Chapter Review
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Chapter 5: Newton's Laws of Motion Chapter Review |
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Chapter Review
In the previous chapters we have studied kinematics which you may recall is the description of motion. In this chapter we begin our study of dynamics. To begin this study we will start with the concept of force. Force goes beyond just a description of motion to consider the causes of various types of motion. The concept of force is governed by three laws known as Newton's laws of motion; these three laws and how to apply them are the principle focus of this chapter.
5-1 Force and Mass
A force is a push or a pull. When a nonzero net force is applied to an object the object's response to this force can be detected in its subsequent motion. Precisely how an object moves in response to a force depends on the object's mass. Mass can be thought of as a measure of the matter content of an object; but, more importantly for motion, mass is a measure of an object's natural tendency to move with constant velocity, referred to as its inertia. That is, mass is a measure of inertia. As discussed in chapter one, the SI unit of mass is the kilogram (kg). We haven't used it much so far; but from now on we'll use it a lot.
5-2 - 5-5 Newton's Laws of Motion
Newton's first law of motion is also known as the law of inertia. This law essentially defines the concept of inertia in the context of motion.
Newton's First Law
An object moving with constant velocity continues to do so unless acted upon by a nonzero net force.
Often, we loosely refer to anything that can detect an object as an observer. Any observer can be treated as the origin of a coordinate system in which it makes measurements. Moving observers carry their coordinate systems with them. We refer to an observer's coordinate system as its frame of reference. An inertial frame of reference (or just inertial frame for short) is one in which the law of inertia holds. Inertial frames move with constant velocity relative to other frames. Newton's three laws of motion are true with respect to these constant velocity reference frames and it is in this sense that all constant velocities are equivalent.
The law of inertia says that an object's velocity will change (i.e., it will accelerate) if a nonzero force is applied to it. Therefore, force causes acceleration. Newton's second law picks up on this theme and tells us, quantitatively, how the acceleration relates to the net force.
Physlet Illustration: Pulling a Block Horizontally | |
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A block is being pulled by a constant force across a frictionless floor, as shown.
The force on the box is represented by the black arrow. The velocity is given in m/s, and the times shown are in seconds. Adjust the
mass (5 kg < m < 200 kg) and/or the pulling force (-1000 N < F
< 1000 N), and
measure the block's acceleration. How can you verify that it obeys Newton's Second Law? Start |
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Hints
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ReferenceSee Walker, Section 5-3 |
Newton's Second Law
The acceleration of an object equals the ratio of the net force on the object to its mass
As an equation this law is most commonly written
.
In these expressions 
represents the net force as the vector sum of all forces acting on the object. From this form of Newton's second law we can also see, from the fact that the acceleration is inversely proportional to the mass, why mass is interpreted as a measure of inertia. Saying that inertia is the tendency to maintain a constant velocity is the same as saying that it is the resistance to acceleration. The above law tells us that the greater an object's mass the smaller its acceleration will be for a given force, and vice versa. Therefore, mass is what determines how strongly an object "wants" to keep its velocity constant.
The SI unit of force is call the newton (N); the Newton's second law equation makes it clear that the unit of force is the product of the units of mass and acceleration: 1 N = 1 kg.m/s2. In the application of Newton's second law it will frequently be convenient to resolve the above vector equation into scalar components
.
In all situations involving force, each of these equations must be satisfied independently. Another very important aspect of force analysis is the use of a free-body diagram. In such a diagram, we isolate the pertinent body, making it a "free body," then we draw all the force vectors acting on this body. In cases of nonrotational motion we will usually (but not always) idealize the body as a point particle without loss of accuracy. As detailed in your text, a good general strategy for doing force analysis is as follows:
Physlet Illustration: Pulling a Block at an Angle | |
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A 20-kg block is being pulled by a rope across a frictionless floor, as shown. The rope makes an angle q
with the horizontal. The velocity is given in m/s, and the times shown are in seconds. Adjust the
angle (q < 90°) and/or the magnitude of the pulling
force (F < 200 N), and measure the block's acceleration. How can you verify that it obeys Newton's Second Law? Start |
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Hints
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ReferenceSee Walker, Section 5-3 |
Example 5.1 Skydiving: Skydiving equipment, including parachute, typically has a mass of about 9.1 kg. At one point during a jump, a 80.0 kg skydiver accelerates downward at 1.50 m/s2. Determine the net force on the skydiver in vector notation.
Picture the Problem The leftmost picture shows the skydiver in the air and the two main forces involved. The rightmost picture is a free-body diagram of an idealized skydiver. The choice of coordinate system is indicated between them.
Strategy We only need the net force on the skydiver so we should draw a free-body diagram and go straight to Newton's second law for the vertical direction with up as +y.
Solution
| 1. Determine the total mass M: | M = 80.0 kg + 9.1 kg = 89.1 kg | 2. By the choice of coordinate system the acceleration is in the negative y-direction: |  |
| 3. Use Newton's second law to get the net force: |  |
Insight The acceleration and net force are written as negative only by choice. I could have easily chosen downward to be the positive direction and no negative sign would have been needed.
Example 5.2 Vehicle Performance: With a full tank of gas the Pontiac Grand AM SE has a mass of about 1500 kg; its 0 => 60 mph time is listed as 6.7 seconds. What net forward force must have been exerted on the vehicle during this performance test?
Picture the Problem The picture shows the car and the net forward force on it.
Strategy Since we don't know for certain that the acceleration is uniform we can only determine the average net force on the vehicle from the average acceleration.
| 1. Convert the speed to SI units: |  |
| 2. Use one of the equations for constant acceleration to determine a: |  |
| 3. Use Newton's laws to get the average net force: |
Insight Only the magnitude was calculated because we stipulated that the direction is "forward."
Physlet Illustration: A Block Sliding Down an Incline | |
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A block slides down a frictionless incline, as shown. The
incline makes an angle q
with the horizontal. The speed is given in m/s, and the times shown are in seconds. Adjust the
mass (100 g < m < 500 g) and/or the angle (5° < q < 45°), and measure the block's acceleration. How can you verify that it obeys Newton's Second Law? Start |
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Hints
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ReferenceSee Walker, Section 5-7 |
Newton's third law of motion is commonly known as the law of action and reaction. The words "action" and "reaction" refer to forces and so "force" is the word I'll use:
Newton's Third Law
For every force that an agent applies to an object, there is an equal in magnitude and oppositely directed reaction force applied by the object back onto the original agent.
An important point to remember here is that a force and its reaction always act on different object. Therefore, these forces never cancel each other. Basically, this law says that a single object cannot act upon others without being acted upon; two objects always interact applying equal and opposite forces to each other.
Practice Quiz
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