Physics 218 Fall 2014

Transcription

1 Physics 218 Fall 2014 Instructor: Robert C. Webb Office: MIST 224; Phone: ; Office Hours: M, T, W from 10:00 am - 12:00 pm, or by appointment Link to Class web site: September 1, 2014 Physics218 1

2 Reminders SmartPhysics pre-lectures and check points are due before lecture. (as of this time I see that there are 113/156 students signed up for SP.) iclicker? 1- yes, 2-not yet. Mastering Physics homework assignments are due Sunday s at midnight (11:59pm) for the preceding week. (There is an introduction to MP that is due with the first assignment, but this doesn t count toward your homework grade. So far 88 of you have claimed your MP access. If you have special issues with MP access, let me know.) iclicker? 1-yes, 2-not yet. 9/3/2014 Physics 218 2

3 More. WebAssign labs begin next week. Before your recitation meets, you should read the lab description in the on-line lab manual on WebAssign and take the pre-lab quiz. Those still having issues getting access, let me know. iclicker? 1-yes, 2-not yet. 9/3/2014 Physics 218 3

4 Lastly.. iclicker2. As mentioned in the previous class meeting, we will be using the iclicker throughout the term to get you input on various questions that may come up. If you haven t been able to obtain your iclicker yet please work to have this sorted out by next week. 9/3/2014 Physics 218 4

5 Solving problems in physics A problem-solving strategy offers techniques for setting up and solving problems efficiently and accurately.

6 Unit consistency and conversions An equation must be dimensionally consistent. Terms to be added or equated must always have the same units. (Be sure you re adding apples to apples. ) Always carry units through calculations. Convert to standard units as necessary. (Follow Problem-Solving Strategy 1.2) Follow Examples 1.1 and 1.2.

7 Uncertainty and significant figures The uncertainty of a measured quantity is indicated by its number of significant figures. For multiplication and division, the answer can have no more significant figures than the smallest number of significant figures in the factors. For addition and subtraction, the number of significant figures is determined by the term having the fewest digits to the right of the decimal point. As this train mishap illustrates, even a small percent error can have spectacular results!

8 Estimates and orders of magnitude An order-of-magnitude estimate of a quantity gives a rough idea of its magnitude.

9 Vectors and scalars A scalar quantity can be described by a single number. A vector quantity has both a magnitude and a direction in space. In this book, a vector quantity is represented in boldface italic type with an arrow over it: A. The magnitude of A is written as A or A.

10 Drawing vectors Draw a vector as a line with an arrowhead at its tip. The length of the line shows the vector s magnitude. The direction of the line shows the vector s direction. Figure 1.10 shows equal-magnitude vectors having the same direction and opposite directions.

11 Adding two vectors graphically Two vectors may be added graphically using either the parallelogram method or the head-to-tail method.

12 Adding more than two vectors graphically To add several vectors, use the head-to-tail method. The vectors can be added in any order.

13 Subtracting vectors Figure 1.14 shows how to subtract vectors.

14 Multiplying a vector by a scalar If c is a scalar, the product ca has magnitude c A. Figure 1.15 illustrates multiplication of a vector by a positive scalar and a negative scalar.

15 Addition of two vectors at right angles First add the vectors graphically. Then use trigonometry to find the magnitude and direction of the sum. Follow Example 1.5.

16 Components of a vector Adding vectors graphically provides limited accuracy. Vector components provide a general method for adding vectors. Any vector can be represented by an x-component A x and a y- component A y. Use trigonometry to find the components of a vector: A x =Acos θ and A y = Asin θ, where θ is measured from the +x-axis toward the +y-axis.

17 Positive and negative components Figure 1.18 The components of a vector can be positive or negative numbers, as shown in the figure.

18 Finding components We can calculate the components of a vector from its magnitude and direction. Follow Example 1.6.

19 Calculations using components We can use the components of a vector to find its magnitude and direction: We can use the components of a set of vectors to find the components of their sum: Refer to Problem-Solving Strategy A A Ax Ay and tan A y R A B C, R A B C x x x x y y y y x

20 Adding vectors using their components

21 Unit vectors A unit vector has a magnitude of 1 with no units. The unit vector î points in the j +x-direction, jpoints in the +ydirection, and kpoints in the k +z-direction. Any vector can be expressed in terms of its components as j k A =A x î+ A y j + A z. Follow Example 1.9. k

22 The scalar product AB AB cos. The scalar product (also called the dot product ) of two vectors is Figures 1.25 and 1.26 illustrate the scalar product.

23 Calculating a scalar product In terms of components, AB A B A B A B x x y y z z. Example 1.10 shows how to calculate a scalar product in two ways. [Insert figure 1.27 here]

24 Finding an angle using the scalar product Example 1.11 shows how to use components to find the angle between two vectors.

25 The vector product The vector product ( cross product ) of two vectors has magnitude A B ABsin and the righthand rule gives its direction. See Figures 1.29 and 1.30.

26 Calculating the vector product Use ABsin to find the magnitude and the right-hand rule to find the direction. Refer to Example 1.12.