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**Final Exam**
Chapter 4: previously assigned material Chapter 13: Problems 3, 5, 11, 13, 29, 21, 43, 49 Chapter 14: Problems 5, 15, 17, 27, 33, 39, 41, 45 Chapter 15: [] Chapter 18: [] Chapter 19: [] Chapter 20: []

Schedule: [|PHYS2400.schedule.pdf] Important dates: [] Hyperphysics: [] Khan academy: [] Giancoli site: [] MIT lecture1 by Professor Lewin (course is Physics I ... 8.01): [] For other lectures do a search in YouTube. Visual Applets: [] Applet that illustrates differences between speed and velocity, and average versus instantaneous values: [] Multimedia site from down under, includes calculus reviews: [] Solutions to some problems for free; more problems for $: [] Projectile motion applets: [][] Class 3 ... Easy problems ... [|PHYS2400.p.1.pdf] Class 3 ... tipers ... [|tipers2.pdf] Class 3 ... free fall with air resistance using Excel ... has links to download the spreadsheets ... [] Class 3 ... Interesting reading on free fall ... look at the section on the Stratos Jump ... [] Class 4 ... Vectors ... [|Vectors.pdf] Class 4 ... Quiz1 ...[|Quiz1.pdf] Class 5 ... Quiz2 ... [|Quiz2.pdf] Class 6 ... Quiz3 ... [|Quiz3.pdf] Class 7 ... Quiz 4 ... [|Quiz 4.pdf] Class 7 ... Freebody diagrams ... [|FBD.pdf] Class 8 ... Exam Class 9 ... Quiz 5 ... [|Quiz 5.pdf] Class 10 ... momentum activity []... Quiz 6 ... [|Quiz 6.pdf]
 * Welcome to PHYS 2400, Winter 2012**

Fluid ... handout ... [|fluidshm.pdf]

Lab schedule: [|lab1sched(1).doc] Lab rules: [|Lab_Rules2011.doc] Lab safety: [|lab_safety.doc] Vernier Caliper Applet: [|http://www.physics.smu.edu/~scalise/apparatus/caliper/tutorial/] Lab 1 review: [| http://www.quia.com/cz/446190.html] Lab 2 review: [] Lab 3 review: [] Lab 4 review: [] Lab 5 review: [] Lab 8 review: []
 * Lab**

There are three basic dimensions: Length, Mass, and Time. They are indicated as [L], [M], and [T] respectively. The SI units corresponding to these dimensions are: meters, kilograms, and seconds respectively. The meter is approximately the distance between the tip of your outstretched hand to the tip of your nose when you are looking away from your outstretched hand. A kilograms is the mass of a liter of water. A liter is the volume of a box whose sides are each 1 decimeter. A decimeter is one tenth of a meter. A decimeter is the average width of a human fist. A second is (approximately) the time it takes an object to fall 4.9 meters. It is also the time it takes a pendulum of length 1 meter to swing from one extreme of its motion to the other. d=(1/2)gt 2 T=2π√(L/g) A person 6 feet tall is 183 cm tall. 1 miles is 1609 meters. Light travels (approximately) one foot in one nanosecond. The typical half liter bottle of water weighs (approximately) one pound. The circumference of the earth is approximately 25,000 miles. The distance from the earth to the sun is approximately 93,000,000 miles. The square root of 9.8 is approximately π.
 * Dimensions and Units**
 * Two formulas given in class**
 * Some info given in class**

For horizontal motion, the standard reference frame is a number line pointing to the right. (For vertical motion it points up.) Coordinates produced by these reference frames are used to indicate the location of a moving particle. (Location = position.) Position is usually represented by “x”. Since the position of a moving particle changes, then x is a function of time: x(t) If a particle moves from x(t 1 ) to x(t 2 ) you cannot calculate the distance traveled, d, unless you know the exact details of the particle's movement. You can, however calculate its displacement: s s = x(t 2 )-x(t 1 ) = ∆x Average speed = = distance divided by the elapsed time = d/∆t Instantaneous speed, u, is calculated using the same expression but requiring that the elapsed time be infinitesimal. Average velocity =  = displacement divided by the elapsed time  = s/∆t Similarly, instantaneous velocity, v, is calculated using the same expression but requiring that the elapsed time be infinitesimal. Average acceleration =  = change in velocity divided by the elapsed time  = ∆v/∆t Instantaneous acceleration, a, is calculated using the same expression but requiring that the elapsed time be infinitesimal. (For horizontal motion, the standard reference frame is a number line pointing to the right. (For vertical motion it points up.) When a particle is moving to the right or when it is moving up, the displacement and velocity are positive. The signs are negative when the particle is moving to the left or when it is moving down. The sign of the acceleration is a different matter altogether. When you are speeding up, the acceleration has the same sign as the velocity. When you are slowing down the acceleration has the opposite sign as the velocity. Note that ... When you step on your car's brakes, your acceleration is negative if you are moving to the right, and positive if you are moving to the left. When a basketball player jumps off the floor his acceleration is negative, and as he falls down, his acceleration is also negative Velocity can be positive or negative. Speed is always positive. Instantaneous speed is the absolute value of the instantaneous velocity. Average speed is not necessarily equal to the absolute value of the average velocity Average velocity is the slope of a secant line on the x-t graph. Instantaneous velocity is the slope of a tangent line on the x-t graph. Displacement is the area of an interval of the v-t graph. Instantaneous speed is calculated using the derivative of the x(t) function. Instantaneous acceleration is calculated using the derivative of the v(t) function. Velocity changes are calculated using the antiderivative of the a(t) function. Displacements are calculated using the antiderivative of the v(t) function. To avoid using calculus in dealing with constant acceleration situations, we use three algebraic equations: These equations apply to the time interval [0,t] with corresponding velocities v o and v. These three equations involve five variables. Each equation involves four variables. The value of three variables must be known so that the fourth variable can be calculated.
 * Frames of reference** = coordinate system. (In one dimension: a number line.)
 * We now define speed, velocity, and acceleration.**
 * Positive or negative?**
 * Speed versus Velocity**
 * Graphs**
 * Calculus**
 * Constant acceleration**
 * v=v o +at**
 * s = v o t+(1/2)at 2 **
 * v 2 =v o 2 +2as**

Constant acceleration means that a(t) = constant. We let the constant be "a". ......... **a(t) = a.** To obtain v(t) we get the antiderivative of a(t). ......... v(t) = at + c, where c is a constant of integration. We write the constant ahead of the "at" term. ......... v(t) = c + at. We note that c = v(0) which we write as as v o. ......... **v(t) = v o + at**. To obtain x(t) we get the antiderivative of v(t). ......... x(t) = v o t + (1/2)at 2 + c', where c' is a constant of integration. We write the constant ahead of the v o t term. ......... x(t) = c' + v o t + (1/2)at 2. We note that c' = x(0) which we write as x o. ......... **x(t) = x o + v o t + (1/2)at 2 .**
 * A more rigorous approach to constant acceleration kinematics **

Free fall = motion free from any influence except gravity. (It includes rise, fall, projectile, and orbital motion.) The word "Fall" can indicate both the rise and fall of the object. As a freely falling object falls it gains speed. 21.9 mph every second. 9.8 m/s every second. As a freely falling object rises it loses speed. 21.9 mph every second 9.8 m/s every second. Free fall acceleration on the earth: a = -9.8 m/s 2 (a = -g, where g = +9.8 m/s 2 ).
 * Free fall**

Introductory definition of a vector: A quantity having magnitude and direction. Introductory definition of a scalar: A quantity having magnitude only. Force is a vector. Time and money are scalars. Vectors are specified by giving their magnitude and direction or by giving their components according to specific coordinate systems. The most common coordinate systems are the rectangular and the polar coordinate systems. Vectors can be added and subtracted. The old way of adding vectors is the parallelogram method. The modern method is the tail-to- head method. The old method of subtracting vectors is the tip--to-tip method. The modern method is the addition of the negative. The algebraic method of adding vectors is to add their rectangular components and, if needed, express the answer in polar coordinates. When two vectors if magnitude A and B are added, the maximum magnitude of the resultant is A+B, and the minimum magnitude is |A-B|.
 * Vectors**

The horizontal acceleration is zero and the vertical acceleration is -g. The overall motion is a superposition of these two motions. The shape of the motion is parabolic. The **simple case** involves launch from ground level and landing on ground level also. For the **simple case** the maximum range occurs when the angle of projection 45°. For the **simple case**, the range is the same for complementary projection angles. For horizontal projection, the time of flight is the same as if the object had been dropped vertically.
 * Projectile motion with no air resistance**

These laws are an incredibly successful attempt to explain the motion of particles. (Particles are small sphere-like objects.) Besides particles we deal with these objects: planet-like objects (uniform spheres), flat surfaces, and strings. All of these objects interact with each other. The strength and direction of these interactions we call forces. In first semester physics we deal only with the following forces. Weight is the attraction of a particle by the the earth (or other planet-like object). Normal and friction are the interactions between a particle and a surface. The normal is outwardly perpendicular to the surface; friction is parallel to the surface. Tension is the pulling force felt by a particle due to a string (rope or wires also). Impacts are short duration contact interactions between a particle against an object or another particle.
 * Newton's Laws**
 * Weight
 * Normal
 * Friction
 * Tension
 * Impacts

When you are sitting down, weight pulls you down (weight), the chairs pushes you up (Normal), and friction between you an the chair prevents you from sliding. Meanwhile the collision of air molecules on your body (impacts) create what we call air pressure.

Newton's first law deals with the absence of interactions. In this case Newton tells us that the acceleration is zero. The second law tells us what happens when there are interactions: their resultant causes an acceleration **a**, whose magnitude and direction are given by **a** = **F**net/mass. Mass is measured in kilograms and is related to the "amount of matter", essentially how many protons and neutrons make up the object. We can also say that mass is a measure of how difficult it is to accelerate an object. The weight of a particle is also proportional to its mass. The third law deals with interactions between two objects. Each object feels a force due to the other: tthird he law tells us that the force the objects feel is equal and opposite. One force is called the action and the other the reaction. For this reason you often hear the third law stated as follows: action is equal and opposite to the reaction.

Mass is measured in kilograms. Acceleration is measured in m/sec 2. Since Force = ma, force is measured in kg·m/sec 2 which is indicated by the single word "Newton". A force of 1 Newton is equivalent to the weight of 1 apple. 4.45 Newtons equal one pound.

A frictionless inclined plane allows objects to slide down with an acceleration less than that of gravity. In free fall objects fall with the full acceleration of gravity. ON an incline, objects are accelerated by the component of the weight in a direction parallel to the incline. The magnitude of this component is w·sin(angle of inclination), The resulting acceleration is g·sin(angle of inclination). An incline plane with an angle of inclination of 30° results in an acceleration of 4.9 m/sec 2.

Friction is a force between an object and a surface, and directed parallel to that surface. If there is relative motion between the object and the surface, the friction is called kinetic friction. If there is no relative motion the force is called static friction. Kinetic friction, ƒk, has a fixed value. Static friction can range from 0 up to a maximum value ƒsmax. Both ƒk and ƒsmax are directly proportional to the normal force the surface exerts on the object. The constant of proportionality is larger for ƒsmax than for ƒk. The constants of proportionality are indicated by ƒs and ƒk respectively.