Rules for Significant Figures
For a whole number with no decimals -- only digits 1 through 9 are counted Example: 54,800 5, 4, and 8 count 3 Sig. Figs.
Exception! The "Sandwich Rule" -- zero between two digits counts Example: 5048 5, 0, 4, and 8 count 4 Sig. Figs.
For a whole number with a decimal point -- all digits (0-9) count Example: 4800. 4, 8, and 2 zeroes count 4 Sig. Figs.
For a number with a whole number and decimal part -- all digits (0-9) count Example: 54.003 5 Sig. Figs.
For a number with only a decimal part -- all digits to the right of place-holder zeroes count Example: 0.00420 4, 2, and last 0 count 3 Sig. Figs.
For Addition or Subtraction - the answer is rounded off to the least number of decimal places of any of the given information used Example: 15.2 + 37.68 = 52.88, rounded to 1 decimal place 52.9
For Multiplication or Division - the answer is rounded off to the least number of significant figures of any of the information used Example: 5.34 X 92 = 491.28, rounded to 2 sig figs 490
Counting numbers (1, 2, 3, or ½…) and equivalencies (1 m = 100 cm) are exact and are not used to determine the number of sig figs.
Example: 14.6805 kg X 2 = 29.3610, 6 sig figs as in the first number.
Dimensional Analysis—Converting Units
1. Start with what you have. Write it as a vertical fraction45 cm → 45cm 1
38 m/s → 38m 1s
2. Find the conversion(s) you need
100 cm = 1 m
1000 m = 1 km, and 3600 s = 1 hr
3. Write each conversion as a vertical fraction. Multiply the fraction you started with by the conversion fraction(s) so that the units you don’t want will cross-cancel. Top cancels with bottom.
45cm 1 x
1m 100cm
38m 1s x
1km 1000mx
3600s 1hr
4. Multiply your fractions. Multiply all the tops together; multiply all the bottoms together. Divide top by bottom. Get your answer and round it to the number of sig.figs. in your original value.
45 1 x
1m 100=
45x1m 1x100=
45m
100=0.45m
38 1 x
1km 1000x
3600 1hr =
38x1km x3600 1x1000x1hr =
136800km
1000hr =136.8 km
0.5 3 2 0.1 0 d (m) t (s) 1
0.2 0.3 0.4 4
E 0°, 360° N 90°
W 180°
S 270°
135º
255º
Slope, Physics Style
You will find slope the same way you did in Algebra—rise over run.
The difference in physics, is that slope is not just a number telling you about the line —it has meaning in the real world. The graph you graphed will be based on real, measured quantities that have sig. figs.
1.
Pick two points that are on the line(x1,y1) and (x2,y2) The x-axis of this graph is time (s) and the y-axis is
distance (m). These are your givens.
(0.4, 4) (0, 0)
2.
Write your equation for slope slope=riserun= ∆ y ∆ x=
y2−y1
x2−x1
3.
Substitute your values into the slope equation. Do not count boxes! In physics, often each division is something other than one, which is why counting boxes usually doesn’t work.slope= 4−0
0.4−0=
4 0.4
4.
Now divide! Do not leave slope as a fraction. In math class exact numbers make sense, but in physics we need sig. figs.slope = 10
5.
Lastly, round to an appropriate number of sig. figs. and put units on it. The units come from the graph. Since slope is equal to ∆y/∆x, units will be the y-axis units over the x-axis units.slope = 10 m/s
Vector Addition
Vectors are scaled-length arrows that represent values that have both a magnitude and a
direction.Consider the example: A river flows 40 m/s south and a boat travels 15 m/s at 135°. What is the velocity of the boat?
1. Draw each vector the correct length and the correct direction.
a. Choose a scale.
1 cm = 10 m/s
b. Use your scale for dimensional analysis to see how long your vectors need to be in cm. (you probably can do this step
in your head, but for complex scales, this is what you do). 40m/s
1 x 1cm
10m/s=4cm
15m/s
1 x 1cm
10m/s=1.5cm
2. Now draw your vectors the correct direction, always measuring the angle from East (0°). Be sure to draw them tip-to-tail. 3. Draw the resultant. Use a dashed arrow to go from the start of the first vector to the end of the last vector.
4. Measure the length of the resultant and rescale it into the correct units. 3.3cm
1 x
10m/s
5. Measure the angle to get your direction. Remember to measure from East (0º). This angle is between 180º and 270º.
Your velocity is 3.3 m/s @ 255º
Name:
Per.
Essential Algebra of Physics:
Isolating Variables
This document covers the level of algebra necessary to be successful in Physics. This is nothing to fear!
There are only two rules to follow. As long as you remember to follow the two rules, you will learn that
Algebra of High School Physics is as easy as playing a board game or sport that only has two rules without
exceptions. That makes this easier than learning to play Uno or Chess!
THE TWO RULES:
1. Do the opposite function.
2. Do it to both sides.
Detailed Explanation of these two rules:
1. You want to isolate (
or often worded “solve for”
) the desired variable. To do this you must identify
how other variables are attached to the variable you want isolated (alone on one side of the equal sign).
a. Undo addition and subtraction first. (Addition is opposite of subtraction)
b. Then, undo multiplication and division. (Multiplication is opposite of division)
c. Lastly, undo square (n
2) and square roots. (Squaring is the opposite of square root)
2. You must always do the same thing to everything on both sides of the equation, so if you multiply
everything on the right side by 5 you must also multiply everything on the left side by 5.
Examples:
same idea as…
PRACTICE
(Just like sports, games, arts, etc., you must practice to get good or you will likely be a loser of
the game.):
1. Solve for y in: x + y = z
2. Solve for Horse: Horse + Donkey =
Mule
3. Solve for m: D=m/V
4. Solve for b: a
2+ b
2= c
25. Solve for t: v
f= at + v
i6. Solve for t: d = (1/2)at
27. Solve for M: (I)(D)(K) = (O)(M)(G)
+ (R)(U)
Solve for a.
v
f= at + v
iSubtract v
ifrom both sides to get it away
from ‘a’. Then divide by ‘t’ on both sides
to isolate ‘a’.
v
f= at + v
i-v
i-v
iv
f– v
i= at
(v
f– v
i)/t = (at)/t
(v
f-v
i)/t = a so
a = (v
f-v
i)/t
Solve for m.
y = mx + b
Subtract b from both sides to get it away
from ‘m’. Then divide by ‘x’ on both
sides to isolate ‘m’.
y = mx + b
-b
-b
y-b = mx
(y-b)/x = (mx)/x
Fall Final Exam Review -
General Knowledge Questions:
Fill in the table below for the terms and units used in the Fall semester
20)
Of the 19 terms listed above which are not vectors?Name of Term
Symbol for
Term
Most Common
Unit for Term
Symbol for Unit
Explanation
1) Time
t
seconds
s
2) distance
3)
m or
ie:
m due
north
A distance with
the direction
traveled
4) speed
5)
ie:
m/s or
m/s due
north
A speed with the
direction traveled
6) Acceleration
(Metric units)
a
7) Acceleration
(English units)
a
8)
a
gm/s
29) Mass
kg
10) Force
Newton
11) Weight
N
12) Radius
m
13) Centripetal
velocity
v
c14)
a
cm/s
215)
F
cN
16) Frequency
Hertz
17)
per Minutes
Revolutions
RPM
18)
Seconds per
Revolution
A
Time (s)
D
ist
an
ce
(m
)
4 8 12 16
30 40
20 10
B
C
D
E
21)
How are Vectors and Scalars different from each other?Fall Final Exam Review -
General Knowledge Questions:
36)
Applying the rules for significant figures, what would 25.92 divided by 6.21 be?
37)
Above are 5 lines on a distance time graph find the slope for each line, putting all work in the data table tothe right
Slope=Rise
Run= ∆ y ∆ x
Fall Final Exam Review -
Veloctiy
Number Number of
Significant Figures Scientific Notation
30)
4506
31)
450.6
32)
0.0036
33)
10.000
34)
0.153800
35)
8900000
Conversion to do
Setup for conversion
Answer
22)
36 cm to m
36❑cmx 1m100cm=
¿¿m
❑
0.36m
23) 36 km to m
24) 36 mm to cm
25) 36 mm to km
26) 36 s to hr
27) 36 cm/s to km/hr
36cms x 1m 100cmx
1km 1000mx
3600s 1hr =
¿¿km
hr
1.3 km/hr
28) 36 km/hr to m/s
d t a) d t b) d t c) e) d t d t d) f) d t t v b) + -0 t v a) + -0 t v c) +
-0 v t
d) + -0 t v e) + -0 t v g) +
-0 v t
h) + -0 t v f) + -0
38)
If Ms. Cassady’s velocity stays the same but she cuts the distance she traveled in half what will happen to the amount of time it took to travel the new distance?39)
If Ms. Cassady’s travels the same distance but she doubles her velocity what will happen to the amount of time it took to travel the same distance?40)
In the table below describe what each of these d/t graphs representa) b)
c) d)
e) f)
41)
In the table below describe what each of these v/t graphs representa) b)
c) d)
e) f)
g) h)
42)
What does the slope of a d-t graph represent?43)
What does the slope of a v-t graph represent?44) If it takes 2 minutes and 5 seconds to cover
866 meters, what is the speed you are
going?
Fall Final Exam Review -
Acceleration
46)
What is the rate of change of velocity with respect to time called?47)
If your rate of acceleration is doubled but the initial speed and distance traveled remains the same what will happen to your final velocity?48)
If your final velocity and initial velocity remain the same but you double the time it takes to change your velocities, what will happen to your rate of acceleration?49)
What is happening if you solve for acceleration and you come up with a negative value?50)
If a person moves at a constant speed in a straight line what is that person’s acceleration? Why?51)
If a person moves at a constant speed around a circular track is that person accelerating? Why?52)
If a ball is dropped from a 6.5 m high balcony how fast will the ball be going as it strikes the ground?53)
If a ball is dropped from a balcony and it takes 1.2 s to strike the ground. a) How high is the balcony?b) How fast will the ball be going as it strikes the ground?
54)
If a ball is thrown straight down from a 6.5 m high balcony at 2.4 m/s, how fast will the ball be going as it strikes the ground?55)
A ball is thrown up into the air and it takes4.4 seconds to come back down to the throwers hand a) How long does it take for the ball to reach the highest point in its flight?b) What is the acceleration of the ball as it leaves the thrower’s hand?
c) What is the acceleration of the ball as it comes back down to where the thrower’s hand is about to catch it?
d) What is the acceleration of the ball as it reaches its highest point?
e) What is the speed of the ball as it reaches its highest point?
f) What is the speed of the ball as it leaves the thrower’s hand?
g) What is the speed of the ball as it comes back down to where the thrower’s hand is about to catch it?
56)
If you start from rest and accelerate to 15m/s in 3.6 seconds. What is his acceleration in m/s/s?57)
During a downhill ski race Lindsay Von started down the frictionless slope accelerating from rest at 6.8 m/s2.After 20 seconds on the course she crashed into Mr. Moriarty who was trying to get a picture with her. After running into him she came to a stop in 0.115 seconds.
a) What was her speed just prior to running into Mr. Moriarty?
b)
Fall Final Exam Review -
Force
58)
What are Newton’s three laws of motion?59)
If a person has a mass of 65kg on earth what would his mass be on the moon?60)
If a person has a mass of 65kg on earth what would his weight be on earth?61)
If a person has a mass of 65kg on earth what would his weight be on the moon?62)
If two people are having a tug of war and one of them exerts a force of 55N to the east what force would the other person have to exert if both people are to be in equilibrium?63)
Can an object in equilibrium be moving at a constant speed?64)
Can an object in equilibrium be accelerating?65)
What does the net force of a system in equilibrium have to be?66)
If a 65 kg parachutist is falling to the earth but the parachute exerts an upward force of 240 N. What is his acceleration as he falls?67)
Why does a flat sheet of paper takes longer to fall to the ground than a wadded up piece of paper?68)
If it takes 2.45 N to keep an object moving at a constant speed what must be true about the force it took to make the object start to move?69)
If it takes 2.45 N to keep an object moving at a constant speed what must be true about the force needed to make the object go faster?70)
If two 35 N forces act at 60º to each other on a 55 kg mass in a frictionless environment what is the acceleration of the mass?d)
c)
a)
89 cm
The ball takes 0.85 seconds to travel 1.2 m before it leaves the table. 1.2 m
?
Launched at 45˚ above horizon.
Fall Final Exam Review -
Motion in 2 Dimensions
72)
If a plane heads due east but the wind is blowing to the north, what direction will the plane actually go?73)
If a gator skier goes off a jump, and quickly estimates that she has a vx of 11 m/sand an upward vy of 14 m/s. How far horizontally will that skier land from where
she took off?
74)
If in the "Ball in the Cup" lab you measured the following data where would the placement of the cup on the floor need to be?75)
If a ball is launched at 45
above the horizontal with a velocity of
12 m/s at an angle of 35
above horizontal, what are the
v
xand v
yas
the ball leaves the launcher?
