161 Spring 2015 Test3A Name:_________________________________________
No cell phones or electronic devices (except scientific calculators).
No graphing calculators.
1 m =102 cm
1 kg = 103 g
1 kN = 103 N
1 J = 1 N. m
1 N = 1 kg.m/s2
g =10 m/s2
G=6.67x10-11 N.m2/kg2
P0=1.0x105 Pa
1
a xt 2
2
x = x0 + v 0 x t +
ar =
vx2 − v02x = 2ax ( x − x0 )
v2
r
Vsphere =
v x = v0 x + a x t
4 3
πr
3
x − x0 =
Vcyl = πr 2 h
r
r
r
f = µN = µFn
Ei + W = E f
W = Fd cosθ = Fparalleld
GPE = mgh
TKE =
1
mv 2
2
SPE =
Fx = −
∂U
∂x
r r
∆U = −W = − F ⋅ dx
Power =
∆E
∆t
v = rω
α=
ω=
∫
√ Fspring = kx
1 2
kx
2
RKE =
sin s = rθ
dθ
dt
a=
∫ xdm
∫ dm
dv
dt
v=
dx
dt
x1m1 + x2 m2
m1 + m2
I = r 2 dm
I = I CM + MD 2
xCM =
L = Iω
L = mvr sin φ
p = mv
∆L
F
=Y
A
L0
I point−mass = MR2
I thin−ring = MR2
I disk =
1
MR 2
2
I rod =
1
ML2
12
I sphericals hell =
I sphere =
I rod =
2
MR 2
3
P=F/A
ρ=
M
V
! 2#$ &
1
ML2
3
I thickring =
Fbuoyant = ρ f gV f
UG = −
M
A
xCM =
(
1
2
2
M R outer
+ R inner
2
A1v1 = A2 v2
σ=
%
2
MR 2
5
1
Iω 2
2
∫
a = rα
dω
dt
1
( v 0 x + v x )t
2
Gm1m2
r
)
I plate =
1
M (a 2 + b 2 )
12
= constant
FG =
%change =
Gm1m2
r2
change
× 100%
initial
A Taco Bell ™ employee is running to the left. A fellow employee throws a soft taco
at his face. Just before impact with his face the taco is travelling right with identical
speed. We are not told if the collision is elastic, inelastic, or perfectly inelastic.
1a) During the collision of the taco with the face, which object experiences the larger
force? Circle the best answer.
The taco
The employee
Same force
Impossible
to determine
1b) During the collision of the taco with the face, which object experiences the larger acceleration (magnitude only)? Circle
the best answer.
The taco
The employee
Same acceleration
magnitude
Impossible
to determine
1c) During the collision of the taco with the face, which object experiences the larger change in momentum (magnitude
only)? Circle the best answer.
The taco
The employee
Same change
in momentum
magnitude
Impossible
to determine
**2) You are standing perfectly still and then take a step forward. Before the step, your momentum was zero, but afterward
you have some momentum. Is the principle of conservation of momentum violated in this case? Explain your answer.
**3) Explain what, if anything, is wrong with the following calculation of final
angular speed:
A rigid rod of length L and mass m is attached to a frictionless pivot at one end.
A student determines the moment of inertia is given by ' )* . The ruler is
(
then held parallel to the ground and released from rest. The student determines
the magnitude of the angular acceleration is + (,
. Finally, the student uses the
%
kinematics equation !- !. 2+∆. They set !. 0 and ∆ 90° rad
(%,
to find !- 6
.
Before
After
!-
A uniform plank (thick black line) with mass M and length L is
supported by a frictionless pivot and a cable. The cable has length L
and is attached to a point on the plank L/5 from the right end. The
small gap between the right end of the plank and the building is
negligible compared to L. A person of mass M/4 walks the plank
starting from the left end (x=0). Scratch paper at end of the test.
Figure not
to scale
x
**4a) Determine a mathematical expression for the tension in the
cable in terms of M, g, x, and L.
*4b) Sketch a plot of the tension in the cable as a function of x (the
distance from the left end of the plank). Use the graph shown
below.
***4c) Determine the magnitude of the reaction force at the pivot
when x = L. Answer as a number with 3 sig figs times Mg.
4a
T
1.0 Mg
0.5Mg
x
0.5L
4c
1.0L
A non-uniform, thin rod has a mass distribution that is given by 789 : ; . Here n is
unknown number greater than 1 and a is an unknown constant. This density assumes the
coordinate system is aligned with the left end of the rod as shown in the figure. The rod has
total length L =1.00 m and mass m=0.100 kg. By balancing the object, you determine the
center of mass is 14.29 cm from the right end of the rod (shown by the black x in the figure). Figure not to scale.
****5) Determine the power of n. Express your answer as a decimal with
3 sig figs.
5)
A block of mass m is tied to a frictionless pulley with the same mass m and radius r. The string is
essentially massless and inextensible. The pulley is not a uniform disk. The moment of inertia of the
pulley is given by kmr2 where k is an unknown constant. You release the system from rest and observe
the block falls 2.00 m in 0.800 sec. For this problem, assume g=10 m/s2 to make the math a little
easier.
*****6) Determine the constant k of the moment of inertia. Write your answer as a decimal with 3 sig
figs.
6)
Before
A ball of clay of mass m hits and sticks to the edge of a disk of radius
R and mass m. The disk was initially at rest just before impact. Just
before impact the clay travelled tangent to the bottom of the disk.
The disk is free to rotate about a fixed axis through a point located at
the top. After the collision, the clay sticks to the disk and the two
objects swing together up to a maximum angle of 60.0°.
After
θ
7a) Between the stages shown (just before the collision and when the
disk/clay has swung up to max height), which of the following are
conserved for the clay/disk system. Circle the best answer:
Linear
Momentum
Angular
Momentum
The combination of linear
and angular momentum
Translational
Kinetic Energy
Rotational
Kinetic Energy
Gravitational
Potential Energy
The combination of
TKE, RKE, and GPE
None of the
others apply
**7b) What is the moment of inertia of the disk about the axis
shown? Answer in terms of m and R.
****7c) Determine the speed of the clay just before impact. Answer
as a number with 3 sig figs times √<=.
7b
7c
I made a list of Samuel L. Jackson pseudo-quotes by replacing a key part of each movie quote with physics terms.
They should’ve hired me as a script-writer for sure. That said, match the pseudo-quote to the appropriate movie
and earn 1 point of extra credit. You must correctly match all four to get the credit.
To Ben Affleck’s character:
“What I want is my morning
back. I need you to give me back
the elapsed time for the hanging
mass to fall a distance h.”
Snakes on a Plane
SLJ: “I want you to go in that
bag and find my wallet”
P: “Which one is it?”
SLJ: “It’s the one that says ‘If
there’s no net external torque on
the system (or if the net external
torque acts for a negligible
amount of time) we know angular
momentum is conserved.’ ”
Pulp Fiction
“Angular momentum. When you
absolutely, positively need to kill
the soul of every student in the
room; accept no substitute.”
Jackie Brown
“No more blocks on the inclined
plane.”
Changing Lanes
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