Unit 2 Overview: Dynamics

2.0 Unit 2 Overview: Dynamics

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Dynamics is the study of the forces 💪, or the interactions of an object with another object, that cause objects and systems to move. The basic understanding of a force as a push or pull helps solidify that it is a vector quantity and has both magnitude and direction 🔁. 

Similar to that of Unit 1, translation is key in Unit 2. In Unit 1, you learned how to analyze the motion of an object.  Unit 2 takes this idea further and teaches you not just how but why translational motion occurs.  

The first major concept that you will learn about in this unit is the idea of defining a system ⚙️ as a portion of the universe that you choose to study.  You will be able to identify internal and external forces to the system.  The aim of the unit is to show the same object–force interactions through different graphs 📈, diagrams, and mathematical relationships. During Unit 2, you will also learn a necessary skill throughout the remaining units of AP Physics 1: how to derive new expressions from fundamental equations to form predictions in unfamiliar scenarios. 

The backbone of this unit is a variety of different types of forces.  These forces are typically classified into two categories: contact forces and non-contact forces.  Contact forces are exactly what they sound like–forces that occur when two objects are directly touching each other 🙏.  Non-contact forces are forces that occur at a distance 🙌. 

The most common forces that you will study in this unit are weight, normal force, tension, friction, and spring force.  Weight is the force exerted on an object by gravity.  It is the only non-contact force you will encounter in this unit, and you calculate it by multiplying the mass of the object by the acceleration due to gravity.  Normal force is the force of a surface pushing against the object’s weight. Tension is the pulling force transmitted by a string, cable, or similar object 🪢. You will find that there are a lot of hanging signs and ropes when you have situations involving tension!  Friction is the force between two surfaces that resists motion.  Rougher surfaces (like sandpaper) have lots of friction, and smoother surfaces (like ice 🧊) have less friction.  Finally, spring force is precisely what it sounds like–the force exerted by springs!  We treat this differently from tension because springs and other elastic items act differently than a rope that is not as stretchy.  We use Hooke’s Law to relate the stretchiness of the spring, how far it stretches, and the spring force.

After learning about the different forces, you will start to add them together using force vectors and Free-Body Diagrams. This tool will allow you to write net force equations and calculate the net force acting on a system. This is probably the hardest part of the unit 😓, but doing practice problems will help you see patterns in the different types of questions.  Once you have that, you can relate it to the mass and acceleration of an object, culminating in Newton’s 2nd Law.  In this section, you will also learn how to determine if a system is in equilibrium (if the net force is zero) or accelerating (net force is not zero).  

There are two special 😎 cases that you will practice in this unit.  The first one is called an Atwood’s Machine.  One of these setups usually involves a pulley, a string, and a system of masses.  To work through these problems, you should be able to decide what your system is and be able to shift between the entire machine as one system and each mass separately.  

The second special case that you will practice is when you need to calculate the Apparent Weight of an object.  The apparent weight of an object will be different from the actual weight of an object when the force of gravity is not balanced by an equal normal force ⚖️.  This case typically arises when an object is accelerating vertically, such as in an elevator. 

The exam weight of this unit is 12-18%, and it tends to span over approximately 19-22 45 minute class periods.

Applicable Big Ideas 💨

Big Idea #1: Systems - Objects and systems have properties such as mass and charge. Systems may have internal structures.

Bid Idea #2: Fields - Fields existing in space can be used to explain interactions.

Big Idea #3: Force Interactions - The interactions of an object with other objects can be described by forces.

Big Idea #4: Change - Interactions between systems can result in changes in those systems.

2.1 Systems

In physics, a system is a collection of objects or particles that interact with each other. The concept of a system is important in physics because it allows us to understand how different parts of a system are connected and how they influence each other.

There are several types of systems in physics, including:

1. Closed systems: These are systems that do not exchange matter or energy with the surroundings. An isolated system is a specific type of closed system that does not exchange matter or energy with the surroundings and is not affected by any external forces.
2. Open systems: These are systems that exchange matter or energy with the surroundings. A thermodynamic system is a specific type of open system that exchanges energy but not matter with the surroundings.
3. Isolated systems: These are systems that do not exchange matter or energy with the surroundings and are not affected by any external forces.
4. Conservative systems: These are systems for which the total mechanical energy is conserved, meaning that the sum of kinetic and potential energy remains constant in time.
5. Non-conservative systems: These are systems for which the total mechanical energy is not conserved, meaning that the sum of kinetic and potential energy is not constant in time. It is also important to note that a system can be defined in different ways depending on the scale or level of detail considered. For example, an object can be considered as a system in one context and as part of a larger system in another context.

2.2 The Gravitational Field

A gravitational field is a region around a massive object within which another massive object will experience a force due to gravity. The strength of the gravitational field is represented by the symbol "g" and is measured in units of acceleration, typically in meters per second squared (m/s^2).

The gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. This relationship is described by Newton's law of gravitation.

The gravitational field strength "g" is defined as the force experienced by a unit mass placed at a certain point in the field, and it points towards the center of the massive object creating the field.

For example, the gravitational field strength at the Earth's surface is 9.8 m/s^2, which means that an object with a mass of 1 kilogram placed on the Earth's surface will experience a force of 9.8 newtons due to gravity. This value is also known as "acceleration due to gravity" or "standard gravity".

It's also worth noting that the gravitational field is a vector field, meaning that it has both a magnitude and direction. The magnitude of the field is dependent on the mass of the object creating the field and the distance from the object. The direction is always towards the center of the object.

As for the gravitational constant "G", it is a universal constant that relates the gravitational force between two objects to the product of their masses and the distance between them. The value of G is approximately 6.67 x 10^-11 N*m^2/kg^2

2.3 Contact Forces

Contact forces are forces that are exerted by one object on another when the two objects are in direct contact with each other. These forces can be divided into two main categories: normal forces and frictional forces.

1. Normal forces: A normal force is the force exerted by a surface on an object that is in contact with it. The normal force is always perpendicular to the surface and its direction is always away from the surface. The normal force is what keeps an object from falling through a surface. The normal force is also known as the "reaction force" since it is always equal in magnitude but opposite in direction to the force exerted by the object on the surface.
2. Frictional forces: Frictional forces are forces that oppose motion between two objects that are in contact with each other. Frictional forces are caused by the roughness and irregularity of the surfaces in contact. There are two types of friction: static friction and kinetic friction. Static friction is the force that opposes motion when an object is at rest, while kinetic friction is the force that opposes motion when an object is in motion. The magnitude of the frictional force is typically proportional to the normal force and is also determined by the coefficients of friction of the two surfaces in contact.

2.4 Newton's First Law

Newton's first law, also known as the law of inertia, states that an object at rest will remain at rest, and an object in motion will continue to move in a straight line with a constant velocity, unless acted upon by an unbalanced force.

In other words, an object will keep moving or staying at rest in a straight line at a constant speed, unless something makes it change its motion. This means that an object that is not being acted upon by a net force will maintain a constant velocity. If the velocity is zero, then the object will remain at rest.

This law is based on the idea that an object has a natural tendency to remain in its current state of motion (at rest or in motion) and that it takes an unbalanced force to change that motion.

It is important to note that in an inertial reference frame (a reference frame in which Newton's first law holds), the net force acting on an object is equal to the mass of the object multiplied by its acceleration.

2.5 Newton's Third Law and Free Body Diagrams

Newton's third law states that for every action, there is an equal and opposite reaction. This means that when one object exerts a force on a second object, the second object exerts an equal and opposite force on the first object. The forces are said to be "action-reaction force pairs" and they are always equal in magnitude and opposite in direction.

For example, when you push a wall, the wall pushes back on you with an equal force. When a car accelerates forward, the road exerts an equal and opposite force (friction) on the car's tires.

A free body diagram is a tool used to help understand the forces acting on an object. A free body diagram is a simplified representation of an object that shows all the forces acting on it. It includes the object, the forces acting on it, and the direction of the forces.

To create a free body diagram, you should:

1. Draw a simple representation of the object.
2. Identify all the forces acting on the object and indicate their direction.
3. Make sure to draw the force vectors to scale and to the correct direction.

2.6 Newton's Second Law

Newton's second law states that the acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to the object's mass. Mathematically, it can be represented as:

F = ma

where F is the net force acting on the object, m is the mass of the object and a is the acceleration of the object.

This means that the greater the net force acting on an object, the greater the acceleration of the object will be; and the greater the mass of an object, the smaller the acceleration of the object will be.

It is important to note that net force is the vector sum of all forces acting on an object, and acceleration is the rate of change of velocity with respect to time.

Newton's second law is a fundamental principle in physics and it is used to analyze the motion of objects and predict how they will respond to forces. It is used to calculate the acceleration of an object given the net force and mass of the object. It also provides a way to calculate the net force on an object given its acceleration and mass.

2.7 Applications of Newton's Second Law

Newton's second law states that the acceleration of an object is directly proportional to the force applied to it and inversely proportional to its mass. It can be mathematically represented as F = ma, where F is the force, m is the mass, and a is the acceleration. Some common applications of Newton's second law include:

1. Understanding the behavior of objects in motion, such as cars, airplanes, and projectiles.
2. Designing and analyzing mechanical systems, such as gears, levers, and pulleys.
3. Describing the motion of celestial bodies, such as planets and satellites.