The theme of Reasoning and Relationships is reinforced throughout the book, helping you master these concepts, apply them to solve a variety of problems, and appreciate the relevance of physics to your career and your everyday life. By understanding the reasoning behind problem solving, you learn to recognize the concepts involved, think critically about them, and move beyond merely memorizing facts and equations.
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Nicholas J. Giordano Publisher: Cengage Learning. Problem Solving in Physics : Reasoning and Relationships ; 1.
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Applying the definition of average velocity to the two intervals, we can estimate the velocity. The intervals of posi- tion can be estimated from the graph in Figure P2. Notice that the average velocity over a time interval is the slope of the line joining the two points on the position vs. Since the position vs. The resulting graph is in Figure Ans 2. Apply graphical analysis of mo- tion, specifically the definition of acceleration. The velocity curve here is a linear relationship.
The slope of the curve at 3 s the instantaneous acceleration is the same as the slope of the entire curve. Taking the rise over the run of the line in Figure P2. The motion of the brick is with constant ac- celeration, so the velocity increases by equal amounts every second. Apply graphical analysis of mo- tion, and specifically the definition of acceleration. The slope at any given point on the graph is equal to the instantaneous acceleration at that time. We can draw tangent lines to the velocity vs.
Three tangent lines are drawn. The rate of change of the velocity changes rapidly between 40 and s. So, in summary, the acceleration begins with its largest nega- tive value for the first roughly 40 s, changes to smaller and smaller negative values from 40 s to roughly s, and then is zero for the rest of the motion. This problem requires the deter- mination of acceleration from a velocity vs. Apply graphical analysis of motion, and specifically the definition of average acceleration.
Therefore, the slope of the tangent to the position vs. Keep in mind that these graphs could shift up or down depending on the initial position. In Figure P2.
There- fore, the position vs. It is the slope of the position vs. Apply graphical analysis of mo- tion, and in particular the definitions of acceleration and ve- locity.
See Figures Ans 2. Knowing how the acceleration varies in time allows you to sketch the shape of the position vs. Applying the average velocity equation to the two time intervals, you can estimate the average velocities.
Since the car covers a much larger distance in the last 3 seconds than in the first 5 seconds, it is not surprising that the average velocity increases from the first interval to the second. Use the concepts of aver- age velocity and average acceleration. Since the positive direction is upward, and the squirrel falls 5 m in the first second and 15 m in the sec- ond, it is expected that it has a nonzero, negative accelera- tion.
Use the concepts of average speed and average velocity. The time to travel this distance is 24 hours and 15 minutes. Apply graphical analysis of mo- tion, and in particular the definitions of average and instanta- neous acceleration.
The average acceleration is calculated from the change in velocity divided by the time interval, while the instantaneous acceleration is the slope of the tangent to the velocity vs. Apply graphical analysis of mo- tion, in particular the relationship between velocity and accel- eration. The graph shows two regions of con- stant acceleration. Note that for a constant acceleration, the velocity is just a linear function of time.
Apply the concept of average velocity. Note that the average velocity tells nothing about how the trip was made; i. You can easily check your answers. The total distance for the three parts of the trip is 1. As the ball rolls up the incline it will slow down at a constant rate until it momentari- ly comes to rest.
The ball will then begin rolling back down the incline speeding up at a constant rate. The sketch of the problem is provided in Figure 2. If we define the positive x- direction to be up the incline then the ball will have a con- stant negative acceleration during its entire motion.
The ball begins with a positive velocity that decreases to zero and then becomes negative and increasing. The velocity vs. The position vs. In fact, the shape of the curve should be a parabola. Since the slope of the velocity vs. As we will see in the next chapter, the force of gravity on the ball is responsible for this ob- served motion and is indeed a constant in this case. See Figure 2. Here the flat surface on which the block slides tends toward a limit of no friction as we go from rough to smooth, which results in a fami- ly of curves illustrating this limit.
See Figures Ans2. The penguin tends to remain in mo- tion at its constant speed, since the force exerted on it by the ice is negligible. Both the man and the baseball share the same constant ve- locity as the railcar see Figure Ans2. When the man releas- es the ball, by the principle of inertia, it keeps its same sideways velocity, exactly that of the railcar.
So it continues to move exactly below the release point and hits the bed of the railcar directly below the release point.
Answer: a. From the point of view of the man on the flatcar, the path of the ball is identical to what it would look like if he were to drop it while standing still on a sidewalk. Use Figure 2. The velocity of the refrigerator will contin- ue to increase as long as the man continues to apply the force.
Although the action—reaction forces are equal and opposite, the accelerations of the man and refrigerator are inversely proportional to the masses of each. Since there is no friction between the floor and either the man or the refrigera- tor, after a brief time during which the two are in contact and push on each other, they will slide in opposite directions at constant but different velocities.
The acceleration is always proportional to the net force on an object and inversely proportional to the mass of the object. Looking at the units, we can see force has dimensions of mass multiplied by length divided by time squared.
While these combinations are dimensionally correct, they do not represent SI units. Looking up the conversion, we find a slug is equal to A slug is a rather large unit of mass com- pared to the kilogram.
Looking up the conversion we find 1 lb is equal to 4. A good rule of thumb is that 1 pound is about 4. Recognize the principle. Make a sketch of the forces on the shell and the cannon. Since the platform rests on an icy surface, which is frictionless, there will be no friction forces when the canon fires.
Also assume no friction force on the shell. Therefore there is only one force on the shell and one force on the can- non. Diagrams like that in Figure 2. In each of the examples, a — h , there are contact forces between two objects. These are the action—reaction pairs of forces. The diagrams for a are shown in Figure Ans2. On- ly forces between the two objects are shown in this diagram.
This force causes the first skater to recoil backwards. To find an action—reaction pair of forces, first isolate the two objects A and B. Then, for every force ex- erted by A on B, find the force exerted back by B on A.
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