Introduction to Electric Forces

The AP Physics 2 writers really want us to review forces and get a deep understanding of dynamics. So let's walk through the famous Newtonian Laws again briefly and remind ourselves of what forces are and how they work.

Sir Isaac Newton's three laws of motion, also known as Newton's laws, are fundamental principles that describe the relationship between a body and the forces acting upon it. These laws form the basis of classical mechanics, which is the study of how objects move and behave under the influence of forces.

Here are brief overviews of each of Newton's laws:

• First Law of Motion: An object will remain at rest or in motion at a constant velocity unless acted upon by an external force. This is often referred to as the law of inertia.

• Second Law of Motion: The acceleration of an object is directly proportional to the force applied to it and inversely proportional to its mass. This can be written as F = ma, where F is the force applied to the object, m is the mass of the object, and a is the acceleration of the object.

• Third Law of Motion: For every action, there is an equal and opposite reaction. This means that if two objects interact, they will exert equal and opposite forces on each other.

These laws are useful in predicting the motion of objects under the influence of forces, and they can be applied to a wide range of physical situations, from the motion of objects on Earth to the orbits of planets and other celestial bodies.

Newton's First Law

• Newton’s First Law states that “every object persists in its state of rest or uniform motion in a straight line unless it is compelled to change that state by forces impressed on it." ⬅️➡️

This law deals with two main concepts in physics: the principle of inertia and the principle of frames of reference. Newton’s First Law is sometimes known as the Law of Inertia because it explains the concept that objects have the tendency to resist a change in motion.

• Inertial Mass—mass that is accelerated (mass in motion)

• Gravitational Mass—mass based on an object’s weight (mass being pulled by the gravitational field)

Newton's Second Law

• Newton’s Second Law states, “The acceleration of an object as produced by a net force is  to the magnitude of the net force, in the same direction as the net force, and to the mass of the object.”

• Key equation: Force = mass x acceleration (F=ma)

Newton's Third Law

• Newton’s Third Law states that

• In other words, an object cannot exert a force on itself.

• Action-Reaction Pair: The force exerted on an object is the action, and the force experienced by the object is the reaction. Action-Reaction pairs occur only when two objects interact. (Example: a book pulling down on a table <-> a table pushing up on a book.)

Electric force at work! Paper sticking to comb!

Example Problem #1:

A car is driving down the road at a constant speed of 50 km/h. The driver suddenly slams on the brakes, causing the car to come to a stop in 5 seconds. What is the acceleration of the car during this time?

Solution:

To solve this problem, we can use Newton's second law, which states that the acceleration of an object is directly proportional to the force applied to it and inversely proportional to its mass. We know that the car starts at a constant speed of 50 km/h and comes to a stop in 5 seconds, so it must have experienced a negative acceleration. We can set up the equation as follows: a = F/m. If we let m be the mass of the car and F be the force applied by the brakes, we can solve for a by rearranging the equation: a = (-50 km/h)/5 s = -10 km/h/s. This means that the car's acceleration was -10 km/h/s, or a deceleration of 10 km/h/s.

Example Problem #2:

A ball is thrown straight up into the air with an initial velocity of 20 m/s. How high does the ball go before it reaches its maximum height and begins to fall back down?

Solution:

To solve this problem, we can use Newton's first law, which states that an object will remain at rest or in motion at a constant velocity unless acted upon by an external force. We know that the ball is initially thrown upward with an initial velocity of 20 m/s, and that it reaches its maximum height before starting to fall back down. Since the ball is not being acted upon by any external forces while it is in the air, it must have a constant velocity of 0 m/s while it is at its maximum height. We can use the equation v^2 = u^2 + 2as to solve for the height of the ball, where v is the final velocity (0 m/s), u is the initial velocity (20 m/s), and a is the acceleration due to gravity (-9.8 m/s^2). Plugging these values into the equation, we get: 0 = 400 + (-19.6)s. Solving for s, we find that s = 20.4 m, which is the height of the ball.

History and Introduction of Electric Forces

After Newton had done his groundbreaking work regarding gravity, charges and electricity were the next big thing. Scientific celebrities like Daniel Bernoulli and Benjamin Franklin worked on finding out more about electric charges and fields as well. Franklin shared his findings with his teacher, John Priestley.

Priestley agreed with the commonly held belief among scientists that the force between charges followed an inverse square pattern just like Gravity. This means that if the distance between charges was decreased by a factor of 2, the force between them would increase by a factor of 4. Priestley's entire theory did have some flaws. Many scientists continued to solve this entangled puzzle about the electric force. Charles Augustin de Coulomb would be the man who would publish a definitive study that electrical force between two point-charges varied inversely with the square of their separation.

The study of electric forces has a long and fascinating history that dates back to ancient civilizations. Here is a brief summary of the key events and milestones in the development of our understanding of electric forces:

• The ancient Greeks, including philosophers such as Thales and Aristotle, observed that certain materials, such as amber, could attract small objects when they were rubbed with fur. This phenomenon, known as triboelectricity, was one of the first known examples of electric forces.

• In the 16th and 17th centuries, scientists such as William Gilbert and Francis Bacon conducted experiments and made observations about electric forces and magnetism. Gilbert is credited with coining the term "electricity" and developing the concept of electric charge.

• In the 18th century, the work of scientists such as Benjamin Franklin and Charles-Augustin de Coulomb laid the foundations for our modern understanding of electric forces. Franklin's experiments with lightning rods helped to demonstrate the nature of electric charge and the concept of grounding. Coulomb developed Coulomb's Law, which describes the electrical force between two charged particles.

• In the 19th and 20th centuries, the study of electric forces continued to advance, with contributions from scientists such as James Clerk Maxwell, who developed a mathematical theory that united electricity, magnetism, and light, and Michael Faraday, who developed the concept of the electromagnetic field.

• Today, our understanding of electric forces continues to evolve and develop through ongoing research and experimentation by scientists and engineers around the world