Physics 1251.2: (Introductory Physics 1)

News (November 28)

Practice problems to prepare for the final exam, particularly in review sessions (recitation on Dec 4, lecture Dec 5, and possibly lecture Dec 3) are found in Practice problems 1 and Practice problems 2. They will be available late Monday Dec. 1 at Copies on Campus, too.

Solutions for one of the test 4 problems are in test 4-1, and test 4-2. No group problem solution is available at this moment. Sorry. They will be available late Monday Dec. 1 at Copies on Campus, too.

Solution for one of the practice group problem 4 is in practice 4. It will be available at Copies on Campus late afternoon of Dec 1, too.

Answer key for multiple-choice test is in MC1 key, MC2 key, MC3 key, and MC4 key. All will be available at Copies on Campus shortly, too, if not already.

Solutions for the test 3 problems are in group test 3, test 3-1 and test 3-2. All are available at Copies on Campus, too.

Solutions for the test 2 problems are in group test 2, test 2-1 and test 2-2. All are available at Copies on Campus, too.

Solutions for the test 1 problems are in group test 1, test 1-1 and test 1-2 All are available at Copies on Campus, too.

It came to my attention that the web version of the syllabus has old curve criteria, which do not have any -'es and +'es. The correct ones are

A: 88% to 100%     A-: 83-88%    
B+:78-83%     B:73-78%     B-:68-73%    
C+:62-68%     C:56-62%     C-:50-56%    
D+:45-50%     D:40-45%     F: 0-40% or incomplete lab

Last week's practice group problem solution is group practice problem and is available at Copies of Campus. It contains modification to the problem (addition of friction), too.

Problems we were going to do on 10/29 (postponed 'til next week) are found here.

Problems we did on 10/23 are found here. The solution for the first problem is in sample prob 10/23-1 and sample prob 10/23-2 .

Formulae that I used last year are found here. I expect that you will be allowed to use more-or-less the same formulae in tests. Solutions for the problems I did (and I was going to do) today (10/8) are in problem 1 and problem 2. They are available at Copies on Campus shortly.

Friday tests are in Phys 166 (A-L) or Ford 55 (M-Z) depending on your initials.

Solutions to the problems you did last Thursday in recitation are found in problem 1, problem 2, problem 3.

Syllabus is in http://www.hep.umn.edu/~yk/syllabus_1251.html

Click here to send comments to Yuichi Kubota (kubota@mnhep.hep.umn.edu).

Solutions to textbook problems are available at bookstore for about $10.

Where are we?

• conversion among various unit.
• scientific notation.

Chapter 2 is about kinematics in 1 dimension, where we study how to describe motion quantitatively. In a few weeks, it will be used to relate motion and its cause (forces) in chapter 4. Students are expected to learn the meaning of

• position
• displacement
• average velocity and speed
• instantaneous velocity and speed
• acceleration both average and instantaneous

• the relations among the above quantities
• how these quantities are represented in various graphs and diagrams.
• application of these ideas to analyse some motion such as constant velocity motion, constant acceleration. Motion of an object under the influence of gravity is an important example of the constant-acceleration motion, and is discussed in more detail in class.

Chapter 3 is review of vectors. Vectors may be defined by their magnitudes and directions, or sets of numbers. The latter may be considered the components of vectors.

Vectors can be useful since their addition and subtraction have counterparts in real life, and mean something. These operations of additions and subtracting are equivalent to addition and subtraction of "arrows" as taught in any math classes.

One can even define useful multiplications of combinations of vectors and a regular number (scalar). One can multiply a vector and a scalar. The result is a vector of the same direction as the input vector and the magnitude being multiplied by the scalar. If a vector represents the number of apples and oranges in a gift box, and the scalar represents the number of gift boxes, the results of multiplication gives the total number of apples and oranges in the gift boxes!

Dot product (inner product, or scalar product) results in a scalar quantity (thus scalar product) from a pair of vectors. If the input vectors are identical, the result is the square of the magnitude of the vector. If the two input vectors are perpendicular, the dot produce it zero. It is useful, for example, to figure out the angle between two lines in 3D space if the direction of the lines can be translated into the direction of vectors pointing in the line directions.

Cross product (outer product) results in a vector (thus vector product) from a pair of vectors. This operation of vectors is used in physics of magnetist quite a bit. It is also used to represent torque (if you don't know what torque is don't worry. We will cover it in winter) or rotational motion. Being able to use at least one form of right-hand rule to figure out the direction of a cross product from the directions of the input vectors is desirable at this point, but not crucial until winter.

Chapter 4 is about kinematics in 2 dimension.

Operationally, not much is new since motion in 2 dimension can be describe by vectors: everything we learned in chapter 2 such as displacement, position, velocity, acceleration becomes vectors. However, as we saw in the last chapter, vectors can be considered to be consist of their components. Once vector quantities are broken down into components, each component behaves like in chapter 2. The x component of velocity is the slope of the x-position graph, or the differential of the x-position function, for example.

However, as results, additional interesting relations among various quantites emerge. For example, the velocity vectors are ALWAYS in the direction of the motion as we intuitively percieve! So the velocity vectors are always parallel to the tangential line to the trajectory in a picture of motion in real space (i.e. x vs. y position picture at various times.) The acceleration vector would be parallel to the velocity vector if the object of interest is speeding up and anti-parallel if it is slowing down. Any perpendicular component of the acceleration vector relative to the velocity vector implies that the direction of motion is changing.

Constant-speed circular motion is a special case when the acceleration vector is ALWAY perpendicular to the velocity since the speed does not change. The magnitude of the acceleration turns out to equal to the velocity (magnitude) squared divided by the radius of the circle if you work out geometry (as in the textbook). Or one can work out using calculus, too. At this point, we keep a vague notion that something we casually call forces causes acceleration and we don't get into details about their relation until the next chapter (5).

Projectile motion is a typical example (application) of 2 dimensional kinematics, where vertical acceleration is ALWAYS -g and horizontal acceleration is ALWAYS 0. These facts to clearer notion of forces, in particular, gravity, will be dealt with in chapter 5. Given these specific acceleration, one can make all kinds of predictions about objects' motion if the only factor influencing the motion is gravity.

We went through procedures you might want to follow to solve all kinds of problems (really only one if you can handle algebra). One of the tricks may be to be able to understand some peculiar terminology in physics in decoding what problems (or real-life situations) are signalling you. For example, "a cannon ball hit the ground" means at that time, y(t) = 0. "At the heighest part of the trajectory" means the vertical velocity at that time is zero since the object is moving purely in the horizontal direction at that instance.

Chapter 5 is about relation between acceleration and force, addressing explicitly agents which "cause" motion.

It turns out that the mechanism which forces influence motion is by changing acceleration of the object being influenced. Hence F=ma. One of the things you want to be careful about applying this Newton's Law is to make sure that all the forces which act on the object of interest are accounted for. This equation should not taken as one which gives the acceleration knowning the net force, though physically, forces "cause" motion, or give rise to acceleration. In many case, one already know the direction of the acceleration, and not knowing some force(s). Often, normal force, for example, is not known a priori. The tension of a rope may not be known if one focus on one object only. It can often be figured out by looking at the motion (acceleration) of the two objects that the rope is connecting. In such a case, one is likely to find out that the accelerations of the two are the same by looking at geometry. Newton's Third Law is a simple idea, and still very difficult to apply for many students. The pair of forces that this law related switches the subject and object of the force. Force A acts on object X by Y, then its partner force B acts on objects Y by X. In general, it is a good idea to pay attention to what is exerting the force you are thinking of, and what is receiving the force.

Chapter 6 is about application of chapter 5 material, ioncorporating friction forces extensively.

Friction forces between solids follow usually a simple law: For a given pair of meterials which are in contact, the friction between them is proportional to the normal force which is exchanged by the two. The ratio is therefore a good measure of friction, and called the coefficient of friction. When the two surfaces are not sliding w.r.t. one another, the friction is usually a bit larger than when they are sliding. The coefficient for the former case (static friction) and the latter (kinetic friction) has to be distinguished.

By this time of the quarter, problems may contain many elements you have learned, and you need to be able to combine them to find answers.

Chapter 7 is about energies. Energy takes various forms: kinetic energy, potential energies due to gravity or spring forces. Electric force is also associated with potential energy. Chemical energy is related to a kind of potential energy of electrons around atoms and molecules. Heat (or thermal energy) has to do with (average) atomic kinetic energies and measured by temperature. All in all, we believe that the total amount of energy is always conserved if energies are defined properly.

In this chapter, we deal only with kinetic energies and their changes due to various forces. The effect of the forces on the kinetic energy is expressed as work. If one define the kinetic energy as K=(1/2)mv^2, One can show using F=ma that the work is given by the product of the force on the object and the displacement of the object.

Note that if a force is perpendicular to the displacement, it does not contribute to work, and hence change in the kinetic energy. Normal force is one such example.

Where are we in the lab?

3rd lab report is due sometime during the next week (11/17-11/21) depending on your lab date.

Problems from the last year's final (i.e. two years ago) and few extra are available on-line.

test	PDF (smaller but less clear images)	JPEG (larger and clearer)	TIFF (larger and clearer)
1	in PDF	page 1, page 2	page 1, page 2

Model solutions to suggested problems of last year, which are 70% the same as this year, are available for a few chapters in in PDF, JPEG and TIFF formats. If you have appropriate viewers to look at these files, you can see them on-line.
For a PDF viewer, download Acrobat Reader
For JPEG viewer on Mac, contact Aaron Giles at giles@med.cornell.edu. Unfortunately, I don't know much about JPEG viewers on PC's, though I am sure they are available.

chapters	PDF (smaller but less clear images)	JPEG (larger and clearer)	TIFF (larger and clearer)
4	HW 4 solutions in PDF		page 1, page 2, page 3, page 4, page 5, page 6,
7	HW 7 solutions in PDF	page 1, page 2, page 3	page 1, page 2, page 3
8	HW 8 solutions in PDF	page 1, page 2, Page 3, Page 4,	page 1, page 2, Page 3, Page 4,
9	HW 9 solutions in PDF	page 1, page 2	page 1, page 2
10	HW 10 solutions in PDF	page 1, page 2, Page 3, Page 4, Page 5

Solutions to last year's tests are available:

test	PDF (smaller but less clear images)	TIFF or JPEG(larger and clearer)
1	test 1 solutions in PDF	page 1, page 2
2	test 2 solutions in PDF (looks fine)	page 1, page 2
3	test 3 solutions in PDF	page 1, page 2