Learning objectives
Section Key Terms
| dynamics | external force | force |
| free-body diagram | net external force | net force |
Defining Force and Dynamics
Force is the cause of motion, and motion draws our attention. Motion itself can be beautiful, such as a dolphin jumping out of the water, the flight of a bird, or the orbit of a satellite. The study of motion is called kinematics, but kinematics describes only the way objects move—their velocity and their acceleration. Dynamics considers the forces that affect the motion of moving objects and systems. Newton’s laws of motion are the foundation of dynamics. These laws describe the way objects speed up, slow down, stay in motion, and interact with other objects. They are also universal laws: they apply everywhere on Earth as well as in space.
A force pushes or pulls an object. The object being moved by a force could be an inanimate object, a table, or an animate object, a person. The pushing or pulling may be done by a person, or even the gravitational pull of Earth. Forces have different magnitudes and directions; this means that some forces are stronger than others and can act in different directions. For example, a cannon exerts a strong force on the cannonball that is launched into the air. In contrast, a mosquito landing on your arm exerts only a small force on your arm.
When multiple forces act on an object, the forces combine. Adding together all of the forces acting on an object gives the total force, or net force. An external force is a force that acts on an object within the system from outside the system. This type of force is different than an internal force, which acts between two objects that are both within the system. The net external force combines these two definitions; it is the total combined external force. We discuss further details about net force, external force, and net external force in the coming sections.
Like displacements, velocities, and accelerations, forces are vectors that have magnitude and direction. We may represent a force as the sum of two vectors at right angles. These are its one-dimensional components, which we can represent by a signed scalar quantity. When we do so, we must choose a coordinate system and the direction along each axis that will be the positive direction. This choice must be the same for all vectors in the problem—forces, accelerations, etc.
Commonly, in a problem set in a vertical plane, horizontal and vertical axes are chosen as the two primary directions. The usual convention is to make the positive directions right and up. Sometimes a problem concerns a sloping plane, and it may be more convenient to choose axes parallel to the plane and normal to it. In this case, it is usual to take positive in each axis as the directions that tend upward.
Thus, a horizontal force of –3 N means pushing with 3 N to the left.
Unknown values are taken to be in the positive direction, so if your calculation of a vertical force comes out as +5.2 N, then you know it is an upward force. A negative result means the force is downward.
Free-Body Diagrams and Examples of Forces
For our first example of force, consider an object hanging from a rope. This example gives us the opportunity to introduce a useful tool known as a free-body diagram. A free-body diagram represents the object being acted upon—that is, the free body—as a single point. Only the forces acting on the body (that is, external forces) are shown and are represented by vectors (which are drawn as arrows). These forces are the only ones shown because only external forces acting on the body affect its motion. We can ignore any internal forces within the body because they cancel each other out, as explained in the section on Newton’s third law of motion. Free-body diagrams are very useful for analyzing forces acting on an object.
View original figure (external; image not reproduced in this text edition)
Original figure description: An object labeled m for mass is attached to a rope. A force vector labeled T for tension is pointing upward from the object and a force vector labeled W for weight of the object is pointing downward from the object. A free body diagram illustrates the T and W force vectors.
Figure_04_01_tension shows the force of tension in the rope acting in the upward direction, opposite the force of gravity. The forces are indicated in the free-body diagram by an arrow pointing up, representing tension, and another arrow pointing down, representing gravity. In a free-body diagram, the lengths of the arrows show the relative magnitude (or strength) of the forces. Because forces are vectors, they add just like other vectors. Notice that the two arrows have equal lengths in Figure_04_01_tension, which means that the forces of tension and weight are of equal magnitude. Because these forces of equal magnitude act in opposite directions, they are perfectly balanced, so they add together to give a net force of zero.
Not all forces are as noticeable as when you push or pull on an object. Some forces act without physical contact, such as the pull of a magnet (in the case of magnetic force) or the gravitational pull of Earth (in the case of gravitational force).
In the next three sections discussing Newton’s laws of motion, we will learn about three specific types of forces: friction, the normal force, and the gravitational force. To analyze situations involving forces, we will create free-body diagrams to organize the framework of the mathematics for each individual situation.
Section Summary
- Dynamics is the study of how forces affect the motion of objects and systems.
- Force is a push or pull that can be defined in terms of various standards. It is a vector and so has both magnitude and direction.
- External forces are any forces outside of a body that act on the body. A free-body diagram is a drawing of all external forces acting on a body.
Check Your Understanding
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Do two bodies have to be in physical contact to exert a force upon one another?
- No, the gravitational force is a field force and does not require physical contact to exert a force.
- No, the gravitational force is a contact force and does not require physical contact to exert a force.
- Yes, the gravitational force is a field force and requires physical contact to exert a force.
- Yes, the gravitational force is a contact force and requires physical contact to exert a force.
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Which forces can be represented in a free-body diagram?
- Internal forces
- External forces
- Both internal and external forces
- A body that is not influenced by any force
Concept Items
What is dynamics?
- Dynamics is the study of internal forces.
- Dynamics is the study of forces and their effect on motion.
- Dynamics describes the motion of points, bodies, and systems without consideration of the cause of motion.
- Dynamics describes the effect of forces on each other.
Two forces acting on an object are perpendicular to one another. How would you draw these in a free-body diagram?
- The two force arrows will be drawn at a right angle to one another.
- The two force arrows will be pointing in opposite directions.
- The two force arrows will be at a 45° angle to one another.
- The two force arrows will be at a 180° angle to one another.
A free-body diagram shows the forces acting on an object. How is that object represented in the diagram?
- A single point
- A square box
- A unit circle
- The object as it is
Critical Thinking
Only two forces are acting on an object: force A to the left and force B to the right. If force B is greater than force A, in which direction will the object move, given that the object starts from rest?
- To the right
- To the left
- Upward
- The object does not move
In a free-body diagram, the arrows representing tension and weight have the same length but point away from one another. What does this indicate?
- They are equal in magnitude and act in the same direction.
- They are equal in magnitude and act in opposite directions.
- They are unequal in magnitude and act in the same direction.
- They are unequal in magnitude and act in opposite directions.
An object is at rest. Two forces, X and Y, are acting on it. Force X has a magnitude of x and acts in the downward direction. What is the magnitude and direction of Y, given that the object remains at rest?
- The magnitude is x and points in the upward direction.
- The magnitude is 2x and points in the upward direction.
- The magnitude is x and points in the downward direction.
- The magnitude is 2x and points in the downward direction.
Three forces, A, B, and C, are acting on the same object with magnitudes a, b, and c, respectively. Force A acts to the right, force B acts to the left, and force C acts downward. What is a necessary condition for the object to move straight down?
- The magnitude of force A must be greater than the magnitude of force B, so a > b.
- The magnitude of force A must be equal to the magnitude of force B, so a = b.
- The magnitude of force A must be greater than the magnitude of force C, so A > C.
- The magnitude of force C must be greater than the magnitude of forces A or B, so A < C > B.
Test Prep Multiple Choice
Which of the following is a physical quantity that can be described by dynamics but not by kinematics?
- Velocity
- Acceleration
- Force
Which of the following is used to represent an object in a free-body diagram?
- A point
- A line
- A vector
Test Prep Short Answer
True or FalseAn external force is defined as a force generated outside the system of interest that acts on an object inside the system.
- True
- False
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A body is pushed downward by a force of 5 units and upward by a force of 2 units. How would you draw a free-body diagram to represent this?
- Two force vectors acting at a point, both pointing up with lengths of 5 units and 2 units
- Two force vectors acting at a point, both pointing down with lengths of 5 units and 2 units
- Two force vectors acting at a point, one pointing up with a length of 5 units and the other pointing down with a length of 2 units
- Two force vectors acting at a point, one pointing down with a length of 5 units and the other pointing up with a length of 2 units
A body is pushed eastward by a force of four units and southward by a force of three units. How would you draw a free-body diagram to represent this?
- Two force vectors acting at a point, one pointing left with a length of 4 units and the other pointing down with a length of 3 units
- Two force vectors acting at a point, one pointing left with a length of 4 units and the other pointing up with a length of 3 units
- Two force vectors acting at a point, one pointing right with a length of 4 units and the other pointing down with a length of 3 units
- Two force vectors acting at a point, one pointing right with a length of 4 units and the other pointing up with a length of 3 units
Test Prep Extended Response
True or FalseWhen two unequal forces act on a body, the body will not move in the direction of the weaker force.
- True
- False
In the figure given, what is Frestore? What is its magnitude?
View original figure (external; image not reproduced in this text edition)
Original figure description: Image a shows a spring with a handle connected to a weight. The length of the spring is x. Image b shows a hand pulling on the spring. The length that the spring extends after being pulled is labeled Triangle x. An arrow pointing from the hand to the weight is labeled F subscript restore. Image c shows a scale with a measurement of 6. The length from 0 to 6 is labeled triangle x. An arrow pointing from the tip of the scale to 6 is labeled F subscript restore.
- Frestore is the force exerted by the hand on the spring, and it pulls to the right.
- Frestore is the force exerted by the spring on the hand, and it pulls to the left.
- Frestore is the force exerted by the hand on the spring, and it pulls to the left.
- Frestore is the force exerted by the spring on the hand, and it pulls to the right.
Glossary
- dynamics
- the study of how forces affect the motion of objects and systems
- external force
- a force acting on an object or system that originates outside of the object or system
- force
- a push or pull on an object with a specific magnitude and direction; can be represented by vectors; can be expressed as a multiple of a standard force; the SI unit of force is the Newton (N)
- free-body diagram
- a diagram showing all external forces acting on a body
- net external force
- the sum of all external forces acting on an object or system
- net force
- the sum of all forces acting on an object or system