Midterm Exam Study Guide 2018-19: Physical Science
Scientific Notation
1. Convert numbers from decimal notation to scientific notation. (Appendix B, pg. 863 and pg. 866)
An exponent is a number that is a superscript to the right of another number. The best way to explain how
an exponent works is with an example. In the value 54, 4 is the exponent on 5. The number with its
exponent means that 5 is multiplied by itself 4 times. 54 = 5 × 5 × 5 × 5 = 625
Powers of the number 10 are used to keep track of the zeros in large and small numbers. Numbers that are
expressed as some power of 10 multiplied by another number with only one digit to the left of the decimal
point are said to be written in scientific notation. The number of zeros corresponds to the exponent to the
right of the 10. The number for 104 is 10,000; it has 4 zeros.
To simplify numbers that are less than 1, use negative exponents. Next, study the negative powers of 10.
To determine the exponent that you need to use, count the number of decimal places that you must move
the decimal point to the right so that only one digit is to the left of the decimal point. To simplify the mass
of the ink in the dot on an i, 0.000000001 kg, you must move the decimal point 9 decimal places to the
right for the numeral 1 to be on the left side of the decimal point. In scientific notation, the mass of the ink
is 1 × 10–9 kg.
[For more examples and information, review the Scientific Notation worksheet attached to this study guide.
Also review the Writing Scientific Notation worksheet you did as classwork.]
2. Convert numbers from scientific notation into decimal notation. (Appendix B, pg. 863 and pg. 866)
Same information as #1 but you are doing the reverse conversion.
3. Add and subtract two (or more) numbers expressed in scientific notation. (Understand and apply the
rules for addition and subtraction with exponents.) (Appendix B, pg. 863 and pg. 866)
When you use scientific notation in calculations, follow the rules for using exponents in calculations. When
you add two numbers expressed in scientific notation, convert the numbers so they have the same
exponent value (the larger number is easier to work with), as shown below.
(4 × 105) + (2 × 103) = (4 × 105) + (0.02 × 105) = 4.02 × 105. Use the same process when subtracting
numbers written in scientific notation.
[For more examples and information, review the Using Scientific Notation worksheet you did as classwork.]
4. Multiple and divide two (or more) numbers expressed in scientific notation. (Understand and apply the
rules of multiplication and division with exponents.) (Appendix B, pg. 863 and pg. 866)
When you use scientific notation in calculations, follow the rules for using exponents in calculations. When
you multiply two numbers expressed in scientific notation, add the exponents, as shown below. (4 × 105) ×
(2 × 103) = [(4 × 2) × 10(5+3))] = 8 × 108 When you divide two numbers expressed in scientific notation,
subtract the exponents.
[For more examples and information, review the Using Scientific Notation worksheet you did as classwork.]
Significant Figures
5. Define, explain and apply the six rules for determining the number of significant figures for a number.
(Appendix B, pg. 868)
You can use a few rules to determining the number of significant figures in a measurement.
1. All nonzero digits are significant. Example 1,246 (four significant figures, shown underlined).
2. Any zeros between significant digits are also significant. Example 1,206 (four significant figures).
3. If the value does not contain a decimal point, any zeros to the right of a nonzero digit are not
significant. Example 1,200 (two significant figures).
4. Any zeros to the right of a significant digit and to the left of a decimal point are significant. Example
1,200. (four significant figures) [Note: the . after the number is a decimal point, not a period.]
5. If a value has no significant digits to the left of a decimal point, any zeros to the right of the decimal
point and to the left of a nonzero digit are not significant. Example 0.0012 (two significant figures).
6. If a measurement is reported that ends with zeros to the right of a decimal point, those zeros are
significant. Example 0.1200 (four significant figures).
[For more examples and information, review the Significant Figures worksheet attached to this study
guide. Also review the Significant Figures worksheet you did as classwork.]
6. Define, explain, and apply the rules for determining the significant figures for the addition and
subtraction of numbers. (Appendix B, pg. 868)
If you are adding or subtracting two measurements, your answer can have only as
many decimal positions as the value with the least number of decimal places. The final
answer in the following problem has five significant figures. It has been rounded to two
decimal places because 0.04 g has only two decimal places.
[For more examples and information, review the Using Significant Figures worksheet you did as classwork.]
7. Define, explain, and apply the rules for determining the significant figures for the multiplication and
division of numbers. (Appendix B, pg. 868)
When you multiply or divide measurements, your final answer can have only as many
significant figures as the value with the least number of significant figures. Examine the
following multiplication problem. The final answer has been rounded to one significant
figure because 0.04 cm has only one. When performing both types of operations
(addition/subtraction and multiplication/division), round the result after you complete each type of
operation, and round the final result.
[For more examples and information, review the Using Significant Figures worksheet you did as classwork.]
Chapter 11 – Motion
8. Define motion, displacement, and frame of reference and explain how they are related. (Section 11.1,
pg. 365 ¶2-3, pg. 366 ¶1-2)
Motion: an object’s change in position relative to a reference point.
Displacement: the change in position of an object. Displacement must contain a magnitude and direction.
It is a straight line measured from the start point to the end point.
Frame of reference: a system for specifying the precise location of objects in space and time.
When an object changes position with respect to a frame of reference, the object is in motion.
9. Define velocity and explain examples of velocity. (Section 11.1, pg. 367 ¶1-2)
Speed is the distance traveled divided by the time interval during which the motion occurred. Sometimes,
you may need to know the direction in which an object is moving. Velocity is the speed of an object in a
particular direction. Speed tells us how fast an object moves, and velocity tells us both the speed and the
direction that the object moves.
10. Define average speed and be able to solve problems involving the average speed equation. (Section
11.1, pg. 368 ¶1-5, pg. 3, pg. 369 Math Skills)
Average speed is the distance traveled by an object divided by the time the object takes to travel that
distance. (See Math Skills sample on page 369)
Example: Suppose that a skater moves 132 m in 18 s. By putting the time and distance into the formula
above, you can calculate her average speed.
11. Understand, explain and create distance vs time (velocity) graphs. (Section 11.1, pg. 370 ¶1-2 + Graph
Skills, pg. 371 ¶1-2)
You can investigate the relationship
between distance and time in many ways.
You can use mathematical equations and
calculations. You can plot a graph showing
distance on the vertical axis and time on
the horizontal axis. Whichever method you
use, you measure either distance or, if you
know the direction, displacement and the
time interval during which the distances or
displacements take place.
In a distance vs. time graph, the distance
covered by an object is noted at equal
intervals of time. As a rule, line graphs are
made with the x-axis (horizontal axis)
representing the independent variable and
the y-axis (vertical axis) representing the dependent variable. Time is the independent variable because
time will pass whether the object moves or not. Distance is the dependent variable because the distance
depends upon the amount of time that the object is moving.
The slope of a distance vs. time graph equals speed. For a car moving at a constant speed, the distance vs.
time graph is a straight line. Figure 6 shows three cars moving at different speeds. The speed of each car
can be found by calculating the slope of the line. The slope of any distance vs. time graph gives the speed
of the object. Notice that the distance vs. time graph for the fast-moving car is steeper than the graph for
the slow-moving car. A car stopped at a stop sign has a speed of 0 m/s. Its position does not change as
time goes by. So, the distance vs. time graph of a resting object is a flat line with a slope of zero. The
third graph in Figure 6 shows a car with changing speed. Between 2 s and 3 s, the car is stopped and the
graph is flat.
12. Define acceleration and be able to solve math problems involving acceleration. (Section 11.2, pg. 372
¶2-3, pg. 373 ¶1, pg. 374 ¶1-4, pg. 375 Math Skills)
Acceleration is the rate at which velocity changes over time; an object accelerates if its speed, direction, or
both change. The average acceleration over a given time interval can be calculated by dividing the change
in the object’s velocity by the time over which the change occurs. The change in an object’s velocity is
symbolized by Δv. (See Math Skills sample on page 375)
Example: A person is slowing down on a bicycle. He starts at a speed of 5.5 m/s and slows to 1.0 m/s over a
time of 3.0 s. The change in speed, Δv, is 1.0 m/s – 5.5 m/s = –4.5 m/s. The change in speed is negative
because he is slowing down. The equation above can be used to find average acceleration:
13. Understand, explain and create speed vs time (acceleration) graphs. (Section 11.2, pg. 376 ¶1-3 + Graph
Skills, pg. 377 ¶1-2)
You have learned that an object’s speed can be determined from a distance vs. time graph of its motion.
You can also find acceleration by making a speed vs. time graph. Plot speed on the vertical axis and time
on the horizontal axis. A straight line on a speed vs. time graph means that the speed changes by the same
amount over each time interval. This is called constant acceleration. The slope of a straight line on a
speed vs. time graph is equal to the acceleration. You can look at a speed vs. time graph and easily see if
an object is speeding up or slowing down. A line with a positive slope represents an object that is speeding
up. A line with a negative slope represents an object that is slowing down.
Acceleration can be seen on a distance vs. time graph.
Imagine that one of the riders in Figure 5 is slowing uniformly from 10.0 m/s to a complete stop over a
period of 5.0 s. A speed vs. time graph of this motion is a straight line with a negative slope. This straight
line indicates that the acceleration is constant. You can find the acceleration by calculating the slope of the
line.
Thus, the rider’s speed decreases by 2.0 m/s each second. The distance vs. time graph, also shown in
Figure 5, is not a straight line when the rider’s velocity is not constant. This curved line indicates that the
object is under acceleration.
14. Define and explain uniform circular motion and centripetal acceleration. (Section 11.2, pg. 373 ¶2-3)
Uniform circular motion has centripetal acceleration. If you move at a constant speed in a circle, even
though your speed is never changing, your direction is always changing. So, you are always accelerating.
The moon is constantly accelerating in its orbit around Earth. A motorcyclist who rides around the inside of
a large barrel is constantly accelerating. When you ride a Ferris wheel at an amusement park, you are
accelerating. All these examples have one thing in common—change in direction as the cause of
acceleration.
Are you surprised to find out that as you stand still on Earth’s surface, you are accelerating? You are not
changing speed, but you are moving in a circle as Earth revolves. An object moving in a circular motion is
always changing its direction. As a result, its velocity is always changing, even if its speed does not change.
The acceleration that occurs in circular motion is known as centripetal acceleration.
15. List the four fundamental forces in nature and compare their relative strengths. (Section 11.3, pg. 380
¶2, pg. 381 ¶1)
Scientists identify four fundamental forces in nature. These forces are the force of gravity, the
electromagnetic force, the strong nuclear force, and the weak nuclear force. The strong and weak nuclear
forces act only over a short distance, so you do not experience them directly in everyday life. The force of
gravity is a force that you feel every day. Other everyday forces, such as friction, are a result of the
electromagnetic force.
The fundamental forces vary widely in strength and the distance over which they act. The strong nuclear
force holds together the protons and neutrons in the nuclei of atoms and is the strongest of all the forces.
However, it is negligible over distances greater than the size of an atomic nucleus. The gravitational and
electromagnetic forces act over longer distances. The electromagnetic force is about 1/100 the strength of
the strong force. The gravitational force is very much weaker than the electromagnetic force. Consider a
proton and an electron in an atom. The electromagnetic force is about 1040 times as great as the
gravitational force between them!
16. Define net force, explain examples of net force. (Section 11.3, pg. 381 ¶3)
Force is an action exerted on a body in order to change the body’s state of rest or motion; force has
magnitude and direction. Net force is the combination (sum) of all forces acting on an object.
Example: Two people are pushing a couch (see figure above). If they are pushing opposite directions with the same
magnitude of force, the combinations of the forces (net force) will equal zero. If they are not pushing in opposite
directions with the same magnitude of force, there will be a net force greater than zero.
17. Compare and contrast balanced and unbalanced forces and give examples of each. (Section 11.3, pg. 381
¶3, pg. 382 ¶3-4)
Whenever there is a net force acting on an object, the object accelerates in the direction of the net force.
An object will not accelerate if the net force acting on it is zero.
When the forces applied to an object produce a net force of zero, the forces are balanced. Balanced forces
do not cause an object at rest to start moving. Furthermore, balanced forces do not cause a change in the
motion of a moving object. For example, a light hanging from the ceiling does not move up or down,
because the force due to tension in the cord pulls the light up and balances the force of gravity pulling the
light down.
When two forces acting on the same object are unequal, the forces are unbalanced. A change in motion
occurs in the direction of the greater force. Suppose that two students push against an object on one side
and only one student pushes against the object on the other side. If the students are all pushing with the
same force, there is an unbalanced force: two students pushing against one student. Because the net force
on the object is greater than zero, the object will accelerate in the direction of the greater force.
18. Define friction and explain how friction affects the motion of an object. (Section 11.3, pg. 382 ¶5-6, pg.
384 ¶1,4,5)
Friction is a force that opposes motion between two surfaces that are in contact. Friction occurs because
the surface of any object is rough.
The rubbing together of two rough surfaces creates heat. The heat from friction causes a match in to
ignite. Surfaces that look or feel very smooth are really covered with microscopic hills and valleys. When
two surfaces are touching, the hills and valleys of one surface stick to the hills and valleys of the other
surface.
19. Differentiate between static friction and kinetic friction. (Section 11.3, pg. 383 ¶1-2)
Static friction is the force that resists the initiation of sliding motion between two surfaces that are in
contact and at rest.
Kinetic friction is the force that opposes the movement of two surfaces that are in contact and are moving
over each other.
Because of forces between the molecules on the two surfaces, the force required to make a stationary
object start moving is usually greater than the force necessary to keep it moving. In other words, static
friction is usually greater than kinetic friction.
Chapter 12 – Forces
20. Define, explain and give examples of inertia. (Section 12.1, pg. 398 ¶1)
Inertia is the tendency of an object at rest to remain at rest or, if moving, to continue moving at a constant
velocity. All objects resist changes in motion, so all objects have inertia. An object that has a small mass,
such as a baseball, can be accelerated by a small force. But accelerating an object whose mass is larger,
such as a car, requires a much larger force. Thus, mass is a measure of inertia. An object whose mass is
small has less inertia than an object whose mass is large does.
21. Define, explain and give examples of Newton’s first law of motion. (Section 12.1, pg. 397 ¶2-3)
Newton’s first law states that an object at rest remains at rest and an object in motion maintains its
velocity unless it experiences a net force.
Objects change their state of motion only when a net force is applied. A book sliding on carpet comes to
rest because friction acts on the book. If no net force acted on the book, the book would continue moving
with the same velocity.
22. Define Newton’s second law of motion and be able to solve math problems involving Newton’s second
law of motion. (Section 12.1, pg. 400 ¶3-4)
Newton’s second law state that the unbalanced force acting on an object equals the object’s mass times its
acceleration.
Net force is equal to mass times acceleration. The unbalanced force on an object determines how much an
object speeds up or slows down. Newton’s second law can also be written as a mathematical equation.
Example: Zoo keepers lift a stretcher that holds a sedated lion. The total mass of the lion and stretcher is
175 kg, and the upward acceleration of the lion and stretcher is 0.657 m/s2. What force is needed to
produce this acceleration of the lion and the stretcher?
Newton’s second law also states that the acceleration of an object is directly proportional to the net force
on the object and inversely proportional to the object’s mass.
The mathematical version of this form of the law is as follows.
For example, the mass of the car shown above is the same in both photos. When the masses are the same,
a greater force causes a greater acceleration.
The topics listed above will appear on the midterm exam. Use this list while studying as a guide to what
topics you need to study. For example, work and energy are not on the list – thus it will not be on the exam.
During review weeks we will be solving a variety of questions (multiple choice, short answer, and problems)
during class to reinforce your studying. While studying at home I would suggest completing the various
sample problems in the textbook (these problems have answers and step-by-step solutions), practice
problems, and chapter review problems. If you have questions about any of the review topics and/or would
like solutions to study problems, please bring them up during class for review.