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HELP: Original Lessons on Gravity and Charge

Site: Mountain Heights Academy OER
Course: Physics Q4
Book: HELP: Original Lessons on Gravity and Charge
Printed by: Guest user
Date: Friday, 4 April 2025, 11:57 AM

Description

Theses are the original lessons on gravity and charge from Q3.  Review as needed.

Table of contents

Introduction to Gravity

Long, long ago, when the universe was still young, an incredible force caused dust and gas particles to pull together to form the objects in our solar system. From the smallest moon to our enormous sun, this force created not only our solar system, but all the solar systems in all the galaxies of the universe. The force is gravity.

Defining Gravity

Gravity has traditionally been defined as a force of attraction between things that have mass. According to this conception of gravity, anything that has mass, no matter how small, exerts gravity on other matter. Gravity can act between objects that are not even touching. In fact, gravity can act over very long distances. However, the farther two objects are from each other, the weaker is the force of gravity between them. Less massive objects also have less gravity than more massive objects.

Earth’s Gravity

You are already very familiar with Earth’s gravity. It constantly pulls you toward the center of the planet. It prevents you and everything else on Earth from being flung out into space as the planet spins on its axis. It also pulls objects that are above the surface—from meteors to skydivers—down to the ground. Gravity between Earth and the moon and between Earth and artificial satellites keeps all these objects circling around Earth. Gravity also keeps Earth and the other planets moving around the much more massive sun.

Q: There is a force of gravity between Earth and you and also between you and all the objects around you. When you drop a paper clip, why doesn’t it fall toward you instead of toward Earth?

A: Earth is so much more massive than you that its gravitational pull on the paper clip is immensely greater.

Gravity and Weight

Weight measures the force of gravity pulling downward on an object. The SI unit for weight, like other forces, is the Newton (N). On Earth, a mass of 1 kilogram has a weight of about 10 Newtons because of the pull of Earth’s gravity. On the moon, which has less gravity, the same mass would weigh less. Weight is measured with a scale, like the spring scale shown in the Figure below. The scale measures the force with which gravity pulls an object downward. To delve a little deeper into weight and gravity, watch this video:

Summary

  • Gravity has traditionally been defined as a force of attraction between things that have mass. The strength of gravity between two objects depends on their mass and their distance apart.
  • Earth’s gravity constantly pulls matter toward the center of the planet. It also keeps moons and satellites orbiting Earth and Earth orbiting the sun.
  • Weight measures the force of gravity pulling on an object. The SI unit for weight is the Newton (N).

Vocabulary

  • gravity: As traditionally defined, force of attraction between things that have mass.

Practice

At the following URL, read about gravity and tides. Watch the animation and look closely at the diagrams. Then answer the questions below.

http://www.mmscrusaders.com/newscirocks/tides/tideanim.htm

  1. What causes tides?
  2. Which has a greater influence on tides, the moon or the sun? Why?
  3. Why is there a tidal bulge of water on the opposite side of Earth from the moon?
  4. When are tides highest? What causes these tides to be highest?
  5. When are tides lowest? What causes these tides to be lowest?

Newton's Law of Universal Gravitation

You may have heard a story about Isaac Newton coming up with the idea of gravity when an apple fell out of a tree and hit him in the head. The story isn’t true, but seeing how things like apples fall to Earth helped Newton form his ideas about gravity, the force of attraction between things that have mass. Of course, people had known about the effects of gravity for thousands of years before Newton came along. After all, they constantly experienced gravity in their daily lives. They observed over and over again that things always fall toward the ground. However, it wasn’t until Newton developed his law of gravity in the late 1600's that people knew gravity applies to everything in the universe that has mass.

Newton’s Law of Universal Gravitation

Newton was the first one to suggest that gravity is universal and affects all objects in the universe. That’s why Newton’s law of gravity is called the law of universal gravitation. Universal gravitation means that the force that causes an apple to fall from a tree to the ground is the same force that causes the moon to keep moving around Earth. Universal gravitation also means that while Earth exerts a pull on you, you exert a pull on Earth. In fact, there is gravity between you and every mass around you—your desk, your book, your pen. Even tiny molecules of gas are attracted to one another by the force of gravity. You can learn more about Newton’s law of gravity and how he developed it in the video at this URL:

Watch This Video

Q: Newton’s law of universal gravitation had a huge impact on how people thought about the universe. Why do you think it was so important?

A: Newton’s law was the first scientific law that applied to the entire universe. It explains the motion of objects not only on Earth but in outer space as well.

Factors that Influence the Strength of Gravity

Newton’s law also states that the strength of gravity between any two objects depends on two factors: the masses of the objects and the distance between them.

  • Objects with greater mass have a stronger force of gravity between them. For example, because Earth is so massive, it attracts you and your desk more strongly that you and your desk attract each other. That’s why you and the desk remain in place on the floor rather than moving toward one another.
  • Objects that are closer together have a stronger force of gravity between them. For example, the moon is closer to Earth than it is to the more massive sun, so the force of gravity is greater between the moon and Earth than between the moon and the sun. That’s why the moon circles around Earth rather than the sun. You can see this in the Figure below.


How to Calculate Gravitational Forces & Sample Problems

In equation form, Newton's Law of Universal Gravitation is:

\( F_g = \frac{Gm_1 m_2}{d^2} \)


Fg stands for the force of gravity (in Newtons), m1 and m2 are the masses of both objects involved (in kilograms), and d is the distance between objects (in meters).  G is the universal gravitational constant, which means its value will never change.  For its value, G = 6.67 x 10-11 Nm2/kg2 .


Here are some examples of calculations and sample problems.


Summary

  • Newton’s law of universal gravitation states that the force of gravity affects everything with mass in the universe.
  • Newton’s law also states that the strength of gravity between any two objects depends on the masses of the objects and the distance between them.

Vocabulary

  • Law of Universal Gravitation: Law stating that gravity is a force of attraction between all objects in the universe and that the strength of gravity is greater when masses of objects are greater or distances between objects are shorter.


Introduction to Electrical Charge

Watch the following video to find out what causes electrical charges:

Electrons can be transferred fairly easily between objects, but protons are more fixed.  Usually the positive protons and the negative electrons will balance out, and objects will have a neutral charge of zero.  But if there is an inbalance between protons and electrons, you get charged objects.  The charge of each individual proton or electron is very small.  So small you wouldn't even notice it.  But usually there are many protons and electrons involved.  When many protons or electrons are involved, we get large, noticeable charges, as in the following video:

Moving electrons will result in a flow of charge.  Some materials allow electrons to move easily, and some materials don't, as in the following video:

The SI unit for charge is called a "Coulomb".  1 Coulomb is actually a pretty huge charge, since each individual electron has an electrical charge of -1.6 x 10-19 C.  Protons have an equal and opposite electrical charge of +1.6 x 10-19 C.  We don't break apart electrons in everyday life, so charge will always come in multiples of 1.6 x 10-19 C.  If an object had two extra electrons, it would have a charge of -3.2 x 10-19 C.  If an object had three extra protons, it would have a charge of +4.8 x 10-19 C.  Watch the following video to see some examples of finding charges on objects:

There are two basic rules for dealing with charges:

1. Opposite charges attract each other, and like charges repel each other.

2. Charge is conserved.


Separation and Transfer of Charge

Watch the following videos about how charges are placed and how charges move:




Coulomb's Law

 

Electric cars are becoming more popular. One large advantage for electric cars is the low cost of operation, which may become an ever bigger advantage as gas prices climb. Energy costs for electric cars average about one-third of the cost for gasoline engine cars, but they can only travel about 200 miles per charge at this point. These cars run using the science of electrical charges and forces.

Coulomb’s Law

The questions regarding the relationship between the electrical force, the size of the charge, and the separation between the charges were solved by Charles Coulomb in 1785. He determined that electrical force between two charges is directly related to the size of the charges and inversely proportional to the distance between the charges. This is known as Coulomb’s Law.

F_e=\frac{Kq_1q_2}{d^2}

In this equation, q1 and q2 are the two charges, d is the distance between the two charges, andK is a constant of proportionality. Fe is the electric force, which occurs as a result of interactions between two charged particles. For the purpose of calculating electric forces, we assume all charge is a point charge, in which the entire charge of the particle is located in a massless point.

The SI unit of charge is the coulomb, C, which is the charge of 6.25 \times 10^{18} electrons. The charge on a single electron is 1.60 \times 10^{-19} \ C. The charge on a single electron is known as the elementary charge. The charge on a proton is the same magnitude but opposite in sign. When the charges are measured in coulombs, the distance in meters, and the force in Newtons, the constant K is 9.0 \times 10^9 \ N \cdot m^2/C^2.

The electrical force, like all forces, is a vector quantity. If the two charges being considered are both positive or both negative, the sign of the electrical force is positive and this force is repulsive. If the two charges are opposite in sign, the force will have a negative sign and the force is attractive.


Example Problem: Object A has a positive charge of 6.0 \times 10^{-6} \ C. Object B has a positive charge of 3.0 \times 10^{-6} \ C. If the distance between A and B is 0.030 m, what is the force on A?

Solution: F_e=\frac{Kq_1q_2}{d^2}=\frac{(9.0 \times 10^9 \ N \cdot m^2/C^2)(6.0 \times 10^{-6} \ C)(3.0 \times 10^{-6} \ C)}{(0.030 \ m)^2}=180 \ N

The positive sign of the force indicates the force is repulsive. This makes sense, because both objects have a positive charge.

Example Problem: In the sketch below, the charges are q_1 = 10.0 \times 10^{-6} \ C, \ q_2 = 2.0 \times 10^{-6} \ C, and q_3 = -6.0 \times 10^{-6} \ C. Calculate the total force on q2.

Solution: F_e=\frac{Kq_1q_2}{d^2}=\frac{(9.0 \times 10^9 \ N \cdot m^2/C^2)(10.0 \times 10^{-6} \ C)(2.0 \times 10^{-6} \ C)}{(2.0 \ m)^2}=0.045 \ N \ (\text{towards} \ q_3)

F_e=\frac{Kq_2q_3}{d^2}=\frac{(9.0 \times 10^9 \ N \cdot m^2/C^2)(2.0 \times 10^{-6} \ C)(-6.0 \times 10^{-6} \ C)}{(4.0 \ m)^2}=-0.007 \ N \ (\text{towards} \ q_3)

Since the two forces act in the same direction, their absolute values can be added together; the total force on q2 is 0.052 N towards q3.

Summary

  • Coulomb determined that electrical force between two charges is directly related to the size of the charges and inversely proportional to the distance between the charges: F_e=\frac{Kq_1q_2}{d^2}
  • The SI unit of charge is the coulomb, C, which is the charge of 6.25 \times 10^{18} electrons.
  • The charge on a single electron is 1.60 \times 10^{-19} \ C and is known as the elementary charge.
  • The electrical force is a vector quantity that is positive in repulsion and negative in attraction.

Practice

The following video covers Coulomb's Law. Use this resource to answer the questions that follow.


  1. What happens when like charges are placed near each other?
  2. What happens when opposite charged are placed near each other?
  3. What happens to the force of attraction if the charges are placed closer together?


Electric Fields


This image is of a plasma ball at a science museum. It shows electricity flowing out of a charged ball. The electricity follows the lines of the electric field. What is an electric field? Read on to find out.


What Is an Electric Field?

An electric field is a space around a charged particle where the particle exerts electric force on other charged particles. Because of their force fields, charged particles can exert force on each other without actually touching. Electric fields are generally represented by arrows which show the direction that a small positive charge would travel, as you can see in the Figure below. The arrows show the direction of electric force around a positive particle and a negative particle. 


Interacting Electric Fields

When charged particles are close enough to exert force on each other, their electric fields interact. This is illustrated in the Figure below. The lines of force bend together when particles with different charges attract each other. The lines bend apart when particles with like charges repel each other. Remember, the arrows show the direction that a small positive test charge would travel, if it were placed at that point.


Q: What would the lines of force look like around two negative particles?

A: They would look like the lines around two positive particles, except the arrows would point toward, rather than away from, the negative particles.  This would show that a positive test charge would be attracted to the negative particles.


The Intensity of an Electric Field

Coulomb’s Law gives us the formula to calculate the force exerted on a charge by another charge. On some occasions, however, a test charge suffers an electrical force with no apparent cause. That is, as observers, we cannot see or detect the original charge creating the electrical force. Michael Faraday dealt with this problem by developing the concept of an electric field. According to Faraday, a charge creates an electric field about it in all directions. If a second charge is placed at some point in the field, the second charge interacts with the field and experiences an electrical force. Thus, the interaction we observe is between the test charge and the field and a second particle at some distance is no longer necessary.

The strength of the electric field is determined point by point and can only be identified by the presence of test charge. When a positive test charge, q, is placed in an electric field, the field exerts a force on the charge. The field strength can be measured by dividing the force by the charge of the test charge. Electric field strength is given the symbol E and its unit is Newtons/coulomb.

E=\frac{F_{onq_t}}{q_t}

The test charge can be moved from location to location within the electric field until the entire electric field has been mapped in terms of electric field intensity.


Example Problem: A positive test charge of 2.0 \times 10^{-5} \ \text{C} is placed in an electric field. The force on the test charge is 0.60 N. What is the electric field intensity at the location of the test charge?

Solution: E=\frac{F}{q}=\frac{0.60 \ \text{N}}{2.0 \times 10^{-5} \ \text{C}}=3.0 \times 10^4 \ \text{N/C}


Practice

The following video covers electric fields. 



Vocabulary

  • electric field: Space around a charged particle where the particle exerts electric force.


Summary

  • An electric field is a space surrounding a charged particle where the particle exerts electric force.
  • When charged particles are close enough to exert force on each other, their electric fields interact. Particles with opposite charges attract each other. Particles with like charges repel each other.
  • An electric field surrounds every charge and acts on other charges in the vicinity.
  • The strength of the electric field is given by the symbol E, and has the unit of Newtons/coulomb.
  • The equation for electric field intensity is E=\frac{F}{q}.