Chapter 1: Physics for Life Sciences

Introduction

This chapter introduces foundational concepts in physics as applied to life sciences, focusing on molecular motion, diffusion, and scaling laws in biology. The problems emphasize estimation, dimensional analysis, and the application of physical laws to biological systems.

Random Walk and Diffusion

• Random Walk: The random walk describes the path of a particle that moves in successive random steps. In biological systems, this models the movement of molecules in a fluid.

• Diffusion Coefficient (D): Quantifies how fast a substance diffuses. For a molecule, can be estimated using the mean squared displacement formula:

• Example: Estimating the time for a small molecule (diameter 0.1 nm) to diffuse a certain distance, given its speed and the mean free path.

Average Speed of Molecules and Molecular Mass

• Root Mean Square Speed: The average speed of molecules is inversely proportional to the square root of their mass: where is Boltzmann's constant, is temperature, and is molecular mass.

• Atomic vs. Molecular Mass: Atomic mass refers to a single atom, while molecular mass refers to a molecule composed of atoms. Both are often measured in atomic mass units (u).

Protein Folding and Molecular Collisions

• Protein Folding: The time it takes for a protein to fold depends on the rate of molecular collisions and the complexity of the folding pathway.

• Collision Frequency: The average time between collisions can be estimated using the mean free path and average speed.

Scaling Laws in Biology

• Allometric Scaling: The total leaf area of a plant scales with the plant's mass as .

• Example: If a tree is replaced by two smaller trees, each with half the mass of the original, the total leaf area increases by a factor determined by the scaling law.

Chapter 2: Describing Motion

Introduction

This chapter covers the basic principles of kinematics, including displacement, velocity, acceleration, and the analysis of motion using graphs and equations.

Constant Acceleration Motion

• Equations of Motion: For constant acceleration :

• Example: Calculating the total distance traveled by a rocket decelerating at a constant rate.

Measurement and Units

• SI Units: Standard units for mass (kg), length (m), and time (s) are used throughout physics.

• Density: , where is mass and is volume.

Position and Displacement

• Reference Frames: The position of an object is always measured relative to a chosen origin.

• Example: Determining the position of a person along a straight line between two points (e.g., home and cinema).

Chapter 3: Motion Along a Line

Introduction

This chapter focuses on one-dimensional motion, including interpreting and relating position, velocity, and acceleration graphs.

Velocity and Position Graphs

• Interpreting Graphs: The slope of a position vs. time graph gives velocity; the area under a velocity vs. time graph gives displacement.

• Example: Analyzing a velocity graph to determine when a cyclist moves fastest.

Relative Motion

• Relative Velocity: The velocity of an object as observed from a particular reference frame.

• Example: Calculating when two travelers meet, given different starting points and speeds.

Projectile and Free Fall Motion

• Free Fall: Objects in free fall experience constant acceleration due to gravity ().

• Example: Calculating the time and velocity of a rock dropped from a cliff.

Chapter 4: Force and Motion

Introduction

This chapter introduces Newton's laws of motion and their application to systems involving forces, including tension, friction, and acceleration.

Newton's Laws of Motion

• First Law (Inertia): An object remains at rest or in uniform motion unless acted upon by a net force.

• Second Law: (Force equals mass times acceleration).

• Third Law: For every action, there is an equal and opposite reaction.

Force Diagrams and Tension

• Free-Body Diagrams: Visual representations of all forces acting on an object.

• Tension: The pulling force transmitted by a string, cable, or similar object.

• Example: Calculating the mass of a glider pulled by a constant tension force.

Applications to Real Systems

• Example: Determining the thrust of jet engines required to accelerate a plane to takeoff speed.

Chapter 5: Interacting Systems

Introduction

This chapter explores systems of interacting objects, focusing on forces in connected systems, friction, and applications to biological and everyday contexts.

Connected Objects and Tension

• Multiple Masses: When objects are connected (e.g., by ropes), their accelerations and tensions must be analyzed together.

• Example: Calculating the tension in a rope when lifting or pulling objects.

Friction

• Kinetic Friction: The force opposing the motion of two surfaces sliding past each other, given by , where is the coefficient of kinetic friction and is the normal force.

• Example: Determining the force needed for a dog to stop sliding on ice.

Drag and Air Resistance

• Drag Coefficient: Quantifies the resistance of an object moving through a fluid. The drag force is given by: where is the drag coefficient, is fluid density, is cross-sectional area, and is velocity.

• Example: Calculating the drag coefficient for a penguin gliding in water.

Gravitational Force

• Newton's Law of Universal Gravitation: where is the gravitational constant, and are masses, and is the distance between centers.

• Example: Finding the gravitational force between the Earth and the Moon, and the Moon's acceleration if it stopped revolving.

Summary Table: Key Physical Quantities and Units

Additional info: Some explanations and formulas have been expanded for clarity and completeness, based on standard introductory physics curriculum for life sciences.