Chapter 4: Conservation Laws
4.1: Newton's Third Law and Momentum
Impulse and Momentum
The textbook (page 80) and Section 4.1 Part 3 video have an error in the equation for impulse. It is explained correctly on Skill & Practice 4C. Impulse is the change in momentum. As we have discussed in class previously, scientists and engineers always mean "final minus initial" when we say "change in" anything. (Sometimes we use the Greek letter delta like Mrs. Morales did in the video. We used delta in Chapter 2 for velocity and acceleration equations.) The equation in the book on page 80 will be correct if you label v2 as "final velocity" and v1 as "initial velocity." I think Mrs. Morales intuitively started using them correctly in the sample problems of the video, but she initially presented the equation from the book. We all intuitively know that 2 comes after 1, so 1 indicates initial and 2 indicates final in that equation. Two Ways to Think of Impulse:
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4.2: Energy and Conservation of Energy
Conservation of Energy
According to the law of conservation of energy, energy cannot be created or destroyed; it can only change forms. You may already be familiar with potential energy and kinetic energy, but we can also think of work as a form of energy! Work, potential energy, and kinetic energy are all measured with the same units. In the metric system, those units are newton meters or joules. |
Chapter 5: Forces in Equilibrium
Types of Forces
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When you print the 5.1 Homework and the Plain Graph Paper, be sure that your printer is set NOT to scale your printout and NOT to fit to printer margins. For some questions, it is important that the squares are 0.5 cm, and printing with the wrong settings will make it impossible to work these problems.
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Graphing Vectors and Their Components
We can use an arrow to represent a vector such as force, velocity, or displacement. In each case, the vector arrow shows the magnitude and direction. In the diagram below, any vector drawn from point P to a point on the arc would have a length of 10 units. Depending on the scale and what you are graphing, that could be 10 meters, 10 newtons, or 10 meters per second. For this example, let’s say each square is 1 newton wide and 1 newton tall. This means that any vector arrow from P to a point on the arc would represent a force of 10 N. The different arrows show forces applied at different angles. Conventionally, we measure the angle between the positive x-axis and the vector. Any vector can be broken down into
an x-component (east-west) and a y-component (north-south). The blue vector shows a force of 10 N in the x-direction. It ends at (10, 0). It has an x-component of 10 N and a y-component of 0 N. The pink vector shows a force of 10 N in the y-direction. It ends at (0, 10). It has an x-component of 0 N and a y-component of 10 N. The orange vector shows a force of 10 N at 45°. It ends at approximately (not exactly!) the point (7,7). This vector has an x-component of 7 N and a y-component of 7 N. The green vector shows a force of 10 N at 30°. It ends at approximately (8.7, 5). It has an x-component of 8.7 N and a y-component of 5 N. Sometimes you know the x and y components of a vector and want to find the magnitude of their resultant vector (the vector that the components would add up to). In this case, you can use the Pythagorean Theorem to find the length of the resultant arrow. For example, if you add together a 3-N force in the x direction and a 4-N force in the y direction, the resultant force has a magnitude of 5 N. Correction to the textbook (Figure 5.16) and video: The direction of rolling friction is in the direction the object rolls. The rolling object pushes against the ground (or other surface) and the ground pushes the object forward. These forces are equal and opposite to one another. Below is a corrected version of the graphic. Here's a link to a video explanation of rolling.
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Chapter 6: Systems in Motion
Video 6.1 ends with a literal cliffhanger. You will find the solution to the problem on page 141 of the textbook.
The Physics Classroom website gives another explanation of projectile motion. It includes a video, which I've included below. |