Physics 2053C – Fall 2001
Review for Final Exam
http://www.hep.fsu.edu/~tadams
Dec. 8, 2001
Prof. Todd Adams,
FSU Department of Physics
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Important Topics
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Kinematics
Forces/Newton’s Laws
Energy/Momentum Conservation
Ideal Gases/Heat
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Variable/Quantity/Units
t
x
v
a
F
E
P
time
distance
velocity
acceleration
force
energy
power
s
m
m/s
m/s2
N = kg.m/s2
J = N .m
W = J .s
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Kinematics
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Position
Velocity – rate of change of position
Acceleration – rate of change of
velocity
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Constant acceleration
Constant velocity
a=0
Constant position
v = 0, a = 0
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Equations of Motion
x = x0 + v0t + ½at2
v = v0 + at
v2 = v02 + 2a(x – x0)
x = position
x0 = initial position
v = velocity
v0 = initial velocity
a = acceleration
t = time
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Forces
Force due to gravity
 Normal force
 Force due to friction
 Tension
 Buoyancy
 External force (e.g. a push)
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Gravity
• acceleration due to gravity (g = 9.80 m/s2)
• force due to gravity F = mg
• Weight = force due to gravity
Newtons
• which direction???
• Also, F = G.(m1m2)/r2
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Types of Energy
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Kinetic
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K = ½mv2
Potential
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Linear
Rotational
Gravitational
Spring
Internal Energy
Heat
Work
U = mgh
U = ½kx2
Q = mcT
W = Fdcos
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Ideal Gas Law
PV = nRT
P = pressure (atm, bar, N/m2)
V = volume (m3)
n = # of moles
R = gas constant
T = temperature (K)
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How to solve FORCE problems
1)
Read the problem.
(identify what you do and don’t know, look for “hidden” knowledge)
2)
Draw a free-body diagram
(identify all forces acting upon object)
3)
Add all forces in one direction together (x?)
F = F1 + F2 + F3 + …
(determine sum of forces, maybe Fnet = 0 or Fnet = ma)
4)
Add all forces in other direction together (y?)
(determine sum of forces, maybe Fnet = 0 or Fnet = ma)
5)
Solve for what you don’t know
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Sample Force Problem
T2
M1
T1
M2
M1 = 20.0 kg
M2 = 10.0 kg
 = 0.3
The boxes are not moving.
1) What is the value of T1?
2) What is the value of T2?
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M1 = 20.0 kg
M2 = 10.0 kg
 = 0.3
Sample Force Problem (cont)
T1
T2
M1
T1
M2
M2
Fg
F = T1 – Fg = 0
T1 = Fg
T1 = M2g = (10.0 kg)(9.80 m/s2)
T1 = 98.0 N
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M1 = 20.0 kg
M2 = 10.0 kg
 = 0.3
Sample Force Problem (cont)
T2
Ffr
FN
M1
T2
M1
T1
T1
M2
Fg
Fy = FN – Fg = 0
FN = F g
FN = M1g = (20.0 kg)(9.80 m/s2)
FN = 196.0 N
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M1 = 20.0 kg
M2 = 10.0 kg
 = 0.3
Sample Force Problem (cont)
T2
Ffr
FN
M1
T2
T1
M1
FN = 196.0 N
T1
M2
Fg
Fx = T1 – T2 – Ffr = 0
T2 = T1 - Ffr
T2 = 98.0 N – (0.3)(196.0 N)
T2 = 39.2 N
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Sample Force Problem (cont)
T2
M1
T1 = 98.0 N
T2 = 39.2 N
T1
M2
M1 = 20.0 kg
M2 = 10.0 kg
 = 0.3
What if the boxes are moving with constant velocity?
What if the boxes are accelerating at a = 2.2 m/s2?
What if we remove T2?
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How to Solve ENERGY Problems
1)
Identify types of energy
Kinetic?
Gravitational Potential?
Spring Potential?
Heat?
Internal Energy?
Work?
2)
3)
Identify initial and final conditions
Find unknown quantities:
W = K + U
(if W  0)
Ki + Ui = Kf + Uf (if W = 0)
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Sample Energy Problem
A 25 kg block is released from rest 5.5 m up a frictionless
plane inclined at 30o. The block slides down the incline
and along a horizontal surface. The horizontal surface
has a coefficient of static friction of 0.32.
5m
What is the velocity of the block at the bottom of the
incline?
How far along the horizontal surface will the block slide?
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Sample Energy Problem (cont)
A
5m
B
C
What kind of energies are present?
Kinetic energy
Gravitational potential energy
Work done by friction
What is the energy at A?
EA = KE + PE = 0 + mgh = mgdsin = (25 kg)(9.80 m/s2)(5 m)(sin 30o)
EA = 612.5 J
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Sample Energy Problem (cont)
A
5m
B
C
What is the energy at B?
EB = EA = 612.5 J
What happens to the energy as the box goes from A to B?
What is the velocity at B?
EB = KE + PE = ½ mvB2 + 0
vB = 7.0 m/s
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Sample Energy Problem (cont)
A
5m
B
C
What happens to the energy as the box goes from B to C?
What is the energy at C?
EC = 0.0 J
How far does the box slide?
W = KE + PE
W = (0.0 J – 612.5 J) + 0 J
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.
Wfr = Ffrd = FNd
Wfr = mgd
W = Wfr
.
-612.5 J = (0.32)(25 kg)(9.8 m/s2)d = (78.4 N)d
d = (612.5 J)/(78.4 N) = 7.81 m
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How to Solve IDEAL GAS Problems
PV = nRT
1) Identify initial and final conditions
2) Take ratio
P1V1 n1RT1
=
P2V2 n2RT2
3) Cancel anything which is constant
4) Solve for what you don’t know
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Sample Problem
V = 10 m/s
V = 18 m/s
M = 250 kg
F = 2500 N
A
30 m
25 m
B
C
0 to 30 m/s in 20 s
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What are the forces on the motorcycle as it accelerates (A)?
What are the forces on the motorcycle as it moves at constant speed (B,C)?
How far does it travel while accelerating from rest to 30 m/s?
What is the kinetic energy at points A, B, C?
How much work is done by motorcycle?
How much work is done by friction getting to A, B, C?
What are the forces on the object as it moves upward from A to B?
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