Asking questions and defining problems Transitional Reasoning Download PDF

Questions

1. 1.

   Two carts on a low-friction track carry magnets with like poles facing each other; Cart 1 holds a strong neodymium magnet, while Cart 2 holds a weaker ceramic magnet. When released from rest, Cart 2 accelerates away significantly faster than Cart 1, leading one student to claim that the stronger magnet exerts a greater magnetic force, while another claims that the mutual forces are equal and Cart 2 only accelerates faster due to having less mass. To define an empirical scientific investigation that directly resolves this disagreement by testing the equal-force claim, which research question should the students investigate?

   • A) Why does a neodymium magnet generate a more powerful magnetic field than an ordinary ceramic magnet?
   • B) How do the magnitudes of the forces exerted by each magnet on the other compare when measured simultaneously with force sensors during the interaction?
   • C) How does increasing the initial separation distance between the two carts affect the final speed reached by Cart 2?
   • D) What is the maximum load that can be added to Cart 1 before static friction completely prevents it from moving?
2. 2.

   A physics student investigates fluid statics and formulates the following research question: “How does the submerged volume of a solid object affect the buoyant force exerted on it by a liquid?” To establish a well-defined experimental problem that produces valid scientific evidence, the student must properly identify the roles of the physical quantities under study. Which of the following correctly identifies the independent variable, the dependent variable, and an essential controlled variable for this investigation?

   • A) Independent variable: buoyant force; Dependent variable: submerged volume; Controlled variable: mass of the object
   • B) Independent variable: density of the liquid; Dependent variable: buoyant force; Controlled variable: submerged volume
   • C) Independent variable: submerged volume; Dependent variable: density of the liquid; Controlled variable: buoyant force
   • D) Independent variable: submerged volume; Dependent variable: buoyant force; Controlled variable: density of the liquid
3. 3.

   While exploring electromagnetism, a student observes that wrapping more loops of insulated copper wire around an iron nail makes the nail pick up steel paper clips more effectively. To transition this qualitative observation into an empirically testable physics problem, the student must operationally define the ambiguous outcome of picking up clips 'more effectively.' Which of the following formulated questions best establishes this operational problem definition?

   • A) Why does wrapping additional wire loops around an iron nail make the resulting magnetic force fundamentally superior?
   • B) How does the number of wire loops wrapped around the nail affect the maximum total mass of paper clips suspended before detachment?
   • C) Which commercially available magnetic device is the most convenient tool for lifting mixed metallic debris in a workshop?
   • D) Does an electromagnet powered by a single cell work better than permanent magnets of different sizes and shapes?
4. 4.

   During a physics inquiry on friction, a student proposes the following research question: “Why do rougher surfaces always produce a worse sliding motion than smooth surfaces?” The teacher notes that this phrasing is unsuitable for guiding an empirical laboratory investigation. Which statement correctly identifies the primary flaw in the student’s question and explains how the problem should be properly defined?

   • A) It fails to incorporate an engineering constraint, meaning the problem must be redefined by specifying the financial budget and material limits of the sliding surfaces.
   • B) It uses a subjective and biased value judgment (“worse sliding motion”), meaning the problem must be redefined to measure an objective physical quantity such as frictional force.
   • C) It asks for a causal explanation rather than a descriptive one, meaning scientific problem definitions must avoid investigating the physical causes behind phenomena.
   • D) It lacks a predefined mathematical equation, meaning a valid scientific problem can only be investigated if a theoretical formula is established beforehand to predict the result.
5. 5.

   A student investigates thermal energy transfer to answer the question: “How does the volume of water affect its rate of cooling?” To test this, the student pours 100 mL of hot water into a tall, narrow cylinder and 300 mL of hot water into a wide, shallow basin, discovering that the water in the basin cools significantly faster over ten minutes. To critically refine the problem definition and resolve the experimental flaw in the student’s conclusion, which of the following questions must be asked?

   • A) How does the difference in exposed surface area between the two containers influence the rate of heat transfer to the surroundings?
   • B) Which container geometry provides greater mechanical stability to prevent hot water from spilling during testing?
   • C) Why does hot water produce visible vapor above the liquid surface when exposed to cooler room air?
   • D) Does the specific heat capacity of liquid water increase when a larger volume of water is heated?
6. 6.

   An engineering team is defining the design problem for an energy-absorbing bumper intended to reduce impact forces during cart collisions in a physics laboratory. To establish a rigorous problem definition, the team must identify both a criterion (a measurable standard of performance) and a constraint (a strict limitation or boundary that the design must satisfy). Which of the following correctly pairs a criterion with a constraint for this design problem?

   • A) Criterion: The bumper must reduce the cart's peak deceleration to less than 20 m/s² during impact. Constraint: The bumper's total mass cannot exceed 0.50 kg.
   • B) Criterion: The bumper's total production cost cannot exceed $15 per unit. Constraint: The bumper should absorb as much kinetic energy as possible during a crash.
   • C) Criterion: The bumper must protrude no more than 8.0 cm from the front of the cart. Constraint: The bumper must dissipate at least 75% of the initial kinetic energy.
   • D) Criterion: The bumper material must consist exclusively of non-toxic polymers. Constraint: The bumper should appear aesthetically sleek and match the cart's color.