Physics Explained Through a Video Game/Forces and Free Body Diagrams

Topic 2.2 - Forces and Free Body Diagrams

Unlike most other sections of this course, this topic is reserved for reading and as a reference. As such, there are fewer practice materials for this topic. Consider the later topics in Unit 2 to broaden and apply the skills discussed below.

Dynamics and Forces

Two players bouncing on a set of colorful springs in the map "Mushroom Forest" by Nexooo. Physical interactions, such as those pictured, involve the presence of numerous forces that affect the motion of the players.

So far during much of this course, we have focused on kinematics, a way of describing the motion of objects, such as through their position, velocity, and acceleration. However, we also need to discuss what causes for objects to move in the first place. In this unit, we will be largely focusing on dynamics. This content area focuses on linking together the existence of forces and how they impact the motion of objects.

A force can be described as a push or a pull that is acting on an object. It is a vector quantity, meaning that it has both a magnitude and direction. We can use the symbol ${\vec {F}}$ to denote the presence of a force. Also, forces have their units in Newtons ($N$). As will be explored closely in the next topic, a Newton is equivalent to ${\text{kg}}\cdot {\frac {\text{m}}{{\text{s}}^{2}}}$. In other words, a force's magnitude is related to the mass of the object (described in $kg$ multiplied by the acceleration of that object (described in ${\frac {\text{m}}{{\text{s}}^{2}}}$). This can give us an intuition that forces—through their ability to push or pull—influence objects in accelerating towards a particular direction.

Characterizing Forces

A video of a rhinoceros walking in the map "Safari" by O_dot.

There are a wide variety of forces that exist, ranging from frictional forces, gravitational forces, tension forces, and many more. To characterize these forces, we distinguish between forces that are external and internal. An external force is a force that is originating from outside of an object or system and is applying a push or pull on it. For instance, assume that we're considering a rhinoceros as a system of interest. The gravitational force exerted by the Earth that pulls the rhinoceros down towards the ground is an example of an external force on the creature.

In contrast, there also exists numerous forces inside of the rhinoceros as well, such as skeletal and muscular forces that enable it to be able to eat, walk, and breathe. These can be characterized as internal forces.

Often, we take a particular interest towards the external forces that are acting on a system. This is because if we combine add all of the external forces vectors together**, we can derive the net external force, denoted by ${\vec {F}}_{\text{net}}$. This vector is important as the direction angle of ${\vec {F}}_{\text{net}}$ determines the direction in which an object is accelerating. With this property and others that will be discussed later in this unit, we can garner information concerning the kinematic behavior of an object directly through considering the forces that are acting on it.

** This requires the use of vector addition. Although this concept will later discussed in Topic 2.3 - Newton's Second Law, consider reading the introduction of vector addition by FHSST Physics, another Wikibooks project.

The Difference Between Mass and Weight

In Topic 2.1 - Systems and Center of Mass, we introduced the concept of mass to describe the distribution of it within an object. However, there's an important distinction to make between mass and weight. To note, these two terms are often used interchangeably in everyday speech.

The amount of mass within an object is the measure of how much matter is within an object. In other words, it describes the amount of "stuff" that is present in an object. In contrast, an object's weight is a measure of the gravitational force that is acting on an object. Mass is an intrinsic property. That means that any object with mass will have the same amount of mass regardless where it is located. Unlike mass, an object's weight varies depending on where the object is because the gravitational force that is exerted on an object varies.

We can define an object's weight with the formula: $({\text{weight}})=({\text{mass}})\cdot ({\text{acceleration due to gravity}})$. To note, using the previously discussed material in this unit:

• Because the weight and gravitational force on an object are interchangeable concepts, we can allow for weight to be represented by the variable ${\vec {F}}_{\text{grav}}$.
• Mass has been previously defined by the variable $m$.
• Acceleration has been previously defined by the variable ${\vec {a}}$. For acceleration due to gravity, we could write it as ${\vec {a}}_{\text{grav}}$. However, it is more commonly represented by the variable $g$.

  

  A diagram using a modified version of "Constellations" by iRedi. It shows that while mass is intrinsic, the weight of an object varies depending on where it is located.
  Note: This diagram is an adaptation of a diagram by VectorVoyager on Wikimedia Commons.

Thus, we could express the formula above as ${\vec {F}}_{\text{grav}}=mg$.

One way of considering how mass and weight differ is by considering a water bottle that has a mass of $2.0\;{\text{kg}}$. Then, we place this water bottle on the Earth. Because the Earth has an acceleration due to gravity of approximately $9.8\;{\frac {\text{m}}{{\text{s}}^{2}}}$, we can calculate for the weight of the water bottle on Earth, ${\vec {F}}_{\text{grav (on Earth)}}$:

${\vec {F}}_{\text{grav (on Earth)}}=(2.0)(9.8)\;{\text{N}}$

${\vec {F}}_{\text{grav (on Earth)}}=19.6\;{\text{N}}$

Likewise if placed on the Moon, the water bottle would still have a mass of $2.0\;{\text{kg}}$. However, the moon has an acceleration due to gravity of approximately $1.6\;{\frac {\text{m}}{{\text{s}}^{2}}}$. With this information, we can solve for ${\vec {F}}_{\text{grav (on Moon)}}$, as shown below:

${\vec {F}}_{\text{grav (on Moon)}}=(2.0)(1.6)\;{\text{N}}$

${\vec {F}}_{\text{grav (on Moon)}}=3.2\;{\text{N}}$

Therefore, the weight of an object varies depending on where the object is. Unlike mass, weight is not a intrinsic attribute of an object; it is only a description of the force due to gravity acting on it.

Free Body Diagrams

A snake is pictured resting on a boulder in Catalina by monkey butler. An example of a free body diagram for a snake (left side) and a list of the external forces that are present on the snake (right side) are provided.
Explanation for the mentioned forces:
* ${\vec {F}}_{\text{grav}}$ is the gravitational force that is acting on the snake. This force acts downwards.
* ${\vec {F}}_{\text{n}}$ be the normal force from the boulder. This force prevents the snake from falling through the boulder. It pushes on the snake perpendicularly from the ground's surface.
* ${\vec {F}}_{\text{fric,static}}$ is the static friction force from the boulder. This force prevents the snake from sliding down the boulder. It pushes the snake parallel up the slope.

To reemphasize, gravitational force is not the only type of force that can exist on an object. In fact, there's oftentimes several significant forces acting on an object in a given physical situation. As such, there's an importance towards being able to find a way to illustrate these forces easily and clearly.

One such method is called a free body diagram (FBD). It is a visualization of all of the external forces that are acting on an object. Through creating a free body diagram, it can become easier to find the net external force, ${\vec {F}}_{\text{net}}$ (as introduced earlier in this topic) as well as gaining an understanding for what is happening in a physical situation.

What's included in a free body diagram:

• A simplified illustration of the object that is being observed (oftentimes, a point or a box is used).
• A labeling of the external forces that are acting on the object.
• Each force is illustrated as a vector beginning at the object's center of mass and ending in the direction in which the force is acting towards.
• The length of each vector signifies the relative magnitude of the force.

What's optional in a free body diagram:

• The usage of vector notation to label a force (eg. ${\vec {F}}$ and $F$)

What's not included in a free body diagram:

• Diagrams of objects apart from the object that's being observed.
• Forces that the object of interest is applying onto other objects (we're only interested in the forces acting onto the object that we're looking at).
• The vector for the net external force, ${\vec {F}}_{\text{net}}$.
• The numerical force magnitudes on the free body diagram itself.

Reference Table of Important Forces

For the rest of the course, we will often be solving problems involving forces or otherwise applying an understanding of them to physical situations. As such, here is a reference table for the types of forces that will be discussed. To note, many of the listed forces have dedicated sections considering them, providing further information.

Group of Forces	Types of Forces Included	Description
Contact Forces	Normal Force, Applied Force, Friction Force, Tension Force, etc.	Any type of force that requires the direct contact between two objects.
Field Forces	In this course, only gravitational force (weight force) is considered.	A type of force that does not require the direct contact between two objects.

Force Name	Types of Forces	Sometimes Can Be Specified As	Common Symbols	Brief Explanation	Introductory Example
Net Force			$F_{\text{net}}$	The sum of all of the external forces that are acting on an object.	Topic 2.3
Gravitational Force (Weight Force)			$F_{\text{grav}}$, $F_{g}$; $F_{\text{weight}}$, $F_{\text{w}}$	Caused by attraction between any two objects with mass at any distance apart from one another. When in the context of a smaller object existing on the surface or near a planet or another large body of mass, the force generally depicted as acting downwards.	Topic 2.2
Normal Force		Ground Force Buoyancy Force	$F_{\text{normal}}$, $F_{n}$; $F_{\text{buoyancy}}$	This force type is used to describe a force from contact with a large surface, such as the ground or inclined plane. The force is applied perpendicular to the surface of contact.	Topic 2.3
Friction Force	Static Friction Force		$F_{\text{fric, static}}$, $F_{\text{f,s}}$	Caused by an object interacting with a surrounding medium when motionless relative to it. This force acts against other forces on an object, preventing an object from being able to move relative to the medium. It is directed opposite of the direction of $F_{\text{net}}$ (had the friction force not been present).	TBA
	Kinetic Friction Force	Air Resistance Force; Drag Force	$F_{\text{fric, kinetic}}$, $F_{\text{f,k}}$; $F_{\text{air}}$; $F_{\text{drag}}$	Caused by an object interacting with a surrounding medium when in motion relative to it. This force acts against against the direction of an object's relative motion, gradually bringing the object to be motionless to the surrounding medium.	TBA
Tension Force			$F_{\text{tension}}$, $F_{\text{T}}$	A pull that can be exerted on an object. Oftentimes, it is present from a string, rope, or chain pulling on an object.	TBA
Applied Force			$F_{\text{applied}}$, $F_{\text{a}}$	A catch-all term for a contact force, particularly for when another force category isn't clear. Generally, this is a force which is applied by a person or another object apart from a surface. The force is applied perpendicular to the surface of contact.	Topic 2.4 (specified as a thrust force)
Centripetal Force			$F_{\text{c}}$	It is not a singular force. Rather, it is the sum of forces acting in the plane in which an object is rotating in circular motion. It is directed towards the point of rotation.	TBA

References