Physics

Page 1: Group Discussion

• Concept Recall

  • A 2 kg ball collides with the floor at angle 0 and rebounds at the same angle and speed.

  • Questions:

    1. Direction of Force by Floor on Ball:

       • The force exerted by the floor on the ball is directed upwards (normal force), opposing the gravitational force acting downwards.

    2. Direction of Impulse by Floor on Ball:

       • The impulse exerted on the ball by the floor is also directed upwards, as it is the result of the collision with the floor.

Page 2: Essential Knowledge

• Conservation of Linear Momentum

  • This principle states: The total linear momentum of a closed system remains constant if no external forces act on it.

  • Equation:

    • P_initial + P_final = m_1 + m_2

  • Example:

    • Two people on frictionless ice push each other.

      • Person 1 (m1 = 120 kg) moves left at 2 m/s, Person 2 (m2 = 80 kg) moves right 3 m/s.

      • Center of Mass Velocity (V_cm): Initially 0, remains 0 when they separate due to conservation.

Page 3: Classwork 1 Lesson Objective

• Objective: Apply conservation of momentum in elastic and inelastic collisions.

  • Scenario: Two blocks A (mass m) and B (mass 2m) on a horizontal surface.

    • Block A moves with speed V_0 toward stationary Block B, causing maximum compression in a spring attached.

  • Key Question: What is center of mass speed of blocks-spring system after separation?

• Answer Options:

  • A) V_0

  • B) V_Qf

  • C) m/m2

  • D)

• Final speeds after collision ranking:

  • UP_cm > VQ_cm > V_rem

Page 4: Classwork 1 Analysis

• Conservation Equation:

  • [ V_{cm} = \frac{m_1V_1 + m_2V_2}{m_1 + m_2} ]

  • For negligible friction:

    • [ V_{cm} = \frac{M_1V_1 + M_2V_2}{M + 2m} ]

  • Using various parameters to determine velocities:

    • For two blocks:

      - Block A moves with speed V_0- Total momentum reflects the center of mass speed consistently.

Page 5: Applied Momentum Assessment

• Question: Identify the pair with a different center of mass velocity.

  • Options provided indicate differing momentum scenarios under momentum conservation.

  • Assess respective speeds:

    • A) 1 m/s and 3 m/s

    • B) 4 m/s and 8 m/s

    • C) 8 m/s and 4 m/s

    • D) 5 m/s and 5 m/s

Page 6: Momentum Charts

• Scenario: Two blocks (M and 2M) at rest, with spring initially compressed, are released.

  • Velocity of 2M after release must be evaluated:

    • Options:

      • A) 0

      • B) 2v

      • C) 3

      • D) 3/2

      • E) -2v

Page 7: Conservation: Example Problems

• Block 1.2 kg and block 1.8 kg both at rest collide. Spring releases:

  1. speed of center of mass (V_cm) = 02. Speed of 1.2 kg block after = -3.0 m/s

  • Momentum conservation equations clarify outcomes.

Page 8: Problems on Elastic Collision

• Collision Analysis: Ball A (0.75 kg) at 5 m/s hits ball B (1.8 kg).

  • Ball B moves with 1.0 m/s after collision.

  • Find: Velocity of Ball A after midnight:

    • • utilization of total momentum equation results in V_1f = 2.6 m/s

    • Show non-elastic collision via energy analysis:

      • Requirements check includes kinetic energy comparison pre- and post-collision.

Page 9: Conservation of Momentum - Embedded Systems

• Case:* Block (0.6 kg) with air rifle pellet (0.02 kg) stuck post-impact.

• Post-Collision Analysis:

  • 1. Find speed of the block with embedded pellet:

    • Eq: Block initial (0) + Pellet (0.02)(45) = (0.6 + 0.02) v_f

  • 2. Kinetic energy change calculation also considered:

    • Decrease = -20.2 J noted post-collision.

Page 10: Classwork 2: Elastic collisions

• Obj: Two blocks with different masses in elastic head-on collision.

  • Block 1 (m) is in motion at V to the right; Block 2 (2m) initially at rest.

  • Find correct velocities post-collision via analysis.

Page 11: (continued) Classwork 2: Cart collisions analysis

• Colliding carts indicate differing post-collision parameters based on mass and initial velocities.

• Find final velocity of both carts after collision.

Page 12: Assessment for Learning

• Scenario: Identify velocity of colliding balls initially at rest, with momentum equations to demonstrate outcomes.

Page 13: Additional Collision Scenarios

• KE and Momentum loss assessments for various mass interactions.

• Ratio questions on energy loss categorized under collision events.

Page 14: Energy Loss Assessment

• Collision of moving (8 kg) and still (4 kg) mass: Calculate total kinetic energy decrease.

Page 15: Glancing collisions

• Pucks Scenario: Analyze initial speeds and angles, resultant velocities after glancing collisions.

Page 16: Classwork Summary

• Assess outcomes on pucks' crucial distances post-collision.

Page 17: Time-varying motion analysis

• Graphs representing tire motion-dependent parameters across different times.

Page 18: Momentum Post-Collision

• Pucks' movements quantified to yield total momentum post-interaction (systematic equations).

Page 19: Energy transfer systems

• Analysis following spring-release energy distributions in blocked systems.

Page 20: Quantitative collision assessments

• Post-impulse mass movements and calculations with friction accounted or unaccounted.

Page 21: Rotational kinematics introduction

• Define angular motion, associated parameters of displacement, velocity, and acceleration with visual and empirical representations.

Page 22: Angular Relationships and Derivations

• Elaborate on functional dependence of angle versus rotational variables, compute resulting outputs shifting through time.

Page 23: Equations of Rotational Kinetics

• Angular velocity affirmative computations leveraging initial equilibria to determine final states of rotational systems.

Page 24: Detailed Rotational Dynamics

• Evaluate several rotational engagements as influences on reported outcomes in systems manipulating angular behaviors.

Page 25: Analyzed rotational shifts

• Generalize relationships between linear displacement and proposed formulas governing angular analogies.

Page 26: Angular Acceleration Investigative Formats

• Construct analyses framing acceleration adjustments about constant angular motions. Results yield significant insights.

Page 27: Summary of Rotational Metrics

• Consolidate properties of angular displacement, velocity and how they are correspondently coded or analyzed through practical applications.

Page 28: Examining Transition Concepts

• Describe changing angular properties under varied influences demonstrating physical applications.

Page 29: Continuous Feedback Originating Variants

• Assign varying potential angular interactions across different rotating entities to yield insights.

Page 30: Angled Velocity Divisions

• Comprehensive understanding of rotating corner systems with applicable derivations and properties viewed properly from a vertical standpoint.

Page 31: Adaptive Lecture Analysis on Angular Displacement

• Time captured momentum outputs representing angular movements regarding force dynamics in systems analyzed from initial to terminal conditions.

Page 32: Applying Connective Rigid Dynamics

• Detailed summation of approaches tied to proper empirical frameworks alongside observable transactions within time-advanced analytical setups.

Page 33: Linear Angular Relationships

• Steps and processes within variable adjustments controlling dynamic systems and their outputs across angular velocities interpolated against physical placements.

Page 34: Combined Result Points

• Convergence of linear angular motions versus standard rules providing framework derivations for mechanical behaviors in applied sciences.

Page 35: Query-Driven Results Sequences

• Session summaries leading to deeper understanding of rigid inertia and its impacts across continuous systems viewed in angular formats.

Page 36: Learning Continuity Initiatives

• Building connections through extended inquiry into angular dynamics manifesting across multi-layered rotational applications.

Page 37: Conclusion of Methodical Examination

• Evaluate end-state conditions addressing linear motion and angular properties within interactive guidelines dependent on measurable outcomes.