Lecture 16: Conservation Laws, Energy, and Work in Physics for Life Sciences

Recap: General Principles

Conservation Laws

Conservation laws are fundamental principles in physics stating that certain physical quantities remain constant in isolated systems, regardless of the processes occurring within the system.

• Conservation of Momentum: The total momentum P of an isolated system (one with no net external force) remains constant.

$\vec{P} = \vec{p}_1 + \vec{p}_2 + \ldots$

$\vec{P}_f = \vec{P}_i$

• Conservation of Angular Momentum: The total angular momentum L of a rotating object or system subject to zero net external torque remains constant.

$L_f = L_i$

Recap: Important Concepts

Momentum and Impulse

• Momentum (\(\vec{p}\)): The product of an object's mass and velocity. $\vec{p} = m\vec{v}$

• Impulse (\(J_x\)): The area under a force vs. time curve; impulse changes an object's momentum. $J_x = \text{area under force curve}$

• Impulse-Momentum Theorem: The change in momentum equals the impulse applied. $\Delta p_x = J_x$

• Rotational Momentum: The rotational analog of linear momentum. $L = I\omega$

System and Isolated System

• System: A group of interacting objects considered together for analysis.

• Isolated System: A system on which the net external force is zero.

• Internal Forces: Forces that objects within the system exert on each other; these do not affect the total momentum of the system.

Before-and-After Visual Overview

• Define the system and use diagrams to represent the state before and after an interaction.

• Identify known information and what needs to be found.

• Example: Two objects before and after a collision, with their respective velocities and masses labeled.

Recap: Applications

Collisions and Explosions

• Collisions: Two or more objects come together. In a perfectly inelastic collision, objects stick together and move with a common final velocity.

• Explosions: Two or more objects move away from each other after an interaction.

Momentum in Two Dimensions

• Both the x- and y-components of momentum must be conserved, resulting in two simultaneous equations for analysis.

Today's Lecture Overview

• Chapter 10: Energy and Work

• Basic Energy Model

• Work

• Kinetic Energy

• Potential Energy