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Midterm 2
1
Nov 5, 2002
PHY131 Midterm Exam II
Name/ID:________________
________ Section:______
SOLUTIONS
Vs.
A
– November 5, 2002
Prob 1
Prob 2
Prob 3
Prob 4
TOTAL
3
×
OK:
4
×
OK:
1.5
×
NOK:
2
×
NOK:
NET:
NET:
Max. 29 points
Max. 30 points
(Out of 90)
Formulae:
Work done by a force
F
over a trajectory:
W
≡
∫
F
⋅
d
x
Examples of forces:
Force of Gravity (on mass
m
near sealevel)
F
G
=
mg
(–
j
)
(downwards)
(
g
=
GM
E
/
R
E
2
= 9.8 m/s
2
)
Force of Gravity (between masses
M
and
m
):
F
G
= (
GMm/r
2
)(–
r
)
(attractive)
±
Force of a spring (spring constant
k
):
F
S
= –
k
x
(opposes displacement
x
)
Rocket Thrust:
F
T
= –
v
gas
dm
/
dt
Friction:
F
f
=
µ
N
(opposes motion)
(
=coef. of friction;
N
=normal force)
Kinetic Energy
K
:
K
≡
½
mv
2
WorkKinetic Energy relationship (using
Σ
F
i
=
m
a
)
Σ
W
i
=
∆
K
≡
K
f
–
K
i
Potential Energy due to a conservative force
F
:
∆
U
F
≡
U
f
–
U
i
=
–W
F
Potential Energy of Gravity (mass
m
near sea level):
U
=
mgy
(
U
(
y=
0) = 0)
Potential Energy of Gravity (of masses
M
and
m
):
U
= –
GMm
/
r
(
U
(
r=
∞
) = 0)
Potential Energy of a spring (spring constant
k
):
U
= ½
kx
2
(
U
(
x=
0) = 0)
Mechanical Energy
E
:
E
≡
K +
Σ
U
i
WorkEnergy relationship:
(
W
NC
: work by nonconservative forces)
W
NC
=
∆
E
≡
E
f
–
E
i
Momentum
p
of mass
m
with velocity
v
:
p
≡
m
v
Force and its consequences:
Σ
F
i
=
m
a =
d
p/
dt
J
≡
∫Σ
F
i
dt
=
∆
p
≡
p
f
– p
i
Conservation of Momentum if (
Σ
F
i
)
ext
= 0
p
i
=
p
f
Angle
θ
(in radians):
≡
s
(=arc length)
/R
Angular velocity
ω
; angular acceleration
α
:
≡
v
TAN
/R
;
≡
a
TAN
/R
Rotational Kinematics for
CONSTANT
:
=
0
+
t;
=
0
+
0
t
+ ½
t
2
;
2
=
0
2
+ 2
(
–
0
)
Torque
τ
by a force
F
attaching at a distance
R
from a rotation axis
τ
≡
R
×
F
(vector product):
magnitude:
τ
=
RF
sin
RF
direction: Righthand Rule
Angular Momentum
L
:
L
≡
R
×
p
(vector product) =
I
ω
Moment of Inertia
I
:
I
≡
Σ
m
i
R
i
2
=
∫
R
2
dm
Parallel Axes Theorem: axis // to CM axis at distance
d
:
I
d
=
I
CM
+
md
2
Perpendicular Axes Theorem:
z
axis
⊥
planar object:
I
z
=
I
x
+
I
y
Torque and its consequences:
Στ
i
=
I
α
=
d
L
/
dt
Conservation of Angular Momentum if (
Στ
i
)
ext
= 0
L
i
=
L
f
Kinetic energy of rotation
K
rot
:
K
rot
= ½
I
2
Equilibrium:
Σ
F
i
= 0;
Στ
i
= 0
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View Full DocumentMidterm 2
2
Nov 5, 2002
1. MULTIPLE CHOICE QUESTION – Fill the circles in front of all statements below that are
. MULTIPLE CHOICE QUESTION – Fill the circles in front of all statements below that are
correct.
A crate of mass
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 Spring '03
 Rijssenbeek

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