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The
Philadelphia High School for Girls
Incoming/Rising Juniors
Summer
Science Assignment – 2009
You will be taking physics next year. Students often
have problems solving the equations. This summer assignment will help you
develop your equation solving skills. I have tried to design it so it will be
self explanatory. Inevitably there will be problems I have not anticipated. As
students email me I will add new hints or sample problems, update this
assignment and post it at
www.geocities.com/richguffanti
Objective:
Students will be prepared to show the steps needed to solve equations similar to
those below. Do not just memorize the answers!
Students will be tested on similar problems during their first week
back.
Directions:
a] Show the steps to solve the following equations.
b] Check your results with the answers below.
c] If you cannot figure out how to solve the equation copy your solution into an
email and send it to me at
RichGuffanti@Yahoo.com.
d] Submit the solutions to your physics teacher on the first day of
school.
General Strategy
Often students find solving problems with all letters
and no numbers confusing. Here is a strategy
a] Substitute numbers in the equation for all but the letter you are solving
for.
b] Then solve the problem.
c] Use this solution as a model for solving the original problem that had
no numbers. See Sample Problem A.
Given: S = D Solve for D S = Speed
T D = Distance
T = Time
Step 1: Substitute 3 for S and 5 for T
3 = D
5
Step 2: Multiply both sides by 5
3∙5 = D 5
Note: The 5’s on the right cancel.
5
3∙5 = D
Step 3: Substitute S for 3 and T for 5
ST = D
Given: S = D Solve for T S = Speed
T D = Distance
T = Time
Step 1: Multiply both sides by T
ST = D T Note: The T’s on the right cancel.
T
ST = D
Step 2: Divide both sides by S
ST = D Note: The S’s on the left cancel.
S S
T = D
S
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-- - - - - -- - - -
1 Given: a = F Solve for F a =
Acceleration
m F = Force
m = Mass
See Sample Problem A for a model.
2 Given: a = F
Solve for m a = Acceleration
m F = Force
m = Mass
See Sample Problem B for a model.
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-- - - - - -- - - -
3 Given: I = V Solve for V V = Voltage
R R = Resistance
I = Current
See Sample Problem A for a model.
4 Given: I = V
Solve for R V = Voltage
R R = Resistance
I = Current
See Sample Problem B for a model.
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-- - - - - -- - - -
Given: A = BC2
Solve for C
2
Step 1: Solve for C2: To
isolate the C2 Multiply both sides by 2/B
2 A = BC2 2
Note: the B and 2 on the right cancel.
B 2 B
2A = C2
B
__
Step 2: Take the square root of both sides: Note: √C2 = C
____
√2A/B = C
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-- - - - - -- - - -
5 Given: 25 = 17t2
Hint: Solve for t2 then
take the square root.
2 Do not multiply/divide until the end.
Solve for t. See Sample Problem C for a model.
6 Given: X = at2
Hint: Solve for t2
then take the square root.
2 X = Distance, a = Acceleration
Solve for t. See Sample Problem C for a model.
7 Given: KE = mV2
See Sample Problem C for a model.
2 KE = Kinetic Energy
m = Mass
Solve for V. V = Velocity
See Sample Problem C for a model.
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Given: _ Solve for L
A = 2π √L/B
Hint: Square both sides. Note (2π)2
= 4π2
Then solve for L
Step 1: Square both sides.
___ ___
A∙A = 2∙2π∙π
√L/B √L/B
A2 = 4π2
L
B
Step 2: Cancel 4π2/B
on the right by multiplying both sides by B/4π2
BA2 = L
4π2
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8 Given: _ T =
Time for the pendulum to swing back & forth once.
T = 2π √L/g L = Length of
the pendulum
g = The Acceleration of Gravity
Solve for L See Sample Problem D for a model.
9 Given: _ g =
The Acceleration of Gravity
3 = 2π √5/g
Solve for g Hint: Square both sides. Note (2π)2
= 4π2
10 Given: _ T =
Time for the pendulum to swing back & forth once.
T = 2π √L/g L = Length of
the pendulum
g = The Acceleration of Gravity
Solve for g See Sample Problem D for a model.
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-- - - - - -- - - -
11 Given: GMm mV2
M = Planet Mass
--- = -- m = Satellite Mass
R2 R R
= Satellite's orbit radius
V = Satellite's velocity
Substitute 2πR for
V G = Universal Gravitational Constant
T T = Satellite’s time for 1 orbit.
Hint: Divide both sides by m.
Solve for M Then solve for M.
Then Substitute 2πR
for V
T
Because all the symbols have physical meaning, it is
necessary to use subscripts. Below there are 15 symbols that need subscripts.
Ex: Vi = Initial Velocity
Vf = Final Velocity
Some students find the subscripts difficult or confusing. To help you with this
the problems have been paired. The first version looks like a standard Algebra
1 equation and the second version is the same equation using physics symbols.
The steps needed to solve both versions are the same. Problems 22 to 25 you
have to solve without this pairing.
Given: Vf -
Vi a = Acceleration
a = ------- Solve for Vf t = Elapsed Time
t Vi = Initial Velocity
Vf = Final Velocity
Step 1: Substitute A for a, B for Vf, C for Vi, D for t
Given: Solve for B
B - C
A = -------
D
Step 1: Multiply both sides by D AD = B - C
Step 2: Add C to both sides C + AD = B
Step 3: Substitute Vi + at = Vf
Vi for C,
a for A,
t for D,
Vf for B,
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-- - - - - -- - - -
Note: If you have trouble
with 12 - 19 see last page for common mistakes.
12 Given:
B - C
A = ------- Solve for C
D
13
Given: a = Acceleration
Vf - Vi t = Elapsed Time
a = ------- Solve for Vi Vi = Initial Velocity
t Vf = Final Velocity
Hint: Use 13 as a model.
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-- - - - - -- - - -
14 Given:
B - C
A = ------- Solve for D
D
15 Given: Vf - Vi
a = Acceleration
a = ------- Solve for t t = Elapsed Time
t Vi = Initial Velocity
Vf = Final Velocity
Hint: Use 15 as a model.
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16 Given: A = (B + C)D Solve for C
2
17 Given: X = (Vi
+ Vf)t X = Distance
2 t = Elapsed Time
Vi = Initial Velocity
Solve for Vf Vf = Final Velocity
Hint: Use 18 as a model.
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18 Given: A = (B + C)D Substitute B + ED for
C and solve for A
2
19 Given: X = (Vi
+ Vf)t Substitute Vi + at for Vf and
solve for X.
2
Hint: Use 19 as a model.
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-- - - - - -- - - -
Given:
AB + CD = AE + CF Solve for E
Step 1: Subtract CF from both sides. AB + CD = AE + CF
- CF CF
AB + CD - CF = AE
Step 2: Factor out C AB + C(D - F) = AE
Step 3: Divide by A B + C(D - F) = E
A
20 Given:
M1 & M2
= Masses of Object 1 & 2
M1V1
+ M2V2
= M1V1'
+ M2V2'
V1 & V2
= Velocities Before Collision
V1'
& V2' = Velocities After
Collision
Solve for V1'
Hint: Use Sample Problem F for a model.
M1
= A, & M2 = B
V1
= C, & V2 = D
V1'=
E, & V2'= F
Light
Given: 1/A = 1/B + 1/C f = Focal Length of a
Lens
Do = Distance to Object
Solve for A Di = Distance to Image
Hint: Multiply both sides by A B C
Step 1: Multiply both sides by ABC
ABC = ABC + ABC
A B C
BC = AC + AB
Step 2: A is a common factor on the right side.
BC = A(C + B)
Step 3: Divide both sided by (C + B)
BC = A
C + B
21 Given: 1/f = 1/Do + 1/Di
f = Focal Length of a Lens
Do = Distance to Object
Solve for f Di = Distance to Image
Hint: Multiply both sides by f Do Di
22 Given: 1/f = 1/Do
+ 1/Di f = Focal Length of a Lens
Do = Distance to Object
Solve for Do Di = Distance to Image
Hint: Multiply both sides by f Do
Di
23 Given: 1/f = 1/Do
+ 1/Di f = Focal Length of a Lens
Do = Distance to Object
Solve for Di Di = Distance to Image
Hint: Multiply both sides by f Do
Di
1 F = ma 2 m = F/a
3 V = IR
4 R = V/I
5 _______
t = √2●25/17 = 1.71
6 _____
t = √2X/a
7 ______
V = √2KE/m
8 L = gT2
4π2
9 g = 4π25
32
10 g = 4π2L
T2
11 M = RV2 = 4π2R3
G GT2
12 C = B - AD
13 Vi = Vf - at
14 B - C
D = -------
A
15 t = Vf - Vi
a
16 C = 2A - B
D
17 Vf = 2X - Vi
t
18 A = BD + ED2
2
19 X = Vit + at2
2
20 V1’
= V1 + M2
(V2 - V2’)
M1
21 f = DiDo
Di + Do
22 Do = fDi
Di - f
23 Di = fDo
Do - f
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