Unit 2: Newton’s First Law of Motion
Did you know that a spacecraft can travel millions of kilometers in outer space without consuming any amount of fuel? After completing this unit, you should be able to explain how this is a natural consequence of Newton’s first law of motion.
Learning Outcomes
By the end of this unit, you should be able to
- explain the differences between Aristotle’s and Galileo’s views of motion.
- discuss the importance of experimental evidence in natural science.
- formulate Newton’s first law of motion.
- define net force and formulate the rule for static equilibrium.
- discuss the conditions for moving objects to be in dynamic equilibrium.
eText Material
Reading Assignment
Read the following sections in Chapter 2 of the eText:
- 2.1: Aristotle on Motion
- 2.2: Galileo’s Experiments
- 2.3: Newton’s First Law of Motion
- 2.4: Net Force and Vectors
- 2.5: The Equilibrium Rule
- 2.6: Support Force
- 2.7: Equilibrium of Moving Things
- 2.8: The Moving Earth
Supplementary learning resources are available on the Mastering Physics learning platform.
Additional Reading
Force
In Newton’s description of nature, force causes and changes the motion of an object. In an ordinary sense, most people think of a force as a push or a pull. That notion works quite well, but physicists should be more specific. Newton’s laws of motion provide a more precise mathematical definition and understanding of force. In this unit, you will learn the definition of Newton’s first law of motion and apply it to objects in mechanical equilibrium.
Vectors
Certainly, numerical values are needed to describe the motion of an object. If a numerical value is sufficient for the description of a physical quantity (e.g., mass), then it is referred to as scalar. However, if a direction is also required to fully describe a physical quantity (e.g., force), then it is called a vector.
Figure 2.1: Graphical representations of force and velocity vectors.
To represent a vector graphically, you must simultaneously show the magnitude and the direction of the vector quantity. This is done by drawing a directed line segment—a straight line with an arrowhead at the end of it, as shown in Figure 2.1. The length of the line represents the magnitude of the vector, and the arrowhead indicates the direction. The end with the arrowhead is called the tip of the directed line segment, and the other end is called the tail. In this course, boldface letters (e.g.,$\bf A$) are used to denote vector quantities.
Vector Addition
If $\bf C$ is the result of adding the vectors $\bf A$ and $\bf B$, then the operation is described as ${\bf A} + {\bf B} = {\bf C}$. The vector $\bf C$ is called the sum, or resultant, of $\bf A$ and $\bf B$. Although we use the same notations and terminology as in the addition of numbers, the process of adding vectors is a bit more complicated. You cannot just add the magnitudes of two vectors to get their sum; instead, vector addition requires a process that combines the magnitudes and directions simultaneously.
Figure 2.2: Vector addition and subtraction using the head-to-tail method.
The head-to-tail method is a convenient graphical process for adding multiple vectors. In this method, the vectors are aligned so the tail of the second vector is at the tip of the first one, the tail of the third vector is at the tip of the second one, and so on (see Figure 2.2). The vector drawn from the tail of the first vector to the tip of the last one gives the magnitude and direction of the resultant vector. Note that subtracting vector $\bf B$ from vector $\bf A$ is equivalent to adding vector $\bf A$ to the opposite (or negative) of vector $\bf B$, which can be expressed as ${\bf A} - {\bf B} = {\bf A} + (-{\bf B})$.
You can also break up a given vector into the sum of two vectors. The process is called decomposing the vector into components. Normally, it is more convenient to choose horizontal and vertical directions when decomposing a vector unless the problem demands that you choose other directions. The components along these two directions are called the $x$ component and the
Figure 2.3: Vector decomposition into two perpendicular components.
Simulation
Run the Vector Addition simulation to explore vectors in 1-D or 2-D and discover how vectors add together.
Simulation by PhET Interactive Simulations, University of Colorado Boulder, licensed under CC-BY-4.0 (https://phet.colorado.edu)
Newton’s First Law of Motion
From experience, you know that a book placed on a shelf will remain in the same spot if it is not disturbed. Imagine a spaceship moving with constant speed in the vacuum of outer space and distant from any celestial object. Can you think of any reason the spaceship would ever slow down and come to a stop?
Newton probably thought along the same line while formulating his first law, which can be stated as follows:
Every object continues in a state of rest or of uniform speed in a straight line unless acted on by net external force.[1]
In other words, it is natural for an object to keep moving at the same speed and in the same direction as long as it is not disturbed by the application of an external force.
Video 2.1: Newton’s first law of motion.
Footnotes
[1] Hewitt, P. G. (2021). Conceptual Physics (13th ed., p. 30) [Ebook]. Pearson.
Questions
The following questions are selected from the end of Chapter 2 of the eText. It is important to your learning that you try to answer each question independently before you read through the answer and explanation given.
For questions that ask you to explain or discuss your answer, the response revealed by the Answer button would earn you only partial marks on a quiz or exam in this course. Use the Answer to help you formulate a complete answer before you select the Explanation button to check your work.
Note that some questions have been adapted to suit the format of this course.
Chapter 2
Question 2
What state of motion did Aristotle attribute to Earth?
Answer
He attributed natural motion to Earth.
Explanation
Aristotle believed that the normal state of objects was one of rest. Until the 16th century, it was evident to most scientists and philosophers that Earth was the center of the universe and, therefore, must be in a proper place. It seemed inconceivable to imagine a force capable of shifting Earth from its position.
Chapter 2
Question 6
Is inertia the reason for moving objects maintaining motion, or is it the name given to this property?
Answer
It is the name given to this property.
Explanation
The intrinsic property of a physical object that causes it to persist in motion at a constant speed in a straight line is called inertia. So an object does not move because of inertia. Note that the notion of inertia is so fundamental that it cannot be explained or expressed in terms of more general concepts.
Chapter 2
Question 18
In symbolic notation, state the equilibrium rule for forces.
Answer
$\sum {\bf F} = {\bf F}_1 + {\bf F}_2 + \cdots + {\bf F}_n = 0$
Explanation
Force is a vector quantity described by its strength (or magnitude) and direction in space. Suppose there are $n$ (one, two, three, or more) forces exerted on an object. When the net force (i.e., the vector sum of external forces) is equal to zero, the object is said to be in mechanical equilibrium.
In printed material, a vector quantity is normally set in bold (${\bf F}$), but in handwriting, it is distinguished by a small arrow above the symbol ($\vec F$).
Chapter 2
Question 22
What is the net force on an object in either static or dynamic equilibrium?
Answer
Zero.
Explanation
An object at rest that remains at rest is said to be in static equilibrium. An object that moves steadily (i.e., no speeding up, slowing down, or changing the direction of motion) is in dynamic equilibrium. In both situations, the velocity is constant (no acceleration) and the net force on the object is equal to zero.
Chapter 2
Question 47
A space probe may be carried by a rocket into outer space. What keeps the probe moving after the rocket no longer pushes it?
Answer
Nothing is required to keep the probe moving.
Explanation
According to Newton’s first law, motion in a straight line with constant velocity does not require any external force. In this question, the rocket is used to accelerate the probe until it achieves the desired speed and direction. After the rocket is turned off, the probe continues to cruise forward at the same speed.
Chapter 2
Question 65
How many significant forces act on a book at rest on a table? Identify the forces.
Answer
Two forces: weight and normal force.
Diagram
Figure Q2.65
Explanation
As shown in Figure Q2.65, two forces act on the book: the downward force of gravity (or weight) and the upward support (or normal) force exerted by the tabletop. Because the book is stationary, the two opposing forces must have equal values resulting in a zero net force.
Chapter 2
Question 70
If you pull horizontally on a crate with a force of 200 N, it slides across the floor in dynamic equilibrium. How much friction is acting on the crate?
Answer
200 N
Diagram
Figure Q2.70
Explanation
The forces acting on the crate are shown in Figure Q2.70. The dynamic-equilibrium rule applies here because the crate is moving at a constant speed in a straight line. So the net external force on the crate must be equal to zero. Since friction is the only force resisting the pull, these two horizontal forces must have equal magnitudes.
Chapter 2
Question 76
A child learns in school that Earth is traveling faster than 100,000 km/h around the Sun and, in a frightened tone, asks why we aren’t swept off. What is your explanation?
Answer
Since the whole system (Earth, atmosphere, and living creatures) travels together in the vacuum of space, we observe only relative speeds.
Explanation
All objects on Earth, including the atmosphere, move together at the same speed around the Sun. Also, there is no medium through which the Earth system travels. Therefore, we feel and notice only the relative motions of objects on Earth. For example, a flight attendant on an airplane flying at a constant speed does not feel its high speed (approximately 900 km/h) and can comfortably push the beverage cart and serve passengers.
Chapter 2
Question 78
Your friend says that inertia is a force that keeps things in their place, either at rest or in motion. Do you agree? Why or why not?
Answer
You should disagree.
Explanation
The inertia of an object is represented quantitatively by its mass, which is a scalar quantity. Force, in contrast, is a vector quantity that has both strength (magnitude) and direction and provides a measure of the interaction between two or more objects.
In the absence of a net external force, an object remains at rest or maintains uniform motion along a straight line. When a net external force acts on the object, it experiences changes in its speed, direction of motion, or both. However, different objects respond differently to an applied force: the more inertia (or mass) an object has, the slower its response to the applied force.
Chapter 2
Question 81
When you push a cart, it moves. When you stop pushing, it comes to rest. Does this violate Newton’s law of inertia? Defend your answer.
Answer
No, it does not.
Explanation
According to Newton’s law of inertia, if no net force is applied on an object (or if the sum of external forces is equal to zero), the object continues in its state of rest or uniform motion in a straight line. In your everyday experience, when you stop pushing a cart, it eventually comes to rest. This is because the forces of friction in the bearings continue to act in the opposite direction of motion and cause the cart to slow down until it stops.
Air drag also provides a counterforce that contributes to the slowing down of the cart. You can feel this force when you extend your hand from the window while riding in a car on the highway. Note that friction can be reduced (but not eliminated) by lubricating the cart’s bearings. Similarly, air drag can be minimized by streamlining the car’s body.
Additional Question
Answer the following additional question (not found in your eText).
Unit 2
Question A
A spherical light fixture hangs at the end of a vertical cord. Indicate the forces that act on the light fixture.
Answer
Two equal forces, weight and tension, act on the light fixture.
Diagram
Figure E2.1
Explanation
As shown in Figure E2.1, the light fixture experiences two opposing forces. The first is the downward force due to gravity, which is weight, and the second is the upward force caused by the tension in the cord. Since the light fixture remains stationary, it is in static equilibrium and experiences a net external force equal to zero. In other words, the tension and weight forces have equal magnitudes.
Exercises
Spend some time completing the following exercises to test your understanding of the main concepts in Chapter 2 and increase your efficiency in answering exam questions.
End-of-Chapter Practice Questions
Answer questions 3, 5, 9, 15, 21, 25, 33, 35, 37, 41, 51, 55, 61, 67, 77, and 85 in Chapter 2 of the eText. If you require assistance, please contact your tutor. The answers are provided at the end of the eText.