TEKS Addressed: 8.1A, 8.2A, 8.2B, 8.2C, 8.2D, 8.2E, 8.3A, 8.3D, 8.4A, 8.4B, 8.6A, 8.6B, 8.6C

Introduction

This unit bundles Student Expectations addressing the relationship between force and motion. Unbalanced forces cause change in the motion of an object that can be measured and calculated. Speed is a ratio of distance traveled to time taken. Acceleration is the rate at which an object changes its velocity. Velocity is the change in position over the amount of time traveled.

Prior to this Unit

• Grade 6

  • 6.8B – Identify and describe the changes in position, direction, and speed of an object when acted upon by unbalanced forces.

  • 6.8C – Calculate average speed using distance and time measurements.

  • 6.8D – Measure and graph changes in motion.

• Grade 6 Mathematics

  • 6.3E – Multiply and divide positive rational numbers fluently.

  • 6.10A – Model and solve one-variable, one-step equations and inequalities that represent problems, including geometric concepts.

  • 6.12A – Represent numeric data graphically, including dot plots, stem-and-leaf plots, histograms, and box plots.

  • 6.13A – Interpret numeric data summarized in dot plots, stem-and-leaf plots, histograms, and box plots.

• Grade 7 Mathematics

  • 7.3A – Add, subtract, multiply, and divide rational numbers fluently.

  • 7.3B – Apply and extend previous understandings of operations to solve problems using addition, subtraction, multiplication, and division of rational numbers.

During this Unit

Students use scientific practices and a variety of tools to investigate, demonstrate (using models), and calculate how unbalanced forces change the speed or direction of an object's motion. Students calculate how a change in force affects the motion of an object. They also calculate the total net force acting upon an object by adding forces acting in the same direction or subtracting forces acting in opposite directions. Students also differentiate between speed, velocity, and acceleration. Furthermore, they are introduced to the relationship between force, mass, and acceleration (F=ma). Students manipulate the formula F=ma to understand how a change in force affects the acceleration (change in motion or direction) of an object. Students investigate and describe applications of Newton’s law of inertia, law of force and acceleration, and law of action-reaction. Students discuss their observations and record and organize data in their notebooks. Additionally, they analyze data to formulate reasonable explanations, communicate valid conclusions supported by the data, and predict trends. Students continue to demonstrate safe practices as outlined in the Texas Education Agency-approved safety standards and consider environmentally appropriate and ethical practices with resources during investigations.

Note: Students will be allowed the use of calculators on the Grade 8 Science STAAR Assessment.

After this Unit

In a subsequent unit, students will describe the applications of Newton’s laws in the context of Earth’s tectonic activities. Students will further their study concepts of force and motion in the High School Integrated Physics and Chemistry (IPC) or Physics course.

Additional Notes

STAAR Note

The Grade 8 Science STAAR will directly assess Student Expectations in the following Reporting Categories:

• Reporting Category 2: Force, Motion, and Energy

  • 8.6A – Readiness Standard

  • 8.6B – Supporting Standard

  • 8.6C – Readiness Standard

Research

The force / motion relationship can be developed more fully now and the difficult idea of inertia be given attention. Students have no trouble believing that an object at rest stays that way unless acted on by a force; they see it every day. The difficult notion is that an object in motion will continue to move unabated unless acted on by a force. Telling students to disregard their eyes will not do the trick—the things around them do appear to slow down on their own accord unless constantly pushed or pulled. The more experiences the students can have in seeing the effect of reducing friction, the easier it may be to get them to imagine the friction-equals-zero case.

“By the end of 8th grade, students should know that:

• An unbalanced force acting on an object changes its speed or direction of motion, or both. 4F/M3a”

American Association for the Advancement of Science. (2009). Benchmarks on-line. Retrieved from http://www.project2061.org/publications/bsl/online/index.php?chapter=4#F3.

Isaac Newton was a physicist and mathematician who developed the principles of modern physics, including the laws of motion and is credited as one of the great minds of the 17th-century Scientific Revolution.

In 1687, he published his most acclaimed work, Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), which has been called the single most influential book on physics. In 1705, he was knighted by Queen Anne of England, making him Sir Isaac Newton.

Early Life and Family

Newton was born on January 4, 1643, in Woolsthorpe, Lincolnshire, England. Using the "old" Julian calendar, Newton's birth date is sometimes displayed as December 25, 1642.

Newton was the only son of a prosperous local farmer, also named Isaac, who died three months before he was born. A premature baby born tiny and weak, Newton was not expected to survive.

When he was 3 years old, his mother, Hannah Ayscough Newton, remarried a well-to-do minister, Barnabas Smith, and went to live with him, leaving young Newton with his maternal grandmother.

The experience left an indelible imprint on Newton, later manifesting itself as an acute sense of insecurity. He anxiously obsessed over his published work, defending its merits with irrational behavior.

At age 12, Newton was reunited with his mother after her second husband died. She brought along her three small children from her second marriage.

The Apple Myth

Between 1665 and 1667, Newton returned home from Trinity College to pursue his private study, as school was closed due to the Great Plague. Legend has it that, at this time, Newton experienced his famous inspiration of gravity with the falling apple. According to this common myth, Newton was sitting under an apple tree when a fruit fell and hit him on the head, inspiring him to suddenly come up with the theory of gravity.

While there is no evidence that the apple actually hit Newton on the head, he did see an apple fall from a tree, leading him to wonder why it fell straight down and not at an angle. Consequently, he began exploring the theories of motion and gravity.

It was during this 18-month hiatus as a student that Newton conceived many of his most important insights—including the method of infinitesimal calculus, the foundations for his theory of light and color, and the laws of planetary motion—that eventually led to the publication of his physics book Principia and his theory of gravity.

Isaac Newton & Robert Hooke

Not everyone at the Royal Academy was enthusiastic about Newton’s discoveries in optics and 1672 publication of Opticks: Or, A treatise of the Reflections, Refractions, Inflections and Colours of Light. Among the dissenters was Robert Hooke, one of the original members of the Royal Academy and a scientist who was accomplished in a number of areas, including mechanics and optics.

While Newton theorized that light was composed of particles, Hooke believed it was composed of waves. Hooke quickly condemned Newton's paper in condescending terms, and attacked Newton's methodology and conclusions.

Hooke was not the only one to question Newton's work in optics. Renowned Dutch scientist Christiaan Huygens and a number of French Jesuits also raised objections. But because of Hooke's association with the Royal Society and his own work in optics, his criticism stung Newton the worst.

Unable to handle the critique, he went into a rage—a reaction to criticism that was to continue throughout his life. Newton denied Hooke's charge that his theories had any shortcomings and argued the importance of his discoveries to all of science.

In the ensuing months, the exchange between the two men grew more acrimonious, and soon Newton threatened to quit the Royal Society altogether. He remained only when several other members assured him that the Fellows held him in high esteem.

The rivalry between Newton and Hooke would continue for several years thereafter. Then, in 1678, Newton suffered a complete nervous breakdown and the correspondence abruptly ended. The death of his mother the following year caused him to become even more isolated, and for six years he withdrew from intellectual exchange except when others initiated correspondence, which he always kept short.

During his hiatus from public life, Newton returned to his study of gravitation and its effects on the orbits of planets. Ironically, the impetus that put Newton on the right direction in this study came from Robert Hooke.

In a 1679 letter of general correspondence to Royal Society members for contributions, Hooke wrote to Newton and brought up the question of planetary motion, suggesting that a formula involving the inverse squares might explain the attraction between planets and the shape of their orbits.

Subsequent exchanges transpired before Newton quickly broke off the correspondence once again. But Hooke's idea was soon incorporated into Newton's work on planetary motion, and from his notes it appears he had quickly drawn his own conclusions by 1680, though he kept his discoveries to himself.

In early 1684, in a conversation with fellow Royal Society members Christopher Wren and Edmond Halley, Hooke made his case on the proof for planetary motion. Both Wren and Halley thought he was on to something, but pointed out that a mathematical demonstration was needed.

In August 1684, Halley traveled to Cambridge to visit with Newton, who was coming out of his seclusion. Halley idly asked him what shape the orbit of a planet would take if its attraction to the sun followed the inverse square of the distance between them (Hooke's theory).

Newton knew the answer, due to his concentrated work for the past six years, and replied, "An ellipse." Newton claimed to have solved the problem some 18 years prior, during his hiatus from Cambridge and the plague, but he was unable to find his notes. Halley persuaded him to work out the problem mathematically and offered to pay all costs so that the ideas might be published, which it was, in Newton’s Principia.

Upon the publication of the first edition of Principia in 1687, Robert Hooke immediately accused Newton of plagiarism, claiming that he had discovered the theory of inverse squares and that Newton had stolen his work. The charge was unfounded, as most scientists knew, for Hooke had only theorized on the idea and had never brought it to any level of proof.

Newton, however, was furious and strongly defended his discoveries. He withdrew all references to Hooke in his notes and threatened to withdraw from publishing the subsequent edition of Principia altogether.

Halley, who had invested much of himself in Newton's work, tried to make peace between the two men. While Newton begrudgingly agreed to insert a joint acknowledgment of Hooke's work (shared with Wren and Halley) in his discussion of the law of inverse squares, it did nothing to placate Hooke.

As the years went on, Hooke's life began to unravel. His beloved niece and companion died the same year that Principia was published, in 1687. As Newton's reputation and fame grew, Hooke's declined, causing him to become even more bitter and loathsome toward his rival.

To the very end, Hooke took every opportunity he could to offend Newton. Knowing that his rival would soon be elected president of the Royal Society, Hooke refused to retire until the year of his death, in 1703.

Newton and Alchemy

Following the publication of Principia, Newton was ready for a new direction in life. He no longer found contentment in his position at Cambridge and was becoming more involved in other issues.

He helped lead the resistance to King James II's attempts to reinstitute Catholic teaching at Cambridge, and in 1689 he was elected to represent Cambridge in Parliament.

While in London, Newton acquainted himself with a broader group of intellectuals and became acquainted with political philosopher John Locke. Though many of the scientists on the continent continued to teach the mechanical world according to Aristotle, a young generation of British scientists became captivated with Newton's new view of the physical world and recognized him as their leader.

One of these admirers was Nicolas Fatio de Duillier, a Swiss mathematician whom Newton befriended while in London.

However, within a few years, Newton fell into another nervous breakdown in 1693. The cause is open to speculation: his disappointment over not being appointed to a higher position by England's new monarchs, William III and Mary II, or the subsequent loss of his friendship with Duillier; exhaustion from being overworked; or perhaps chronic mercury poisoning after decades of alchemical research.

It's difficult to know the exact cause, but evidence suggests that letters written by Newton to several of his London acquaintances and friends, including Duillier, seemed deranged and paranoiac, and accused them of betrayal and conspiracy.

Oddly enough, Newton recovered quickly, wrote letters of apology to friends, and was back to work within a few months. He emerged with all his intellectual facilities intact, but seemed to have lost interest in scientific problems and now favored pursuing prophecy and scripture and the study of alchemy.

While some might see this as work beneath the man who had revolutionized science, it might be more properly attributed to Newton responding to the issues of the time in turbulent 17th century Britain.

Many intellectuals were grappling with the meaning of many different subjects, not least of which were religion, politics and the very purpose of life. Modern science was still so new that no one knew for sure how it measured up against older philosophies.

Gold Standard

In 1696, Newton was able to attain the governmental position he had long sought: warden of the Mint; after acquiring this new title, he permanently moved to London and lived with his niece, Catherine Barton.

Barton was the mistress of Lord Halifax, a high-ranking government official who was instrumental in having Newton promoted, in 1699, to master of the Mint—a position that he would hold until his death.

Not wanting it to be considered a mere honorary position, Newton approached the job in earnest, reforming the currency and severely punishing counterfeiters. As master of the Mint, Newton moved the British currency, the pound sterling, from the silver to the gold standard.

The Royal Society

In 1703, Newton was elected president of the Royal Society upon Robert Hooke's death. However, Newton never seemed to understand the notion of science as a cooperative venture, and his ambition and fierce defense of his own discoveries continued to lead him from one conflict to another with other scientists.

By most accounts, Newton's tenure at the society was tyrannical and autocratic; he was able to control the lives and careers of younger scientists with absolute power.

In 1705, in a controversy that had been brewing for several years, German mathematician Gottfried Leibniz publicly accused Newton of plagiarizing his research, claiming he had discovered infinitesimal calculus several years before the publication of Principia.

In 1712, the Royal Society appointed a committee to investigate the matter. Of course, since Newton was president of the society, he was able to appoint the committee's members and oversee its investigation. Not surprisingly, the committee concluded Newton's priority over the discovery.

That same year, in another of Newton's more flagrant episodes of tyranny, he published without permission the notes of astronomer John Flamsteed. It seems the astronomer had collected a massive body of data from his years at the Royal Observatory at Greenwich, England.

Newton had requested a large volume of Flamsteed's notes for his revisions to Principia. Annoyed when Flamsteed wouldn't provide him with more information as quickly as he wanted it, Newton used his influence as president of the Royal Society to be named the chairman of the body of "visitors" responsible for the Royal Observatory.

He then tried to force the immediate publication of Flamsteed's catalogue of the stars, as well as all of Flamsteed's notes, edited and unedited. To add insult to injury, Newton arranged for Flamsteed's mortal enemy, Edmund Halley, to prepare the notes for press.

Flamsteed was finally able to get a court order forcing Newton to cease his plans for publication and return the notes—one of the few times that Newton was bested by one of his rivals.

Final Years

Toward the end of this life, Newton lived at Cranbury Park, near Winchester, England, with his niece, Catherine (Barton) Conduitt, and her husband, John Conduitt.

By this time, Newton had become one of the most famous men in Europe. His scientific discoveries were unchallenged. He also had become wealthy, investing his sizable income wisely and bestowing sizable gifts to charity.

Despite his fame, Newton's life was far from perfect: He never married or made many friends, and in his later years, a combination of pride, insecurity and side trips on peculiar scientific inquiries led even some of his few friends to worry about his mental stability.

Death

By the time he reached 80 years of age, Newton was experiencing digestion problems and had to drastically change his diet and mobility.

In March 1727, Newton experienced severe pain in his abdomen and blacked out, never to regain consciousness. He died the next day, on March 31, 1727, at the age of 84.

Legacy

Newton's fame grew even more after his death, as many of his contemporaries proclaimed him the greatest genius who ever lived. Maybe a slight exaggeration, but his discoveries had a large impact on Western thought, leading to comparisons to the likes of Plato, Aristotle and Galileo.

Although his discoveries were among many made during the Scientific Revolution, Newton's universal principles of gravity found no parallels in science at the time.

Of course, Newton was proven wrong on some of his key assumptions. In the 20th century, Albert Einstein would overturn Newton's concept of the universe, stating that space, distance and motion were not absolute but relative and that the universe was more fantastic than Newton had ever conceived.

Newton might not have been surprised: In his later life, when asked for an assessment of his achievements, he replied, "I do not know what I may appear to the world; but to myself I seem to have been only like a boy playing on the seashore, and diverting myself now and then in finding a smoother pebble or prettier shell than ordinary, while the great ocean of truth lay all undiscovered before me."

Isaac Newton’s Discoveries

Newton made discoveries in optics, motion and mathematics. Newton theorized that white light was a composite of all colors of the spectrum, and that light was composed of particles.

His momentous book on physics, Principia, contains information on nearly all of the essential concepts of physics except energy, ultimately helping him to explain the laws of motion and the theory of gravity. Along with mathematician Gottfried Wilhelm von Leibniz, Newton is credited for developing essential theories of calculus.

Isaac Newton Inventions

Newton's first major public scientific achievement was designing and constructing a reflecting telescope in 1668. As a professor at Cambridge, Newton was required to deliver an annual course of lectures and chose optics as his initial topic. He used his telescope to study optics and help prove his theory of light and color.

The Royal Society asked for a demonstration of his reflecting telescope in 1671, and the organization's interest encouraged Newton to publish his notes on light, optics and color in 1672. These notes were later published as part of Newton's Opticks: Or, A treatise of the Reflections, Refractions, Inflections and Colours of Light.

Isaac Newton’s Laws of Motion

In 1687, following 18 months of intense and effectively nonstop work, Newton published Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), most often known as Principia.

Principia is said to be the single most influential book on physics and possibly all of science. Its publication immediately raised Newton to international prominence.

Principia offers an exact quantitative description of bodies in motion, with three basic but important laws of motion:

First Law

An object at rest will stay at rest, and an object in motion for stay in motion, unless acted upon by an unbalanced forced.

Second Law

Force is equal to mass times acceleration, and a change in motion (i.e., change in speed) is proportional to the force applied.

Third Law

For every action, there is an equal and opposite reaction (equal in force and opposite in direction).

Newton and the Theory of Gravity

Newton’s three basic laws of motion outlined in Principia helped him arrive at his theory of gravity. Newton’s law of universal gravitation states that two objects attract each other with a force of gravitational attraction that’s proportional to their masses and inversely proportional to the square of the distance between their centers.

These laws helped explain not only elliptical planetary orbits but nearly every other motion in the universe: how the planets are kept in orbit by the pull of the sun’s gravity; how the moon revolves around Earth and the moons of Jupiter revolve around it; and how comets revolve in elliptical orbits around the sun.

They also allowed him to calculate the mass of each planet, calculate the flattening of the Earth at the poles and the bulge at the equator, and how the gravitational pull of the sun and moon create the Earth’s tides. In Newton's account, gravity kept the universe balanced, made it work, and brought heaven and Earth together in one great equation.