Physics Final Review Lecture Notes

Overview

• Review of comprehensive physics final
• Focus on big topics from first semester
• Additional focus on oscillations and fluids
• Structure: Solving problems, reviewing concepts

Projectile Motion

Example Problem

• Tennis ball hit at 23 m/s at an angle of 58° above horizontal.
• Goals:
  • Find horizontal and vertical components of velocity
  • Max height, time to max height
  • Velocity and acceleration at highest point
  • Time in the air, distance hit

Solution Steps

1. Vector Components:

   • Horizontal (Vx) = V * cos(θ) = 12.2 m/s
   • Vertical (Vy) = V * sin(θ) = 19.5 m/s

2. Max Height:

   • Use kinematic equation: Δy = (V² - Vy²) / (2 * g)
   • Result: 19.4 meters

3. Time to Max Height:

   • Vy = V0y - g * t
   • Time = 2 seconds

4. Velocity at Highest Point:

   • Only horizontal component present: 12.2 m/s

5. Acceleration at Highest Point:

   • Acceleration = -g

6. Time in the Air:

   • Total time: 4 seconds

7. Distance Hit:

   • Δx = Vx * t = 48.8 meters*

Force Problems

Problem 1

• 500-Newton crate pulled at 30° above horizontal.
• Coefficient of kinetic friction = 0.4.
• Find: Strength of pull for constant velocity.

Solution Steps

1. Free Body Diagram:

   • Forces: weight, normal force, tension, friction

2. Sum Forces (Y-Direction):

   • N + T * sin(30) - weight = 0

3. Sum Forces (X-Direction):

   • T * cos(30) - friction = 0
   • Friction = μ * N

4. Solve for Tension (T):

   • Result: 188 newtons*

Problem 2

• Book on table, mass = 3 kg
• Coefficients: Static (0.4), Kinetic (0.2)
• Find: Normal force, friction, minimum force to slide

Momentum and Collisions

Problem 1

• Car (1000 kg) north at 15 m/s, truck (2000 kg) east at 10 m/s.
• Find: Velocity and direction post-collision.

Solution Steps

1. Momentum Conservation:

   • Initial momentum = final momentum
   • Use Pythagorean theorem for components

2. Final Velocity:

   • Result: 8.3 m/s

3. Direction Calculation:

   • Result: 36.9°

Problem 2

• Three boxcars at 24 m/s collide with a fourth at rest.
• Find: Speed of cars post-collision, energy dissipated

Energy Conservation

Problem

• Bicycle wheel rolls downhill (50m height), initial speed 10 m/s
• Find: Speed at bottom, total energy, spring constant

Angular Momentum and Rotational Dynamics

Problem

• Diver changes moment of inertia from 18 to 3.6 kg m².
• Find: Number of revolutions post-momentum change.

Rotational Equilibrium

Problem

• Balance unknown forces on a beam for equilibrium

Oscillations and Periodic Motion

Problem

• Mass on spring, amplitude = 0.15m, period = 0.45s
• Find: Velocity at equilibrium, total energy, spring constant

Fluid Mechanics Concepts

Pascal's Principle

• Pressure depends on depth and initial pressure

Archimedes' Principle

• Buoyancy equals weight of displaced fluid

Key Concepts

• Force and motion (Newton's laws, kinematics)
• Energy conservation
• Momentum conservation
• Rotational dynamics
• Fluid dynamics

Conclusion

• Comprehensive review of major topics
• Final tips and encouragement for exam preparation