I. A cart attached to a spring is displaced from equilibrium and then released. A graph of the cart’s displacement as a function of time is shown below.

a) Complete the equation below that describes the cart’s position as a function of time, including all numeric quantities you can know.

x(t)a = b) The experiment in part (a) is changed; the cart is replaced by a cart that is 1.5 times as massive, 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). 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 quantities you can know.

period =

frequency =

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.

NT9A‐CRTll:DIsPLACEMENTVS.TIMEGRAPH― DIsPLACEMENT,VELOCITY,&AccELERAT10N

A cart attached to a spring is displaced from equilibrium and thenreleased. A grailh of displacement as a function of time for the cart isshown below. There is no friction.

4

2

0

-2

(a) What is the mathematical expression for the displacement of the cart as a function of time?

Explain.

(b) What is the mathematical expression for the velocity of the cart as a function of time?

ExpIain.

(c) What is the mathematical expression for the acceleration of the mass as a function of time?

Explain.

+x

NT9A‐CRTll:DIsPLACEMENTVS.TIMEGRAPH― DIsPLACEMENT,VELOCITY,&AccELERAT10N

A cart attached to a spring is displaced from equilibrium and thenreleased. A grailh of displacement as a function of time for the cart isshown below. There is no friction.

4

2

0

-2

(a) What is the mathematical expression for the displacement of the cart as a function of time?

Explain.

(b) What is the mathematical expression for the velocity of the cart as a function of time?

ExpIain.

(c) What is the mathematical expression for the acceleration of the mass as a function of time?

Explain.

Time, s

6 3 0

-3 -6

x(t)

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:

Object Mobject Distance from center A – disc 3.0 kg centered B – hoop 2.0 kg centered C – large sandbag 3.0 kg R/2 D – small sandbag 1.5 kg 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) 30/R

b) 30R

c) 3R/10

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

R

A

v

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

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

mass m

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.

11) Two sinusoidal waves,y1(x,t) = (0.6 m)sin(πx/3 − 30t) and y2(x,t) = (0.6 m)sin(πx/3 +

30t), travel on a 18 m stretched string which is clamped at each end. Including the nodes at the ends, how many nodes appear in the resulting standing wave?

a) 4 b) 8 c) 3 d) 7 e) 5

12) A pipe of length L is open at both ends, and a sound source is brought nearby that sets up the standing wave pattern shown, where the wavelength is 30 cm.

Assuming that the speed of sound in air is 340 m/s, which of the 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

TIPERS

E3-CRT17= Prpe Open er Born Enos-SouND FneouENcy, WIveLENGTH, AND VelocrwA pipe of length L is open at both ends. Sound is created in the pipe at four different frequencies. The diagramshows the location of nodes (N) and antinodes (A) in the pipe for the four different modes. The table to the righthas an entry for wave speed of the first overtone, and an entry for the wavelength of the second overtone.Use the given information to find the length L of the pipe. Then complete the table of frequencies,wavelengths, and waye speeds for the four modes.

Fundamental

Frequency Wavelength Wave speed

340耐s

40cm

トーーーーーー L=

御鳳

淵1

Third overtone(Fourth harmonic)

ExplE」 nyourreasoning.

Copyright @ 2015 Pearson Education, lnc.420

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.