 # Document 220006

```Name: _____________________
Period: _____________________
Unit 6:S1
How to Solve Word Problems
Variable Sheet
Step 1: Use the Variable Sheet to Assign Variables
The units tell you what variable to use.
Variable
Units
Variable Name
Problem: A spring pulls with 30 N on a 6 kg metal cart.
Find the acceleration that occurs.
d
m (meters)
distance
v
m/s
velocity
t
sec
time
F = 30 N
m = 6 kg
a = ____
Always assign variables here!
This is your unknown. It MUST
Make sure your variables are in
STANDARD UNITS (convert centimeters
to meters, for instance). Most equations
will only work with standard units!
a
m/s
F
N (newtons)
force
m
kg
mass
p
kgm/s
momentum
W
J (joules)
work
Find an equation that contains all the variables in
Equations
Equations
d
t
v f − vi
W = Fd
v=
Problem: A spring pulls with 30 N on a 6 kg metal cart.
Find the acceleration that occurs.
F = ma
acceleration
Equation Sheet
Step 2: Use the Equation Sheet to Select a Formula.
F = 30 N
m = 6 kg
a = ____
2
a=
here: WITHOUT NUMBERS!
P=
t
F = ma
W
t
PE = mgh
p = mv
KE =
1
mv 2
2
Step 3: Put in the Numbers and Do the Math.
(See “Algebra Help”, if you need help with the math.)
Sometimes it is easier
to solve for the unknown
BEFORE putting
in the numbers.
Problem: A spring pulls with 30 N on a 6 kg metal cart.
Find the acceleration that occurs.
F = 30 N
m = 6 kg
a = ____
F = ma
30 = 6a
30 6a
=
6
6
a=5
Big Hint
Variable Sheet
Step 4: Make Sure the Answer Has the Correct Units.
In science, the answer is not completely correct without units.
Problem: A spring pulls with 30 N on a 6 kg metal cart.
Find the acceleration that occurs.
F = 30 N
m = 6 kg
a = 5 m/s2
F = ma
30 = 6a
30 6a
=
6 6
a = 5 m/ s2
The chart shows
that acceleration has
the units of m/s2.
list, where it will be easy to find if you
need it for another problem or step.
cstephenmurray.com
Variable
Units
Variable Name
d
m (meters)
distance
v
m/s
velocity
t
sec
time
2
a
m/s
F
N (newtons)
force
m
kg
mass
p
kgm/s
momentum
W
J (joules)
work
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acceleration
Name: _____________________
Unit 6:S1
Period: _____________________
How To Do the Algebra
Addition and subtraction are notated the same in physics equations
as in basic mathematics, but not so for multiplication or division.
Notation
Two letters or
numbers next to
each other show
multiplication.
F = ma = m x a
A letter below
another letter
means division.
Correct, but confusing
Still correct, but less confusing
2
PE = (25)(10)(5)
PE = (25kg )(10m/s )(5m )
Equations are Equal
Not Equal
d
= d ÷t
t
Use units to assign variables and to be sure you are using standard units (meters
instead of centimeters, for instance), then put in just the numbers—no units! Make
sure, though, to put the units back on the answer at the end.
Do Not Keep Units
Equal
v=
The equal sign means that both sides are equal. Therefore, anything done
to one side must be done to the other or the equation is no longer equal.
35 = v f − 10
35 = v f − 10 + 10
Equal
35 = vf −10
Still Equal
35 +10 = vf −10 +10
The following shows only the four most common algebraic operations.
There are many more. They will be presented to you as necessary.
The Algebra
Division Moves Multiplication
Multiplication Moves Division
Variables
Numbers
Variables
Numbers
F = ma
F ma
=
m m
F
=a
m
35 = 7a
W
t
W
Pt = t
t
Pt = W
W
3
W
12(3) =
3
3
36 J = W
35 7 a
=
7
7
5m/s 2 = a
P=
12 =
Variables
Numbers
Variables
Numbers
Fnet = F1 + F2
15 = F1 + 6
∆V = V f − Vi
24 = V f − 8
Fnet − F2 = F1 + F2 − F2
15 − 6 = F1 + 6 − 6
∆V + Vi = V f − Vi + Vi
24 + 8 = V f − 8 + 8
Fnet − F2 = F1
9 N = F1
∆V + Vi = V f
32m/s = V f
operations: Parenthesis; Exponents; Multiply; Divide; Add; Subtract.
Order Matters!
Correct
Incorrect
2(4 − 2) + 3 = 2(2) + 3 = 4 + 3 = 7
2(4 − 2) + 3 = 2(2) + 3 = 2(5) = 10
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Name: _____________________
Period: _____________________
A bike moves 30 m in 5 seconds.
Calculate the speed of the bike.
Variables:
Unit 6:S2
Practice with Word Problems
A car starts at rest. After 4 seconds it is going 24 m/s.
What was the car’s acceleration?
Solve:
Variables:
Equation:
Solve:
Equation:
A 12 N force pushes on a 3 kg object.
Find the object’s acceleration.
Variables:
A 10 N force pushes for 3 m.
How much work was done on the object?
Solve:
Variables:
Equation:
Solve:
Equation:
Using the same procedure as above,
solve the following word problems.
Challenge problems:
A person walks 240 meters at 3 m/s. How long did it take?
A bike goes 10 m/s for 20 seconds. Calculate how far the bike
traveled.
A 2 kg object is moving 12 m/s. How much momentum does
the object have?
Grandma lives 120 miles away. Dinner is at 5 p.m. The speed
limit is 60 mph. What time do you need to leave to be on time?
If a person pushes with 3 N and does 18 J of work. How far did
they push the object?
Position vs. Time
50
45
40
0:00.0
Constant Speed
Position (m)
0:04.0
35
30
25
20
15
10
5
0
0
2
4
6
8
10
12
14
16
18
20
Tim e (sec)
How fast is Nigel moving, if he is at constant speed?
Find the slope of the graph (including units).
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Name: _____________________
Period: _____________________
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