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[IB Physics HL/SL] 2017 Paper 1 — Question 4: Circular Motion & Centripetal Dynamics
This question assesses key circular motion principles from the IB Physics curriculum, specifically requiring you to balance tension and gravitational vectors to derive net centripetal acceleration. Working through this problem reinforces critical algebra techniques, free-body diagram interpretation, and significant figure rules tested consistently in Paper 1 and Paper 2.
💡 Key Concept & Principle
This question focuses on Centripetal Acceleration and Resultant Net Force. Centripetal force is not an independent physical force; it represents the net radial vector sum of real forces (e.g., tension, gravity, normal reaction) directed toward the instantaneous center of curvature.
Primary Equations:a_c = v² / r = ω²rF_net = (m * v²) / r
🎯 What This Question Tests
- Resolving forces accurately on perpendicular Cartesian axes.
- Connecting angular velocity (ω) with linear tangential speed (v).
- Identifying boundary conditions for tension when the rotating bob passes through the lowest point.
- Rigorous conversion between standard SI units prior to substitution.
How to Approach
Follow this systematic procedure to guarantee maximum credit on similar IB physics problems:
- Construct a Clear Free-Body Diagram (FBD): Identify and sketch every real physical force acting on the mass. At the bottom of the loop, Tension (T) points upward toward the center, while Weight (mg) acts downward.
- Extract Given Quantities & Boundary Conditions: Extract known parameters with explicit units:
r = 0.50 m,m = 0.25 kg, andv = 3.2 m s⁻¹. - Select & Formulate the Governing Equation: The net force toward the center supplies centripetal acceleration:
T - mg = (m * v²) / r. Rearrange symbolically:T = m(g + v²/r). - Substitute Carefully & Calculate: Use standard constants (
g = 9.81 m s⁻²). Show raw algebraic substitution clearly to secure method marks even if a calculator typing slip occurs. - Sanity-Check the Final Result: Verify that the final magnitude matches expected physical scales, contains correct SI units (
N), and adheres to significant figure constraints.
Step by Step Solution
Always state the raw un-substituted equation first. If you make a numerical computation error later, examiners can still award method marks (M marks) solely based on your written algebraic formulation.
⚠️ Common Mistakes to Avoid
- Drawing Centripetal Force as an Additional Vector: Labeling a separate “centripetal force arrow” on an FBD is penalized immediately in IB markschemes. Only draw contact and gravitational field forces.
- Radian vs. Degree Mode: Forgetting to verify calculator mode when dealing with angular velocities or trig components.
- Unit Conversion Slips: Failing to convert grams to kilograms (
g → kg) before evaluating kinetic terms.
Exam Reminder: An answer exceeding the question stem’s significant figures by more than ±1 s.f. incurs an automatic deduction on final marks.
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