the acceleration. By differentiating the given equation twice to find the acceleration, then multiplying by the mass, the net force can be calculated to be 31 N. Conservation Laws Question: In a closed system, which of the following is a statement of the conservation of energy? a) Energy cannot be created or destroyed b) Energy can be created but not destroyed c) Energy can be destroyed but not created d) Energy can be created and destroyed freely Answer: a) Energy cannot be created or destroyed Rationale: According to the first law of thermodynamics, energy cannot be created or destroyed, only transformed from one form to another within a closed system. Wave Motion Question: What is the relationship between the speed, frequency, and wavelength of a wave? a) Speed = frequency x wavelength b) Speed = wavelength / frequency c) Speed = frequency / wavelength d) Speed = wavelength + frequency Answer: b) Speed = wavelength / frequency Rationale: The speed of a wave is equal to the product of its frequency and wavelength, as given by the equation v = fλ. Thermodynamics Question: Which of the following processes is classified as an isothermal process? a) Compression of a gas at constant temperature b) Expansion of a gas at constant volume c) Compression of a gas at constant pressure d) Expansion of a gas at constant pressure Answer: a) Compression of a gas at constant temperature Rationale: An isothermal process occurs at constant temperature, expansion and compression processes? a) To maximize the work output of the engine b) To minimize the temperature difference in the engine c) To maintain the efficiency of the engine d) To eliminate heat transfer in the engine Answer: c) To maintain the efficiency of the engine Rationale: The isothermal processes in a Carnot engine help maintain the efficiency of the engine by allowing heat to be exchanged at constant temperature. Entropy Question: What is the relationship between entropy and the reversibility of a process? a) Entropy increases in reversible processes b) Entropy decreases in reversible processes c) Entropy remains constant in reversible processes d) Entropy is irrelevant in reversible processes Answer: a) Entropy increases in reversible processes Rationale: In reversible processes, the entropy of a closed system tends to increase, reflecting the natural tendency of systems to move towards a state of greater disorder. Dynamics of Particles and Rigid Bodies Question: What is the relationship between the linear momentum and the kinetic energy of a particle? a) Linear momentum is equal to the square of the kinetic energy b) Linear momentum is directly proportional to the kinetic energy c) Linear momentum is inversely proportional to the kinetic energy d) Linear momentum has no relationship to the kinetic energy Answer: b) Linear momentum is directly proportional to the kinetic energy Rationale: The linear momentum of a particle is directly proportional to the square root of its kinetic energy, as given by the equation p = √2mE, where p is the momentum, m is the mass, and E is the kinetic energy. Conservation Laws Question: Which of the following quantities is conserved in both elastic and inelastic collisions? a) Kinetic energy b) Potential energy c) Total mechanical energy d) Linear momentum Answer: d) Linear momentum Rationale: In both elastic and inelastic collisions, the total linear momentum of the system is conserved, regardless of any changes in kinetic or potential energy. Wave Motion Question: What is the relationship between the frequency and the period of a wave? a) Frequency = 1 / period b) Frequency = period / wavelength c) Frequency = wavelength / period d) Frequency = period x wavelength Answer: a) Frequency = 1 / period Rationale: The frequency of a wave is inversely proportional to its period, as given by the equation f = 1/T, where f is the frequency and T is the period.