Physics for Life Sciences I – Lecture 17 (Sections 10.5–10.9): Energy, Thermal Energy, Conservation, Molecular Bonds, Collisions, and Power

Recap: General Principles

Kinetic Energy Model

The kinetic energy model describes how energy can be transformed and transferred within and between systems. Energy transformations and transfers are fundamental to understanding physical processes.

• Energy Transformation: Energy can change forms within a system (e.g., kinetic to potential).

• Energy Transfer: Energy can move into or out of a system in two basic ways:

  • Work: Transfer of energy by mechanical forces.

  • Heat: Nonmechanical transfer of energy from a hotter to a colder object.

Example: Pushing a box across the floor involves work (mechanical energy transfer) and friction (thermal energy transfer).

Recap: Important Concepts

Kinetic and Potential Energy

Energy in physical systems is often categorized as kinetic or potential energy.

• Kinetic Energy: Energy of motion. For a particle, the total kinetic energy is the sum of translational and rotational components:

$K = \frac{1}{2}mv^2 + \frac{1}{2}I\omega^2$

• Potential Energy: Energy stored due to the position or configuration of objects.

  • Gravitational Potential Energy: $U_g = mgy$

  • Elastic Potential Energy (Spring): $U_s = \frac{1}{2}kx^2$

Example: A ball held at height y above the ground has gravitational potential energy; a compressed spring stores elastic potential energy.

Work

Work is the process by which energy is transferred to or from a system by the application of mechanical forces.

• When a particle moves through a displacement $\vec{d}$ under a constant force $\vec{F}$, only the component of force parallel to displacement does work:

$W = F_{\parallel} d = Fd \cos \theta$ Example: Pulling a sled at an angle; only the horizontal component of force does work.

Today's Lecture Topics

• Thermal Energy

• Conservation of Energy

• Energy Diagrams

• Molecular Bonds and Chemical Energy

• Energy in Collisions

• Power

Additional info: These topics are foundational for understanding energy transformations in biological and physical systems.

Section 10.5: Thermal Energy

Definition and Generation

Thermal energy is the sum of the kinetic energy of atoms/molecules and the elastic potential energy stored in molecular bonds. It is generated when work is done against friction or drag.

• Friction and drag convert mechanical energy into thermal energy.

• Change in thermal energy due to friction: $\Delta E_{th} = f_{k} \Delta x$

• Change in thermal energy due to drag: $\Delta E_{th} = D \Delta x$

• Work-energy equation including thermal energy: $\Delta K + \Delta U + \Delta E_{th} = W$

Example: Swimming in water—energy expended is converted to thermal energy due to drag.

Section 10.6: Conservation of Energy

Law of Conservation of Energy

The total energy of an isolated system remains constant. Energy can change forms but cannot be created or destroyed.

• General equation: $\Delta K + \Delta U + \Delta E_{th} = W$

• For isolated systems ($W = 0$): $K_i + U_i + E_{th,i} = K_f + U_f + E_{th,f}$

• Analogous to conservation of momentum.

Example: A spring-loaded toy gun launches a ball; energy is transferred from the spring to the ball's kinetic energy.

Section 10.7: Energy Diagrams

Interpreting Energy Diagrams

Energy diagrams graph potential energy as a function of position. They help visualize energy transformations and equilibrium points.

• Gravitational potential energy: linear graph ($U_g = mgy$)

• Spring potential energy: parabolic graph ($U_s = \frac{1}{2}kx^2$)

• At any position, the vertical distance from the axis to the PE curve is the object's potential energy.

• The distance from the PE curve to the total energy line is the kinetic energy.

• Turning points occur where the total energy line crosses the PE curve.

• Equilibrium positions are at local minima or maxima of the PE curve.

Example: A mass oscillating on a spring; the object reverses direction at turning points.

Section 10.8: Molecular Bonds and Chemical Energy

Molecular Bonds

Molecular bonds are electrical interactions between electrons and nuclei, storing electric potential energy.

• Bonds can be visualized with energy diagrams similar to springs.

• Bond energy is the energy required to break a bond.

• When the total energy exceeds the bond energy, the bond breaks.

Example: Absorption of ultraviolet photons can break molecular oxygen bonds, producing ozone.

Chemical Reactions and Energy

Chemical reactions involve breaking and forming molecular bonds, with energy changes represented by reaction coordinates.

• Activation energy: Energy barrier that must be overcome to break reactant bonds.

• Chemical energy: Total electric potential energy stored in all molecular bonds.

• Catalysts lower activation energy, increasing reaction rates.

Example: Enzymes in biological systems act as catalysts.

Section 10.9: Energy in Collisions

Types of Collisions

Collisions are classified based on energy conservation:

• Perfectly Inelastic Collision: Objects stick together; mechanical energy is not conserved, but momentum is.

• Perfectly Elastic Collision: Both mechanical energy and momentum are conserved.

• In inelastic collisions, some mechanical energy is converted to thermal energy.

Example: Railroad cars coupling together—kinetic energy is lost as thermal energy.

Elastic Collision Equations

• Conservation of momentum: $m_1 v_{1i} + m_2 v_{2i} = m_1 v_{1f} + m_2 v_{2f}$

• Conservation of energy: $\frac{1}{2}m_1 v_{1i}^2 + \frac{1}{2}m_2 v_{2i}^2 = \frac{1}{2}m_1 v_{1f}^2 + \frac{1}{2}m_2 v_{2f}^2$

Example: Air hockey pucks—after a head-on elastic collision, the moving puck stops and the stationary puck moves with the initial velocity.

Section 10.10: Power

Definition and Calculation

Power is the rate at which energy is transformed or transferred.

• General definition: $P = \frac{\Delta E}{\Delta t}$

• When work is done: $P = \frac{W}{\Delta t}$

• Unit: watt ($1 \text{W} = 1 \text{J}/\text{s}$)

• Output power of a force: $P = Fv$ (for force $F$ acting on an object moving at velocity $v$)

Example: Students running up stairs—those who complete the climb in less time have higher power output.

Summary Tables

Energy Types and Formulas

Type	Formula	Description
Kinetic Energy	$K = \frac{1}{2}mv^2$	Energy of motion
Rotational Kinetic Energy	$K_{rot} = \frac{1}{2}I\omega^2$	Energy due to rotation
Gravitational Potential Energy	$U_g = mgy$	Energy due to position in a gravitational field
Elastic Potential Energy	$U_s = \frac{1}{2}kx^2$	Energy stored in a spring
Thermal Energy (friction)	$\Delta E_{th} = f_k \Delta x$	Energy generated by friction
Thermal Energy (drag)	$\Delta E_{th} = D \Delta x$	Energy generated by drag
Power	$P = \frac{\Delta E}{\Delta t}$	Rate of energy transformation
Power (force)	$P = Fv$	Rate of energy transfer by force

Collision Types

Type	Momentum Conserved?	Mechanical Energy Conserved?	Example
Perfectly Elastic	Yes	Yes	Air hockey pucks
Perfectly Inelastic	Yes	No	Railroad cars coupling

Additional info:

• These notes cover the core concepts from Lecture 17 of Physics for Life Sciences I, focusing on energy transformations, conservation, and applications in biological and physical contexts.