2012 Ap Physics C Mechanics Frq

2012 AP Physics C Mechanics Free Response Questions: A Comprehensive Review

The 2012 AP Physics C Mechanics Free Response Questions (FRQs) presented a challenging yet rewarding assessment for students. This comprehensive guide will delve into each question, providing detailed solutions, highlighting key concepts, and offering strategies for tackling similar problems in future exams. Understanding these questions is crucial for mastering the fundamental principles of Newtonian mechanics.

Question 1: Circular Motion and Energy Conservation

This question focused on the principles of circular motion, energy conservation, and Newton's second law. It involved analyzing the motion of a block attached to a string moving in a vertical circle.

Part (a): Finding the Tension

This part required calculating the tension in the string at the bottom of the circle. The key here was to apply Newton's second law in the radial direction. The net radial force is the difference between the tension and the weight, and this net force provides the centripetal acceleration:

T - mg = mv²/r

where:

• T = tension
• m = mass of the block
• g = acceleration due to gravity
• v = speed of the block at the bottom
• r = radius of the circle

The speed, v, was given, allowing for direct calculation of the tension. Understanding the direction of forces and applying Newton's second law correctly was paramount here. Students needed to correctly identify that the tension points upwards and the weight points downwards.

Part (b): Minimum Speed at the Top

Part (b) involved determining the minimum speed the block needs at the top of the circle to maintain circular motion. At the top, the tension can be zero (the minimum speed case). Applying Newton's second law again:

mg = mv²/r

Solving for v provides the minimum speed required to ensure the block remains in circular motion. This part emphasized the understanding of the limiting condition where the tension becomes zero. Any speed lower than this would result in the string going slack and the block falling.

Part (c): Energy Conservation

This section tested the application of energy conservation. Students needed to relate the kinetic energy at the bottom of the circle to the kinetic and potential energy at the top. The energy conservation equation is:

1/2mv_bottom² = 1/2mv_top² + 2mgr

By substituting the minimum speed found in part (b) into this equation and solving for the speed at the bottom, one could determine the minimum initial speed needed for the block to reach the top with the minimum speed calculated. Careful consideration of potential energy at different points was vital. Students needed to correctly account for the change in height between the top and bottom of the circle.

Question 2: Inclined Plane and Friction

Question 2 presented a problem involving an object sliding down an inclined plane with friction. This tested understanding of forces on an inclined plane, friction, and kinematics.

Part (a): Free-Body Diagram and Net Force

Drawing a correct free-body diagram was essential. The forces acting on the object included its weight (mg), the normal force (N), and the force of kinetic friction (f_k). Resolving these forces into components parallel and perpendicular to the inclined plane was crucial for finding the net force causing the acceleration down the plane.

ΣF_parallel = mg sinθ - f_k = ma

where:

• θ = angle of inclination
• f_k = μ_kN = kinetic frictional force
• μ_k = coefficient of kinetic friction
• a = acceleration down the plane

Part (b): Acceleration and Distance Traveled

Using the net force calculated in part (a), students could determine the acceleration of the object down the plane. Then, using kinematic equations (specifically, one that relates initial velocity, acceleration, displacement, and final velocity), they could calculate the distance the object traveled before coming to rest. Choosing the correct kinematic equation and applying it correctly was key. This part required careful attention to signs and units.

Part (c): Coefficient of Kinetic Friction

Part (c) required determining the coefficient of kinetic friction. This involved setting the final velocity in the kinematic equation to zero (since the object comes to rest). Solving for the coefficient of kinetic friction (μ_k) would require using the equation of motion and plugging in the given values for time and distance traveled. Analyzing the given information effectively was crucial. Students should have recognized the relationships between the variables and understood how to manipulate them to find the unknown coefficient.

Question 3: Spring-Mass System and Simple Harmonic Motion (SHM)

This question dealt with a spring-mass system undergoing simple harmonic motion. This tested knowledge of Hooke's law, energy conservation in SHM, and period of oscillation.

Part (a): Spring Constant and Amplitude

Part (a) involved determining the spring constant (k) using Hooke's law:

F = kx

where:

• F = applied force
• x = displacement from equilibrium

The problem provided the force and displacement, allowing for a direct calculation of the spring constant. Determining the amplitude of oscillation simply involved recognizing the maximum displacement from the equilibrium position.

Part (b): Maximum Speed and Maximum Acceleration

This part required calculating the maximum speed and maximum acceleration of the mass. Using conservation of energy, the maximum speed could be calculated from:

1/2kA² = 1/2mv_max²

where:

• A = amplitude
• v_max = maximum speed

The maximum acceleration could then be calculated using:

a_max = kA/m

This section highlighted the interconnectedness of energy and motion in SHM. Understanding the energy transformations between potential and kinetic energy was crucial.

Part (c): Period of Oscillation

The final part involved finding the period of oscillation. The formula for the period of a simple harmonic oscillator is:

T = 2π√(m/k)

Students could directly substitute the mass and the spring constant previously calculated to determine the period. This part tested the basic understanding of the characteristics of SHM and the relationship between the period, mass, and spring constant.

General Strategies for AP Physics C Mechanics FRQs

Success on the AP Physics C Mechanics FRQs relies on several key strategies:

• Thorough understanding of fundamental concepts: Mastering Newton's laws, energy conservation, circular motion, and simple harmonic motion is paramount.
• Practice, practice, practice: Solving numerous practice problems is crucial for developing problem-solving skills and building confidence.
• Detailed free-body diagrams: Always start by drawing clear and labeled free-body diagrams to visualize the forces acting on objects.
• Systematic approach: Follow a step-by-step approach, clearly outlining your reasoning and showing your work.
• Correct units and significant figures: Pay close attention to units and use an appropriate number of significant figures.
• Check your work: Review your calculations and ensure your answers are reasonable.

By thoroughly understanding the concepts involved in these 2012 FRQs and employing effective problem-solving strategies, students can significantly improve their performance on the AP Physics C Mechanics exam. Remember, consistent practice and a deep understanding of the underlying principles are the keys to success. Good luck!