AZSCI Physical Science 2 — Questions and Answers
Question 1: A student builds a simple circuit with a variable resistor, a battery, and an ideal ammeter. They observe that as they decrease the resistance, the current increases, as predicted by Ohm's Law (V=IR). However, when they decrease the resistance to a very low value, approaching zero, the current stops increasing and levels off at a maximum value. Which of the following provides the most likely explanation for this edge case observation?
- The ammeter has reached its maximum reading capacity.
- The battery has a non-zero internal resistance that limits the total current. (Correct answer)
- The connecting wires have gained significant resistance due to heating.
- Quantum tunneling effects begin to dominate at very low external resistance.
Correct answer: The battery has a non-zero internal resistance that limits the total current.
While Ohm's law is a fundamental concept, real-world components have limitations. An ideal battery has zero internal resistance, but a real battery has a small internal resistance. In the circuit, the total resistance is the sum of the external variable resistor and the battery's internal resistance (R_total = R_ext + R_int). The current is I = V / R_total. As the external resistance (R_ext) approaches zero, the total resistance is limited by the internal resistance (R_int), so the current approaches a maximum value of I_max = V / R_int. This prevents the current from becoming infinite.
Question 2: Two figure skaters, Skater A (80 kg) and Skater B (50 kg), are standing motionless on frictionless ice. They push off from each other. According to the law of conservation of momentum, which of the following statements accurately describes the situation immediately after they separate?
- Both skaters will have the same magnitude of momentum and the same amount of kinetic energy.
- Skater A, being more massive, will have a greater magnitude of momentum.
- Skater B will experience a greater change in velocity (acceleration) than Skater A. (Correct answer)
- The total kinetic energy of the system will be zero after the push.
Correct answer: Skater B will experience a greater change in velocity (acceleration) than Skater A.
The total momentum of the system (both skaters) is initially zero. By the law of conservation of momentum, the total momentum must remain zero after they push off. This means the momentum of Skater A (p_A = m_A * v_A) must be equal in magnitude and opposite in direction to the momentum of Skater B (p_B = m_B * v_B). Since Skater B has less mass, they must have a greater velocity to have the same magnitude of momentum as Skater A. A greater change in velocity implies a greater acceleration (F=ma). While momenta are equal and opposite, kinetic energy (KE = 1/2 * mv^2) will not be equal; the less massive skater will have more kinetic energy.
Question 3: A scientist is studying a chemical reaction in a sealed, insulated container (a closed system). The reaction is highly exothermic, releasing a large amount of thermal energy. According to the fundamental laws of thermodynamics and matter, which quantity within the closed system must remain constant throughout the reaction?
- The temperature of the system.
- The pressure inside the container.
- The total mass of the reactants and products. (Correct answer)
- The phase (solid, liquid, gas) of the substances.
Correct answer: The total mass of the reactants and products.
This question tests the Law of Conservation of Mass. In any closed system, mass is neither created nor destroyed by chemical reactions. The total mass of the products must equal the total mass of the reactants. Because the reaction is exothermic, the temperature will increase. This increase in temperature will likely cause an increase in pressure (according to gas laws if gases are involved) and could potentially cause a phase change (e.g., a liquid boiling into a gas).
Question 4: An astronomer observes light from a distant star and notices that its spectrum is shifted towards the blue end. The star is also known to be rotating. Which scenario best explains the 'blueshift' observation?
- The star is moving away from Earth at a high velocity.
- The light is being observed from the side of the star that is rotating away from Earth.
- The star is moving towards Earth, causing the wavelengths of its light to be compressed. (Correct answer)
- The star is passing through a dense interstellar dust cloud that scatters red light.
Correct answer: The star is moving towards Earth, causing the wavelengths of its light to be compressed.
This is an application of the Doppler effect for light. A 'blueshift' occurs when a light source is moving towards the observer, causing the observed wavelengths to be shorter (compressed) and shifted towards the blue end of the electromagnetic spectrum. A 'redshift' occurs when the source moves away. The rotation of the star would cause a redshift on the side moving away and a blueshift on the side moving towards, but the overall shift of the star's spectrum indicates its net motion relative to Earth. Scattering by dust is a different phenomenon and is not the primary cause of a uniform spectral shift.
Question 5: When a radioactive isotope undergoes alpha decay, it emits an alpha particle (which is a helium nucleus, ²⁴He). If an atom of Uranium-238 (⁹²²³⁸U) undergoes alpha decay, what is the resulting nucleus?
- Protactinium-238 (⁹¹²³⁸Pa)
- Uranium-234 (⁹²²³⁴U)
- Neptunium-239 (⁹³²³⁹Np)
- Thorium-234 (⁹⁰²³⁴Th) (Correct answer)
Correct answer: Thorium-234 (⁹⁰²³⁴Th)
In alpha decay, the nucleus loses an alpha particle, which consists of 2 protons and 2 neutrons. This means the atomic number (number of protons) decreases by 2, and the mass number (total protons and neutrons) decreases by 4. For Uranium-238 (⁹²²³⁸U), the new atomic number will be 92 - 2 = 90. The new mass number will be 238 - 4 = 234. The element with atomic number 90 is Thorium (Th). Therefore, the resulting nucleus is Thorium-234 (⁹⁰²³⁴Th).
Question 6: A student is designing an experiment to test Newton's second law (F=ma) by pulling a cart of mass (m) along a frictionless surface with a constant force (F). To analyze the relationship between force and acceleration, they need to measure acceleration. Which of the following methods would provide the most direct measurement of the cart's acceleration?
- Measuring the final velocity of the cart after a set time and dividing velocity by time.
- Using a motion sensor to plot a velocity-time graph and calculating the slope. (Correct answer)
- Measuring the total distance the cart travels in a set amount of time.
- Placing the cart on a balance to measure the force applied.
Correct answer: Using a motion sensor to plot a velocity-time graph and calculating the slope.
Acceleration is defined as the rate of change of velocity. A velocity-time graph visually represents this relationship. The slope of a velocity-time graph (change in velocity divided by change in time) is the definition of average acceleration. If the acceleration is constant, the graph will be a straight line, and its slope will be the acceleration. Measuring only the final velocity assumes the initial velocity was zero and gives the average acceleration, but plotting the graph provides a more robust and direct analysis of the constant acceleration. Measuring distance requires more complex kinematic equations (like d = v₀t + ½at²) to find 'a'. A balance measures mass or weight (force due to gravity), not the applied horizontal force or resulting acceleration.
AZSCI Physical Science 2
A student builds a simple circuit with a variable resistor, a battery, and an ideal ammeter.
They observe that as they decrease the resistance, the current increases, as predicted by Ohm's Law (V=IR).
However, when they decrease the resistance to a very low value, approaching zero, the current stops increasing and levels off at a maximum value.
Which of the following provides the most likely explanation for this edge case observation?