DIsPLACEMENT,VELOCITY,&AccELERAT10N
NT9A‐ CRTll:DIsPLACEMENTVS.TIMEGRAPH―
from
equilibrium
is
and then
to
displaced
a
spring
A
cart
attached
DIsPLACEMENT,VELOCITY,&AccELERAT10N
NT9A‐ CRTll:DIsPLACEMENTVS.TIMEGRAPH―
released. A grailh of displacement as a function of time for the cart is
A cart attached to a spring is displaced from equilibrium and then
shown below. There is no friction.
released. A grailh of displacement as a function of time for the cart is
I.
A
cart
attached
tofriction.
a spring is displaced from equilibrium and then
is no
shown below. There
released. A graph of the cart’s displacement as a function of time is
shown below.
4
64
2
32
0
00
-2
-3-2
-6
(a) What is the mathematical expression for the displacement of the cart as a function of time?
a) Complete
the equationexpression
below thatfor
describes
the cart’s position
as a as
function
of time,
including
(a) What
is the mathematical
the displacement
of the cart
a function
of time?
all numeric quantities you can know.
Explain.
Explain.
x(t) =
a
(b) What is the mathematical expression for the
velocity of the cart as a function of time?
b) The
experiment
in partexpression
(a) is changed;
thevelocity
cart is replaced
by as
a cart
that is 1.5
times as massive,
(b) What
mathematical
for the
is the
of the cart
a function
of time?
and the spring is replaced by one with a spring constant that is six times larger. The new cart is
released from a position initially that is one-third as far from equilibrium as it was in part (a).
ExpIain.
What will
the period, frequency and amplitude of the oscillation be in this case? Complete the
equation below that describes the cart’s position as a function of time, including all numeric
ExpIain.
quantities you can know.
(c) What is the mathematical expression for the acceleration of the mass as a function of time?
(c) What is the mathematical expression for the acceleration of the mass as a function of time?
period =
Explain.
frequency =
Explain.
amplitude =
x(t)b =
c) Use a dashed line to draw the position vs time graph from part (b) on the axes below. x(t)a
from part (a) is shown for reference.
x(t)
Time, s
III. A platform of radius R (in meters) can rotate at a constant angular speed.
The friction in its bearings is negligible.
You conduct an experiment during which you drop an object onto the rotating platform, and you
measure the angular speed of the system after you drop the object. You do this experiment four
times, changing the object each time. The objects you use are listed below:
A
B
C
D
–
–
–
–
Object
disc
hoop
large sandbag
small sandbag
Mobject
3.0 kg
2.0 kg
3.0 kg
1.5 kg
Distance from center
centered
centered
R/2
R
a) Rank the final angular speeds - ωA, ωB, ωC, and ωD - after each of the experiments A, B, C,
and D from LARGEST to SMALLEST. Assume the platform is rotating at the same initial speed
in each case before the object is dropped. Explain your reasoning.
LARGEST to SMALLEST rankings of ω:
______
______
______
______
b) What assumptions are you making in part (a) that is not already mentioned in the problem
statement?
c) After you finish this experiment with object D, you increase the angular speed of the platform
until ωsystem = 3 rad/s and the sandbag slides off. If it takes 1.5 seconds for the sandbag to hit the
floor, find how far away it lands horizontally from the rotating platform in terms of R. What
assumptions are you making?
Assumptions:
4) The diagrams shown below show forces of magnitude F applied to an equilateral triangular
block of uniform thickness. In which diagram is the block in static equilibrium?
5) A wheel of radius R (in SI units) rolls at a constant speed of v = 3 m/s. Which of the
following expressions describe the angular displacement of the point A after 10 s?
A
a) 30/R
b) 30R
c) 3R/10
v
R
d) 3/(10R)
e) R/30
6) A ruler, balanced at its center point, has two coins placed on it as shown below. One coin, of
mass M1, is placed at the zero mark. The other, of mass M2, is placed at the 4.7 inch mark.
The ruler is perfectly balanced. Which of the following is correct?
a) M2 = 4.7 M1
b) M2 = (4.7/3) M1
c) M2 = (3/4.7) M1
d) M2 = (1.7/3) M1
e) M2 = (3/1.7) M1
7) A block of wood of length L=0.21 m, width w=9.5 x 10-2 m, and height h=5.9 x 10-2 m is just
barely immersed in water by placing a mass m on top of the block. The density of the wood is
ρwood=390 kg/m3 and the density of water is ρwater=1000 kg/m3. The value of m is closest to
a) 0.36 kg
b) 0.58 kg
mass m
c) 0.72 kg
d) 1.2 kg
e) 1.6 kg
8)
In the four cases below Tlow refers to the same temperature in each case, and Thigh refers to
the same higher temperature in each case. Rank the following quantities from LARGEST to
SMALLEST:
1: the work done on one mole of a monatomic ideal gas in an adiabatic process going
from temperature Tlow to a higher temperature Thigh
2: heating of one mole of a monatomic ideal gas during an isovolumetric process going
from temperature Tlow to a higher temperature Thigh
3: heating of one mole of a monatomic ideal gas in an isobaric process going from
temperature Tlow to a higher temperature Thigh
4: the internal energy change of one mole of a monatomic ideal gas in an isothermal
process at Thigh
a) 3 > 2 = 1 > 4
b) 2 = 3 > 4 > 1
c) 1 = 2 > 3 > 4
d) 4 > 2 = 3 = 1
e) 2 > 3 = 1 > 4
9) In a cyclic process, a real heat engine takes in 400 J at a 900 K reservoir and deposits 200 J
into a 300 K reservoir. What is the absolute value of the TOTAL entropy change of the two
reservoirs?
a) (2/9) J/K
b) (1/3) J/K
c) (1/2) J/K
d) (10/9) J/K
e) (2/3) J/K
10)
One mole of an ideal gas is compressed isothermally in an ideal engine. During the
compression, N J of work is done on the gas and no work is done by the gas. Which of the
following statements is TRUE?
a) By the 2nd law, more than N J of energy must leave the gas through cooling.
b) By the 1st law, exactly N J of energy leaves the gas through cooling.
c) The compression is isothermal so there is no heating or cooling.
d) By the 1st law, exactly N J of energy enters the gas through heating.
e) By the 2nd law, more than N J of energy must enter the gas through heating.
TIPERS
11)
Two sinusoidal waves,y1(x,t) = (0.6 m)sin(πx/3 − 30t) and y2(x,t) = (0.6 m)sin(πx/3 +
E3-CRT17= Prpe Open er Born Enos-SouND FneouENcy, WIveLEN
30t), travel on a 18 m stretched string which is clamped
at length
each end.
Including
the nodes at
A pipe of
at both ends. Sound is created in the pipe at
L is open
the ends, how many nodes appear in the resulting standing
location of nodes (N) and antinodes (A) in the pipe for the fou
shows the wave?
has an entry for wave speed of the first overtone, and an entry for the wavel
Use the given information
a)
4
b)
8
c)
3
d)
7
e)
5
to find the length L of the pipe. The
wavelengths, and waye speeds for the four modes.
Freque
Fundamental
御鳳
淵1
12)
A pipe of length L is open at both ends, and a sound source
Third overtone
is brought nearby that sets up the standing wave pattern
(Fourthshown,
harmonic)
where the wavelength is 30 cm.
ト
ーーーーーー
Assuming that the speed of sound in air is 340 m/s, which of the
ExplE」 nyourreasoning.
following statements is TRUE?
Harmonic shown
Length of pipe, L, in cm
a)
3rd
60
b)
4th
120
c)
3rd
120
d)
4th
60
e)
5th
75
L=
13)
Standing on the platform, you hear a frequency of 444 Hz from the whistle of an
approaching train. After the train passes, the observed frequency of the whistle is 364 Hz.
Assuming the speed of sound in air is 340 m/s, which of the following is closest to the train's
speed?
a) 34 m/s
b) 80 m/s
c) 42 m/s
d) 67 m/s
e) 26 m/s
14)
In the figure shown, the diagram on the left shows a thick rope (not
massless) of uniform density hanging vertically from an oscillator that
is turned off. When the oscillator is on and set at a certain frequency,
the rope forms the standing wave shown in the diagram on the right. P
and Q are two points on the rope.
Which of the following explanations is supported by the standing wave
shown in the diagram on the right?
a) Due to the weight of the rope, the mass density at point P is greater
than it is at point Q, so the wave travels faster at the top than it
does at the bottom. Since the frequency is constant, the
wavelength is smaller at the bottom.
b) Even though the rope is massive, the medium is uniform so the wave speed is uniform.
The wavelength changes along the rope because the frequency decreases along the rope.
The rope gets harder to shake.
c) Due to the weight of the rope, the tension at point P is greater than the tension at point Q,
so the wave travels faster at the top than it does at the bottom. Since the frequency is
constant, the wavelength is smaller at the bottom.
d) Due to the weight of the rope, the mass density at point P is greater than it is at point Q,
so the wave travels slower at the top than it does at the bottom. Since the frequency is
constant, the wavelength is longer at the bottom.
e) Due to the weight of the rope, the tension at point P is less than the tension at point Q, so
the wave travels slower at the top than it does at the bottom. Since the frequency is
constant, the wavelength is smaller at the bottom.