Sarah and her biological sister Danielle have some physical characteristics that are the same and some that are different, as shown in the table below.
a. Identify the molecule that stores the hereditary information for these characteristics in the chromosomes of every body cell.
b. Identify the total number of chromosomes that should be in one of Sarah’s body cells and the number of chromosomes that should have been contributed by each biological parent.
c. Explain the roles of meiosis and fertilization in achieving the chromosome numbers you identified in part (b).
d. Explain why Sarah and Danielle have some physical characteristics that are different from each other, even though they have the same biological parents.
A Ferris wheel is a large structure consisting of a rotating upright wheel, with multiple passenger cars. The cars are attached to the rim in such a way that as the wheel turns, they are kept upright by gravity.
The original Ferris Wheel was designed and constructed by George Washington Gale Ferris Jr. as a landmark for the 1893 World’s Columbian Exposition in Chicago. The generic term Ferris wheel is now used for all such structures, which have become the most common type of amusement ride at state fairs in the United States.
Forces in the wheel itself
The wheel keeps its circular shape by the tension of the spokes, pulling upward against the lower half of the framework and downward against the huge axle.
This animation shows simultaneous views of a ball tossed up and then caught by a ferris wheel rider from one inertial and two non-inertial points of view. Although Newton’s predictions are easier to track from the inertial point of view, it turns out that they still work locally in accelerated frames and curved spacetime if we consider “geometric accelerations and forces” that act on every ounce of an object’s being and can be made to disappear by a suitable vantage point change.
Created by P. Fraundorf, licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
Net work done on the wheel = 0?
AP Physics problem solving
The Expanse is a series of science fiction novels, novellas and stories by James S. A. Corey – the pen name of authors Daniel Abraham and Ty Franck. The first novel, Leviathan Wakes, was nominated for the Hugo Award for Best Novel in 2012. In 2017 the series as a whole was nominated for the ‘Best Series’ Hugo Award.
These novels are the basis of an American science fiction television series developed by Mark Fergus and Hawk Ostby. The series received positive reviews from critics, who highlighted its visuals, character development, and political narrative. It received a Hugo Award for Best Dramatic Presentation as well as a Saturn Award nomination.
- Leviathan Wakes (June 15, 2011)
- Caliban’s War (June 26, 2012)
- Abaddon’s Gate (June 4, 2013)
- Cibola Burn, (June 5, 2014)
- Nemesis Games (June 2, 2015)
- Babylon’s Ashes (December 6, 2016)
- Persepolis Rising (December 5, 2017)
- Tiamat’s Wrath (December, 2018)
- “The Butcher of Anderson Station” (The Expanse short story) (2011)
- Gods of Risk (The Expanse novella) (2012)
- “Drive” (The Expanse short story) (2012)
- The Churn (The Expanse novella) (2014)
- The Vital Abyss (The Expanse novella) (2015)
- Strange Dogs (The Expanse novella) (2017)
Possible rocket engines
from ATOMIC ROCKETSHIPS OF THE SPACE PATROL or “So You Wanna Build A Rocket?” by Winchell D. Chung Jr..
Here is your handy-dandy cheat-sheet of rocket engines. Use this as a jumping-off point, there is no way I can keep this up-to-date. Google is your friend!
I’ll point out a few of the more useful items on the sheet:
Aluminum-Oxygen is feeble, but is great for a lunar base (the raw materials are in the dirt).
VASIMR is the current favorite among ion-drive fans. Use this with orbit-to-orbit ships that never land on a planet. It can “shift gears” like an automobile.
Solar Moth might be a good emergency back-up engine.
Nuclear Thermal Solid Core is better than feeble chemical rockets, but not as much as you’d expect.
Nuclear Thermal Vapor Core is what you design along the way while learning how to make a gas core atomic rocket.
Nuclear Thermal Gas Core Open-Cycle is a full-blown honest-to-Heinlein atomic rocket, spraying glowing radioactive death in its exhaust.
Nuclear Thermal Gas Core Closed-Cycle is an attempt to have the advantages of both nuclear solid core and gas core, but often has the disadvantages of both. It has about half the exhaust velocity of an open-cycle atomic rocket.
Orion Nuclear Pulse is a rocket driven by detonating hundreds of nuclear bombs. If you can get past freaking out about the “bomb” part, it actually has many advantages. Don’t miss the Medusa variant.
Magneto Inertial Fusion This is the best fusion-power rocket design to date.
Zubrin’s Nuclear Salt Water This is the most over-the-top rocket. Imagine a continuously detonating Orion drive. There are many scientist who question how the rocket can possibly survive turning the drive on.
The cortical homunculus is the part of the brain responsible for processing and integration of motor information (muscles, motion) and tactile information (touch, senses)
The reason for the distorted appearance is that the amount of cortex is proportional to how richly innervated that region is, not to its size.
The resulting image appears as a disfigured human with disproportionately huge hands, lips, and face in comparison to the rest of the body.
The top box shows an outbreak in a community in which a few people are infected (shown in red) and the rest are healthy but unimmunized (shown in blue); the illness spreads freely through the population.
The middle box shows a population where a small number have been immunized (shown in yellow); those not immunized become infected while those immunized do not.
In the bottom box, a large proportion of the population have been immunized; this prevents the illness from spreading significantly, including to unimmunized people.
In the first example, most healthy unimmunized people become infected, whereas in the bottom example only one fourth of the healthy unimmunized people become infected.
from “An Introduction to Chemistry by Mark Bishop”
According to the Arrhenius theory of acids and bases, when an acid is added to water, it donates an H+ ion to water to form H3O+ (often represented by H+).
The higher the concentration of H3O+ (or H+) in a solution, the more acidic the solution is.
An Arrhenius base is a substance that generates hydroxide ions, OH–, in water. The higher the concentration of OH– in a solution, the more basic the solution is.
Pure water undergoes a reversible reaction in which both H+ and OH– are generated.
H2O(l) H+(aq) + OH–(aq)
The equilibrium constant for this reaction, called the water dissociation constant, Kw, is 1.01 × 10-14 at 25 °C.
Kw = [H+][OH–] = 1.01 × 10-14 at 25 °C
Because every H+ (H3O+) ion that forms is accompanied by the formation of an OH– ion, the concentrations of these ions in pure water are the same and can be calculated from Kw.
Kw = [H+][OH–] = (x)(x) = 1.01 × 10-14
x = [H+] = [OH-] = 1.01 × 10-7 M
(1.005 × 10-7 M before rounding)
The equilibrium constant expression shows that the concentrations of H+ and OH– in water are linked. As one increases, the other must decrease to keep the product of the concentrations equal to 1.01 × 10-14 (at 25 °C).
If an acid, like hydrochloric acid, is added to water, the concentration of the H+ goes up, and the concentration of the OH– goes down, but the product of those concentrations remains the same.
An acidic solution can be defined as a solution in which the [H+] > [OH–].
The example below illustrates this relationship between the concentrations of H+ and OH– in an acidic solution.
EXAMPLE 1 – Determining the Molarity of Acids and Bases in Aqueous Solution: Determine the molarities of H+ and OH– in a 0.025 M HCl solution at 25 °C.
Kw = [H+][OH–] = 1.01 × 10-14 at 25 °C
We assume that hydrochloric acid, HCl(aq), like all strong acids, is completely ionized in water. Thus the concentration of H+ is equal to the HCl concentration.
[H+] = 0.025 M H+
We can calculate the concentration of OH– by rearranging the water dissociation constant expression to solve for [OH–] and plugging in 1.01 × 10-14 for Kw and 0.025 for [H+].
Note that the [OH–] is not zero, even in a dilute acid solution.
If a base, such as sodium hydroxide, is added to water, the concentration of hydroxide goes up, and the concentration of hydronium ion goes down. A basic solution can be defined as a solution in which the [OH–] > [H+].
EXAMPLE 2 – Determining the Molarity of Acids and Bases in Aqueous Solution: Determine the molarities of H+ and OH– in a 2.9 × 10-3 M NaOH solution at 30 °C.
Kw = [H+][OH–] = 1.47 × 10-14 at 30 °C (From Table)
Sodium hydroxide is a water-soluble ionic compound and a strong electrolyte, so we assume that it is completely ionized in water, making the concentration of OH- equal to the NaOH concentration.
[OH–] = 2.9 × 10-3 M OH–
Note that the [H+] is not zero even in a dilute solution of base.
Typical solutions of dilute acid or base have concentrations of H+ and OH– between 10-14 M and 1 M. The table below shows the relationship between the H+ and OH– concentrations in this range.
Concentrations of H+ and OH– in Dilute Acid and Base Solutions at 25 °C
|1.0 M||1.0 × 10-14 M|
|1.0 × 10-3 M||1.0 × 10-11 M|
|1.0 × 10-7 M||1.0 × 10-7 M|
|1.0 × 10-10 M||1.0 × 10-4 M|
|1.0 × 10-14 M||1.0 M|
We could describe the relative strengths of dilute solutions of acids and bases by listing the molarity of H+ for acidic solutions and the molarity of OH– for basic solutions. There are two reasons why we use the pH scale instead.
The first reason is that instead of describing acidic solutions with [H+] and basic solutions with [OH–], chemists prefer to have one scale for describing both acidic and basic solutions. Because the product of the H+ and OH– concentrations in such solutions is always 1.01 × 10-14 at 25 °C, when we give the concentration of H+, we are indirectly also giving the concentration of OH–.
For example, when we say that the concentration of H+ in an acidic solution at 25 °C is 10-3 M, we are indirectly saying that the concentration of OH– in this same solution is 10-11 M.
When we say that the concentration of H+ in a basic solution at 25 °C is 10-10 M, we are indirectly saying that the OH– concentration is 10-4 M.
The pH concept makes use of this relationship to describe both dilute acid and dilute base solutions on a single scale.
The next reason for using the pH scale instead of H+ and OH– concentrations is that in dilute solutions, the concentration of H+ is small, leading to the inconvenience of measurements with many decimal places, such as 0.000001 M H+, or to the potential confusion associated with scientific notation, as with 1 × 10-6 M H+.
In order to avoid such inconvenience and possible confusion, pH is defined as the negative logarithm of the H+ concentration.
pH = -log[H+]
Instead of saying that a solution is 0.0000010 M H+ (or 1.0 × 10-6 M H+) and 0.000000010 M OH– (or 1.0 × 10-8 M OH–), we can indirectly convey the same information by saying that the pH is 6.00.
pH = -log[H+] = -log(1.0 × 10-6) = 6.00
When taking the logarithm of a number, report the same number of decimal positions in the answer as you had significant figures in the original value.
Because 1.0 × 10-6 has two significant figures, we report 6.00 as the pH for a solution with 1.0 × 10-6 M H+.
The table below shows a range of pH values for dilute solutions of acid and base.
pH of Dilute Solutions of Acids and Bases at 25 °C
|1.0||1.0 × 10-14||0.00|
|1.0 × 10-1||1.0 × 10-13||1.00|
|1.0 × 10-2||1.0 × 10-12||2.00|
|1.0 × 10-3||1.0 × 10-11||3.00|
|1.0 × 10-4||1.0 × 10-10||4.00|
|1.0 × 10-5||1.0 × 10-9||5.00|
|1.0 × 10-6||1.0 × 10-8||6.00|
|1.0 × 10-7||1.0 × 10-7||7.00|
|1.0 × 10-8||1.0 × 10-6||8.00|
|1.0 × 10-9||1.0 × 10-5||9.00|
|1.0 × 10-10||1.0 × 10-4||10.00|
|1.0 × 10-11||1.0 × 10-3||11.00|
|1.0 × 10-12||1.0 × 10-2||12.00|
|1.0 × 10-13||1.0 × 10-1||13.00|
|1.0 × 10-14||1.0||14.00|
This table illustrates several important points about pH. Notice that
- When the solution is acidic ([H+] > [OH–), the pH is less than 7.
- When the solution is basic ([OH–] > [H+]), the pH is greater than 7.
- When the solution is neutral ([H+] = [OH–]), the pH is 7. (Solutions with pH’s between 6 and 8 are often considered essentially neutral.)
Also notice that
- As a solution gets more acidic (as [H+] increases), the pH decreases.
- As a solution gets more basic (higher [OH–]), the pH increases.
- As the pH of a solution decreases by one pH unit, the concentration of H+ increases by ten times.
- As the pH of a solution increases by one pH unit, the concentration of OH– increases by ten times.
- The pH, [H+], and [OH–] of some common solutions are listed in the figure below. Notice that gastric juice in our stomach has a pH of about 1.4, and orange juice has a pH of about 2.8. Thus, gastric juice is more than ten times more concentrated in H+ than orange juice.
The pH difference of about 4 between household ammonia solutions (pH about 11.9) and milk (pH about 6.9) shows that household ammonia has about ten thousand (104) times the hydroxide concentration of milk.
pH of Common Substances Acidic solutions have pH values less than 7, and basic solutions have pH values greater than 7. The more acidic the solution is, the lower its pH. The more basic a solution is, the higher the pH.
The corresponding H+ and OH– concentrations are shown in units of molarity. Notice that a decrease of one pH unit corresponds to a ten-fold increase in [H+], and an increase of one pH unit for a basic solution corresponds to a ten-fold increase in [OH–].
EXAMPLE 3 – pH Calculations: In Example 1, we found that the H+ concentration of a 0.025 M HCl solution was 0.025 M H+. What is its pH?
pH = -log[H+] = -log(0.025) = 1.60
EXAMPLE 4 – pH Calculations: In Example 2, we found that the H+ concentration of a 2.9 × 10-3 NaOH solution was 5.1 × 10-12 M H+. What is its pH?
pH = -log[H+] = -log(7.5 × 10-12) = 11.29
We can convert from pH to [H+] and [OH–] using the following equations, as demonstrated in Examples 5 and 6.
[H+] = 10-pH
EXAMPLE 5 – pH Calculations: What is the [H+] in a glass of lemon juice with a pH of 2.12?
[H+] = 10-pH = 10-2.12 = 7.6 × 10-3 M H+
EXAMPLE 6 – pH Calculations: What is the [OH–] in a container of household ammonia at 25 °C with a pH of 11.900?
[H+] = 10-pH = 10-11.900 = 1.26 × 10-12 M H+
HS-PS1-9 (MA). Relate the strength of an aqueous acidic or basic solution to the extent of an acid or base reacting with water, as measured by the hydronium ion concentration (pH) of the solution. Make arguments about the relative strengths of two acids or bases with similar structure and composition.
Science and Engineering Practices
Mathematical and computational thinking in 9–12 builds on pre-K–8 and experiences and progresses to using algebraic thinking and analysis, a range of linear and nonlinear functions including trigonometric functions, exponentials and logarithms, and computational tools for statistical analysis to analyze, represent, and model data.
Most cells function best within a narrow range of temperature and acidity. At very low temperatures, reaction rates are too slow. High temperatures and/or extremes of acidity can irreversibly change the structure of most protein molecules. Even small changes in acidity can alter the molecules and how they interact. 5C/H7
The temperature and acidity of a solution influence reaction rates. Many substances dissolve in water, which may greatly facilitate reactions between them. 4D/M4
From middleschoolchemistry.com, contact staff at ACS. Copyright 2015 American Chemical Society
Online textbook: Chapter 5: Acids Bases and their reactions
Andy Maldonado, on Quora, writes
An action potential is the way by which neurons communicate.
Neurons are negatively charged on the inside and positively charged on the outside.
This is due to the different concentrations of Na+, K+, Cl-, Ca2+, and charged proteins distributed both in and outside the neuron.
An action potential begins when a disruption of this distribution causes Na+ to flow into the neuron, through Na+ channels, causing the inside to become more positive.
The more positively charged inside of the neuron triggers adjacent voltage-gated Na+ channels to open and allow more ions to flow through.
The increase in charge inside the neuron triggers K+ channels to open – allowing for ions to flow outside of the cell, and thus lowering the inside charge back to its original state.
This increase and decrease in charge causes a wave-like motion of ions that propagates down the axon of a neuron – and ultimately causes the release of neurotransmitters from the dendrites – which stimulate the next neuron to either initiate or inhibit an action potential.
Action potentials trigger neuronal pathways which can stimulate or inhibit certain functions in our body. For example, action potentials in the motor region of the brain may stimulate a neural pathway with leads to the muscles in your arms resulting in flexion. Action potentials also facilitate communication between neuronal networks in the brain which allow us to have conscious thoughts, emotions, and memories.
As a nerve impulse travels down the axon, there is a change in polarity across the membrane.
The Na+ and K+ gated ion channels open and close in response to a signal from another neuron. At the beginning of action potential, the Na+ gates open and Na+ moves into the axon. This is depolarization. Repolarization occurs when the K+ gates open and K+ moves outside the axon. This creates a change in polarity between the outside of the cell and the inside. The impulse continuously travels down the axon in one direction only, through the axon terminal and to other neurons.
2016 Massachusetts Science and Technology/Engineering Curriculum Framework
HS-LS1-2. Develop and use a model to illustrate the key functions of animal body systems: Emphasis is on the primary function of the following body systems… nervous (neurons, brain, spinal cord).
College Board Science Standards
LSH-PE.5.5.4 Construct a simple representation of a feedback mechanism that maintains the internal conditions of a living system within certain limits as the external conditions change.
LSH-PE.5.5.5 Construct a representation of the interaction of the endocrine and nervous systems (e.g., hormones and electrochemical impulses) as they interact with other body systems to respond to a change in the environment (e.g., touching a hot stove). Explain how the representation is like and unlike the phenomenon it is representing.