newton's first law assignment answer key

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Chapter 7 Answer Key: Equilibrium and Newton’s First Law

Chapter 7: Equilibrium & Newton’s First Law (Key)

7.1 Right Angle Trigonometric Functions

1. 0.743145

2. 0.484810

3. 0.906308

4. 0.484810

5. 0.194380

6. 1.53986

7. 0.190810

8. 0.544639

17. z = 27.36 (≈ 27), ø = 26.6° (≈ 27°)

18. y = 19.6 (≈ 20), ø = 44.4° (≈ 44°)

19. x = 16, ø = 53.1° (≈ 53°)

20. x = 21.2 (≈ 21), y = 13.2 (≈ 13)

21. x = 892 (≈ 890), y = 803 (≈ 800)

22. z = 242 (≈ 240), ø = 24.4° (≈ 24°)

23. x = 9.8, y = 6.9

24. x = 37.6 (≈ 38), y = 42.6 (≈ 43)

25. z = 25, ø = 53.1° (≈ 53°)

26. y = 75, ø = 36.9° (37°)

27. y = 4, ø = 53.1° (≈ 53°)

28. y = 11.1 (≈ 11), z = 27.4 (≈ 27)

29. z = 28.6 (≈ 29), ø = 44.4° (≈ 44°)

30. y = 19.6 (≈ 20), ø = 44.4° (≈ 44°)

31. y = 8.9, ø = 41.8° (≈ 42°)

32. x = 35, y = 61

7.2 Vector Resolution into Components

1. v y = 25.4 (≈ 25), v x = 40.7 (≈ 41)

2. v y = 11, v x = 19.1 (≈ 19)

3. F y = 15, F x = 28.3 (≈ 28)

4. F y = 53.7 (≈ 54), F x = 79.6 (≈ 80)

5. a y = 13.6, a x = 15.2

6. a y = 22.0, a x = 45.1

7. v y = 25.4 (≈ 25), v x = 40.7 (≈ 41)

8. v y = 11, v x = 19.1 (≈ 19)

9. F y = 15, F x = 28.3 (≈ 28)

10. F y = 53.7 (≈ 54), F x = 79.6 (≈ 80)

11. a y = 13.6, a x = 15.2

12. a y = 22.0, a x = 45.1

7.3 Static Equilibrium (Concurrent Forces)

1. T y = 980 N2. T y = 5.0 N

3. T 1 = 228 N (≈ 230 N), T 2 = 541 N (≈ 540 N)

4. T 1 = 89.2 N (≈ 89 N), T 2 = 261 N (≈ 260 N)

5. T 1 = 769 N (≈ 770 N), T 2 = 663 N (≈ 660 N)

6. T 1 = 8502 N (≈ 8500 N), T 2 = 5557 N (≈ 5600 N)

7. T = 6685 N ( ≈ 6700 N), FC = – 5268 N (≈ – 5300 N)

8. F C = – 14 300 N (≈ – 14 000 N)

7.4 Limits of a Cable

(i) 0.49 m from the top (ii)

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5.2 Newton's First Law

Learning objectives.

By the end of this section, you will be able to:

Describe Newton's first law of motion
Recognize friction as an external force
Define inertia
Identify inertial reference frames
Calculate equilibrium for a system

Experience suggests that an object at rest remains at rest if left alone and that an object in motion tends to slow down and stop unless some effort is made to keep it moving. However, Newton’s first law gives a deeper explanation of this observation.

Newton’s First Law of Motion

A body at rest remains at rest or, if in motion, remains in motion at constant velocity unless acted on by a net external force.

Note the repeated use of the verb “remains.” We can think of this law as preserving the status quo of motion. Also note the expression “constant velocity;” this means that the object maintains a path along a straight line, since neither the magnitude nor the direction of the velocity vector changes. We can use Figure 5.7 to consider the two parts of Newton’s first law.

Rather than contradicting our experience, Newton’s first law says that there must be a cause for any change in velocity (a change in either magnitude or direction) to occur. This cause is a net external force, which we defined earlier in the chapter. An object sliding across a table or floor slows down due to the net force of friction acting on the object. If friction disappears, will the object still slow down?

The idea of cause and effect is crucial in accurately describing what happens in various situations. For example, consider what happens to an object sliding along a rough horizontal surface. The object quickly grinds to a halt. If we spray the surface with talcum powder to make the surface smoother, the object slides farther. If we make the surface even smoother by rubbing lubricating oil on it, the object slides farther yet. Extrapolating to a frictionless surface and ignoring air resistance, we can imagine the object sliding in a straight line indefinitely. Friction is thus the cause of slowing (consistent with Newton’s first law). The object would not slow down if friction were eliminated.

Consider an air hockey table ( Figure 5.8 ). When the air is turned off, the puck slides only a short distance before friction slows it to a stop. However, when the air is turned on, it creates a nearly frictionless surface, and the puck glides long distances without slowing down. Additionally, if we know enough about the friction, we can accurately predict how quickly the object slows down.

Newton’s first law is general and can be applied to anything from an object sliding on a table to a satellite in orbit to blood pumped from the heart. Experiments have verified that any change in velocity (speed or direction) must be caused by an external force. The idea of generally applicable or universal laws is important—it is a basic feature of all laws of physics. Identifying these laws is like recognizing patterns in nature from which further patterns can be discovered. The genius of Galileo, who first developed the idea for the first law of motion, and Newton, who clarified it, was to ask the fundamental question: “What is the cause?” Thinking in terms of cause and effect is fundamentally different from the typical ancient Greek approach, when questions such as “Why does a tiger have stripes?” would have been answered in Aristotelian fashion, such as “That is the nature of the beast.” The ability to think in terms of cause and effect is the ability to make a connection between an observed behavior and the surrounding world.

Gravitation and Inertia

Regardless of the scale of an object, whether a molecule or a subatomic particle, two properties remain valid and thus of interest to physics: gravitation and inertia. Both are connected to mass. Roughly speaking, mass is a measure of the amount of matter in something. Gravitation is the attraction of one mass to another, such as the attraction between yourself and Earth that holds your feet to the floor. The magnitude of this attraction is your weight, and it is a force.

Mass is also related to inertia , the ability of an object to resist changes in its motion—in other words, to resist acceleration. Newton’s first law is often called the law of inertia . As we know from experience, some objects have more inertia than others. It is more difficult to change the motion of a large boulder than that of a basketball, for example, because the boulder has more mass than the basketball. In other words, the inertia of an object is measured by its mass. The relationship between mass and weight is explored later in this chapter.

Inertial Reference Frames

Earlier, we stated Newton’s first law as “A body at rest remains at rest or, if in motion, remains in motion at constant velocity unless acted on by a net external force.” It can also be stated as “Every body remains in its state of uniform motion in a straight line unless it is compelled to change that state by forces acting on it.” To Newton, “uniform motion in a straight line” meant constant velocity, which includes the case of zero velocity, or rest. Therefore, the first law says that the velocity of an object remains constant if the net force on it is zero.

Newton’s first law is usually considered to be a statement about reference frames. It provides a method for identifying a special type of reference frame: the inertial reference frame . In principle, we can make the net force on a body zero. If its velocity relative to a given frame is constant, then that frame is said to be inertial. So by definition, an inertial reference frame is a reference frame in which Newton’s first law is valid. Newton’s first law applies to objects with constant velocity. From this fact, we can infer the following statement.

Inertial Reference Frame

A reference frame moving at constant velocity relative to an inertial frame is also inertial. A reference frame accelerating relative to an inertial frame is not inertial.

Are inertial frames common in nature? It turns out that well within experimental error, a reference frame at rest relative to the most distant, or “fixed,” stars is inertial. All frames moving uniformly with respect to this fixed-star frame are also inertial. For example, a nonrotating reference frame attached to the Sun is, for all practical purposes, inertial, because its velocity relative to the fixed stars does not vary by more than one part in 10 10 . 10 10 . Earth accelerates relative to the fixed stars because it rotates on its axis and revolves around the Sun; hence, a reference frame attached to its surface is not inertial. For most problems, however, such a frame serves as a sufficiently accurate approximation to an inertial frame, because the acceleration of a point on Earth’s surface relative to the fixed stars is rather small ( < 3.4 × 10 −2 m/s 2 < 3.4 × 10 −2 m/s 2 ). Thus, unless indicated otherwise, we consider reference frames fixed on Earth to be inertial.

Finally, no particular inertial frame is more special than any other. As far as the laws of nature are concerned, all inertial frames are equivalent. In analyzing a problem, we choose one inertial frame over another simply on the basis of convenience.

Newton’s First Law and Equilibrium

Newton’s first law tells us about the equilibrium of a system, which is the state in which the forces on the system are balanced. Returning to Forces and the ice skaters in Figure 5.3 , we know that the forces F → 1 F → 1 and F → 2 F → 2 combine to form a resultant force, or the net external force: F → R = F → net = F → 1 + F → 2 . F → R = F → net = F → 1 + F → 2 . To create equilibrium, we require a balancing force that will produce a net force of zero. This force must be equal in magnitude but opposite in direction to F → R , F → R , which means the vector must be − F → R . − F → R . Referring to the ice skaters, for which we found F → R F → R to be 30.0 i ^ + 40.0 j ^ N 30.0 i ^ + 40.0 j ^ N , we can determine the balancing force by simply finding − F → R = −30.0 i ^ − 40.0 j ^ N . − F → R = −30.0 i ^ − 40.0 j ^ N . See the free-body diagram in Figure 5.3 (b).

We can give Newton’s first law in vector form:

This equation says that a net force of zero implies that the velocity v → v → of the object is constant. (The word “constant” can indicate zero velocity.)

Newton’s first law is deceptively simple. If a car is at rest, the only forces acting on the car are weight and the contact force of the pavement pushing up on the car ( Figure 5.9 ). It is easy to understand that a nonzero net force is required to change the state of motion of the car. As a car moves with constant velocity, the friction force propels the car forward and opposes the drag force against it.

Example 5.1

When does newton’s first law apply to your car.

(a) Your car is parked outside your house. Does Newton’s first law apply in this situation? Why or why not?

(b) Your car moves at constant velocity down the street. Does Newton’s first law apply in this situation? Why or why not?

When your car is parked, all forces on the car must be balanced; the vector sum is 0 N. Thus, the net force is zero, and Newton’s first law applies. The acceleration of the car is zero, and in this case, the velocity is also zero.
When your car is moving at constant velocity down the street, the net force must also be zero according to Newton’s first law. The car’s frictional force between the road and tires opposes the drag force on the car with the same magnitude, producing a net force of zero. The body continues in its state of constant velocity until the net force becomes nonzero. Realize that a net force of zero means that an object is either at rest or moving with constant velocity, that is, it is not accelerating. What do you suppose happens when the car accelerates? We explore this idea in the next section.

Significance

Check your understanding 5.2.

A skydiver opens their parachute, and shortly thereafter, they are moving at constant velocity. (a) What forces are acting on them? (b) Which force is bigger?

Interactive

Engage the simulation below to predict, qualitatively, how an external force will affect the speed and direction of an object’s motion. Explain the effects with the help of a free-body diagram. Use free-body diagrams to draw position, velocity, acceleration, and force graphs, and vice versa. Explain how the graphs relate to one another. Given a scenario or a graph, sketch all four graphs.

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Access for free at https://openstax.org/books/university-physics-volume-1/pages/1-introduction

Authors: William Moebs, Samuel J. Ling, Jeff Sanny
Publisher/website: OpenStax
Book title: University Physics Volume 1
Publication date: Sep 19, 2016
Location: Houston, Texas
Book URL: https://openstax.org/books/university-physics-volume-1/pages/1-introduction
Section URL: https://openstax.org/books/university-physics-volume-1/pages/5-2-newtons-first-law

© Jan 19, 2024 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.

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Newton's Laws
Einstein's Theory of Special Relativity
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Newton's Laws of Motion
Newton's First Law
Newton's Third Law
Inertia and Mass
State of Motion

Newton's first law of motion is often stated as

An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force .

Two Clauses and a Condition

There are two clauses or parts to this statement - one that predicts the behavior of stationary objects and the other that predicts the behavior of moving objects. The two parts are summarized in the following diagram.

There is an important condition that must be met in order for the first law to be applicable to any given motion. The condition is described by the phrase "... unless acted upon by an unbalanced force." As the long as the forces are not unbalanced - that is, as long as the forces are balanced - the first law of motion applies. This concept of a balanced versus and unbalanced force will be discussed in more detail later in Lesson 1 .

Suppose that you filled a baking dish to the rim with water and walked around an oval track making an attempt to complete a lap in the least amount of time. The water would have a tendency to spill from the container during specific locations on the track. In general the water spilled when:

the container was at rest and you attempted to move it
the container was in motion and you attempted to stop it
the container was moving in one direction and you attempted to change its direction.

Everyday Applications of Newton's First Law

There are many applications of Newton's first law of motion. Consider some of your experiences in an automobile. Have you ever observed the behavior of coffee in a coffee cup filled to the rim while starting a car from rest or while bringing a car to rest from a state of motion? Coffee "keeps on doing what it is doing." When you accelerate a car from rest, the road provides an unbalanced force on the spinning wheels to push the car forward; yet the coffee (that was at rest) wants to stay at rest. While the car accelerates forward, the coffee remains in the same position; subsequently, the car accelerates out from under the coffee and the coffee spills in your lap. On the other hand, when braking from a state of motion the coffee continues forward with the same speed and in the same direction , ultimately hitting the windshield or the dash. Coffee in motion stays in motion.

There are many more applications of Newton's first law of motion. Several applications are listed below. Perhaps you could think about the law of inertia and provide explanations for each application.

Blood rushes from your head to your feet while quickly stopping when riding on a descending elevator.
The head of a hammer can be tightened onto the wooden handle by banging the bottom of the handle against a hard surface.
A brick is painlessly broken over the hand of a physics teacher by slamming it with a hammer. (CAUTION: do not attempt this at home!)
To dislodge ketchup from the bottom of a ketchup bottle, it is often turned upside down and thrusted downward at high speeds and then abruptly halted.
Headrests are placed in cars to prevent whiplash injuries during rear-end collisions.
While riding a skateboard (or wagon or bicycle), you fly forward off the board when hitting a curb or rock or other object that abruptly halts the motion of the skateboard.
Meaning of Force

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Newton's 1st & 2nd Laws

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