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04%4ATopic #3(. Motion in a Straight Line
1. Solving Physics Problems {using a problem-solving format like GFESA}
2. Motion
3. Scalar and Vector Quantities
4. Vector Addition - Graphical Method
5. Distance and Displacement
6. Instantaneous Speed and Velocity
7. Average Speed and Velocity
8. Acceleration
9. Final Velocity After Uniform Acceleration
10. Displacement During Uniform Acceleration
11. Acceleration Due to Gravity
Notes should include:
Solving Physics Problems: Solving a problem requires critical reading skills and critical problem solving skills. Critical reading is required to insure that the important information that will lead to a logical, correct answer in a problem-solving situation be found. Critical problem solving is required to insure that the information necessary to solving the problem is processed accurately to insure the accuracy of an answer. In this course being able to lay out the information in a coherent written form is essential to the whole problem solving process. The process used in this course is summarized as the GFESA problem solving process. GFESA breaks down into Given, Find, Equation, Substitution, and Answer. Critical reading focuses on the Given and Find, while Critical problem solving focuses on the Equation, substitution and answer.
Motion: The mathematical description of motion is called kinematics. In the study of motion you will be studying speed, velocity, and acceleration. For now we will concentrate on motion in a straight line.
Scalar and Vector Quantities: A scalar quantity is described by the magnitude (size) of the measurement and includes units as appropriate. For example, a distance measurement of 6 km or a speed measurement of 40 km / hr are examples of scalar quantities. On the other hand, a vector quantity is described both by its magnitude, with appropriate units, and by direction. For example, a displacement measurement of 2.5 km, north and a velocity measurement of 30 km / hr, E (east) are examples of vector quantities. Note the difference in the way scalar and vector quantities are expressed. Scalar quantities are measurements that are most familiar to you. They involve no statement of direction. They have only a numerical value followed by one or more units of measure. Vectors, on the other hand, must have a statement of direction following the numerical value and its unit(s). Statements of direction can have many forms such as forward, reverse, up, down, a compass angle and a unit circle angle. Never ignore direction unless a question only asks for the magnitude. In such a situation you need not report a direction in an answer.
(Vector Addition - Graphical Method: Vectors can be combined. We usually say they are added, though, except in the case of straight-line motion the combination of two or more vector quantities involves more that simple arithmetic. (i.e., for motion in two dimensions, vector quantities are combined using Trig. functions) Vector addition can be accomplished with reasonable results using a few simple skills learned in geometry. Equipped with a ruler and a protractor, you can achieve fairly good results when combining (adding) vector quantities. This approach will be used in your study of vectors, but will be replaced with mathematical solutions later on in order to save time.
Distance and Displacement: Distance (d) measurements are scalar quantities. For example, the distance between to points found on a map are 5 km apart. Notice that no reference is made to one or the other point as being the point from which the measurement is made from. Also there is no apparent statement of direction in the expression of this measurement. You could also call distance the length moved. On the other hand, displacement (d) measurements are vector quantities. For example, the displacement of a person after having taken a walk is 1.5 km 20o to the east of north. In this situation you are using the person's starting point as a reference point and you are stating the person's displacement both in terms of a distance and in terms of a direction. Displacement measurements should always inform you of where the person is now with respect to their starting point. In a sense distance doesn't allow for you to find them while displacement does. Distance is normally expressed in meters (m), though kilometers are often used too. Displacement also uses meters for the scalar portion of the measurement. Direction is often described using angles expressed in degrees (o) on a compass or unit circle.
Instantaneous Speed and Velocity: Speed (v) is often defined as the distance an object travels per unit of time. Instantaneous Speed (vi or vf) is the speed an object is moving at any given instant of time. Speed is normally expressed in meters / second (m/s). A speedometer is frequently used to measure instantaneous speed. An example of speed is 25 km/h. Velocity (v) being a vector quantity uses a scalar measurement, which is its magnitude, and a direction. Instantaneous Velocity (vi or vf) is the velocity an object has at a given instant of time. It includes the measure of instantaneous velocity followed by a statement of direction. For example 25 km/h, west is an example of an instantaneous velocity.
Average Speed and Average Velocity: When you travel somewhere, it is highly unlikely that you move with a constant speed or experience a constant velocity. What is more likely to be happening is that your speed and possibly your velocity are constantly changing. As a consequence, it is far easier to express your average speed for the entire trip you have made than it is to keep track of all of the instantaneous velocities during the trip. The equation for average speed is vAVE = d / t , where d is the distance traveled and t is the time over which the distance was traveled. Average velocity is found using the same equation vAVE = d / t, if the direction of motion is in a straight line, because only the magnitude (size) of the velocity is changing. If the object changes direction then the (situation becomes more complicated and may require other equations be used. These equations will be introduced later in the course.
Acceleration: Acceleration (a) is usually defined as the rate of change in velocity, much as velocity is often defined as the change in position, which is another way of describing displacement. The acceleration can be found by the following equation when travel is along a straight line. a = (vf - vi)/ t, which tells us that acceleration is the change in velocity divided by the time interval through which the acceleration occurs.
Calculating Final Velocity After Uniform Acceleration: After an object experiences acceleration, it may be necessary to calculate the object's final velocity. To do this we rearrange the equation above and end up with vf = vi + a t. What would the equation look like if you were to solve for the initial velocity after an object experienced an acceleration?
Calculating Displacement During Uniform Acceleration: The equation d = vAVE / t is valid for both an object traveling with constant speed or an object experiencing uniform (constant) acceleration. The equation can be written in another form as shown. d = vAVE / t = (vf + vi / 2) / t
Calculating Displacement From Acceleration and Time: The equation for displacement in this situation is d = vi t + 0.5 ( a ) t2. It allows you to calculate displacement when all you know is the initial velocity, the rate of acceleration, and the time interval through which the acceleration occurred.
An Equation Independent of Time: If you are looking for final velocity when you have no information about time, you may find the following equation useful. vf2 = vi2 + 2 a d.
Calculating Acceleration From Displacement and Velocity: The above equation can be changed around (algebraically) to solve for displacement. This form is
d = (vf2 - vi2) / 2 a.
Acceleration Due to Gravity: All objects close to the earth's surface fall downwards, that is they accelerate downwards, at the same rate, if we do not factor in air resistance. In vacuum chambers on earth and on the moon where there is no air resistance, because there is no air, all objects even coins and feathers all fall at the same rate. The rate of downwards acceleration is 9.81 m / s2 (when rounded, 9.8 m/s2) at sea level. As you move farther from the surface this value represented by the symbol g and called the acceleration due to gravity, decreases. You will see that this decrease in acceleration, due to an increase in distance between the two objects, in this case the earth and the object being accelerated downwards, is the effect distance has on the force of gravity between the two objects. Of most significance to you in terms of problem solving is that the equations you already learned concerning acceleration in a straight line on horizontal surfaces also apply to falling objects. The only difference in your calculations is that you will replace the more generic variable symbol a (acceleration in general) with the more specific variable symbol g (the acceleration due to gravity). Always remember that g does (NOT represent gravity or the force of gravity. It is a symbol that represents acceleration, acceleration that is caused by gravitational force.
Compare the following equations:
Horizontal Motion Equations Vertical Motion Equations (falling bodies)
vf = vi - a t vf = vi - g t
vf2 = vi2 + 2 a d vf2 = vi2 + 2 g d
d = vi t + 0.5 ( a ) t2 d = vi t + 0.5 ( g ) t2
Vocabulary: motion diagram, operational definition, particle model, coordinate system, origin, position vector, scalar quantity, vector quantity, displacement, time and time interval, distance, displacement, speed, instantaneous and average velocity, instantaneous and average acceleration, final velocity and initial velocity, uniform motion, acceleration due to gravity, kinematics.
Skills to be learned: You should learn to solve for any of the variables concerning straight-line motion, either horizontal or vertical, as described in the above information.
Assignments:
Textbook: Read / Study / Learn Chapter 3 Sections 3.1 and 3.2 about motion, Section 3.3 about velocity and acceleration, and Chapter 4 references to solving motion problems mathematically using equations as defined in table 5-2 on page 101 of the textbook.
WB Exercise(s): PS#3-1, 4-1, 4-2, 4-4 no. 1->4
Activities: TBA
Resources:
This Handout and the Overhead and Board Notes discussed in class
Textbook: Chapter 3 and Example Problems in Chapter 5 as applies to solving motion problems using equations.
Workbook: Lessons & Problem Sets:
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