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PHYS 101 Exams
UIUC
Instructor
Unit 3: Homework / Homework / Homework / Schulte, Elaine

Student

Homework: Hour Exam 3
Deadline: 100% until Thursday, November 21 at 8:00 AM

Problems Print Assignment View
Standard Exercise

The Mass and The Spring
1 2 3

The Mass and The Spring

Standard Exercise

The Pendulum

Standard Exercise

The Hydraulic Lift

Standard Exercise

Archimedes and the King's Crown

Standard Exercise

The Garden Hose

Standard Exercise

The Guitar String
A block of mass m = 5 kg is connected to a vertical spring as shown in the diagram. When the mass is at rest, the spring stretches y0 = 5 cm beyond its natural length lspring = 14 cm.

Standard Exercise

The Intense Speakers

1) For this system, in the vertical configuration, y0 = 5 cm gives the equilibrium position. False True
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The Speeding Car

Standard Exercise

Heating a Metal Strip

Solution: This question asks about the effect of gravity on the equilibrium position of a spring. Remember that the effect of a gravitational force is to stretch the spring an amount Δx = mg/k. This stretch in the spring represents an offset in the natural (horizontal) equilibrium position of the spring. While the question is strangely worded, the answer is true, the change in position y0 = 5 cm represents the new equilibrium position.

Standard Exercise

Compressing a Gas

2) You pull straight down on the block with a force F = 147.15 N. How far does the spring stretch if the spring constant is k = 980 N/m? y = 15 cm y = 5 cm y = 45 cm
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Solution: This is just a question on the nature of the restoring force of a spring. Remember F = -kx so x = F/k = F = (147.15 N)/(k = 980 N/m)/100 = 15 cm

3) With what frequency will the block oscillate? f = 2.2 s-1 f = 0.011 s-1 f = 8.1 × 10-4 s-1 f = 14 s-1 f = 0.071 s-1
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Solution: This is a question about the natural frequency of harmonic motion. For a spring the angular frequency for the oscillation is ω2 = k/m. We know both k and m so we can substitute directly recalling f = ω/(2 π) = 2.2 s-1.

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PHYS 101 Exams
UIUC
Instructor
Unit 3: Homework / Homework / Homework / Schulte, Elaine

Student

Homework: Hour Exam 3
Deadline: 100% until Thursday, November 21 at 8:00 AM

Problems Print Assignment View
Standard Exercise

The Pendulum
1 2 3 4

The Mass and The Spring

Standard Exercise

The Pendulum

Standard Exercise

The Hydraulic Lift

Standard Exercise

Archimedes and the King's Crown

Standard Exercise

The Garden Hose
A simple pendulum hangs from the ceiling. The bob has mass mbob = 0.21 kg. The string has length L = 5 m. The pendulum is gently released from rest at an angle θ = 4.6o.
Standard Exercise

The Guitar String
1) Find the potential energy of the pendulum bob just before it is released? U = 10.3 J U = 0.826 J U = 0.0332 J
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Standard Exercise

The Intense Speakers

Standard Exercise

Solution: The potential energy is U=mgh = mgL(1-cosθ). Substituting we get U = 0.0332 J.

The Speeding Car

Standard Exercise

Heating a Metal Strip
2) What is the maximum speed of the pendulum bob?
Standard Exercise

v = 0.397 m/s v = 0.562 m/s v = 0.258 m/s
Submit Hide Solution

Compressing a Gas

Solution: Again conservation of energy is the easiest way to solve the problem: U = T = (1/2)mv2 = mgL(1-cosθ). After substituting we find v = 0.562 m/s.

3) Find the period of this pendulum. T T T T T = = = = = 4.5 s 8.8 s 0.71 s 1.4 s 0.2 s
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Submit

Solution: The period of a pendulum is related to the square root of its length, or T2 = (2 π)2(L/g). Substituting and taking the square root of the result gives T = 4.5 s.

4) You would like to use this pendulum as a clock. What is the length of the string needed to obtain a period of T = 1.0 s? L = 0.102 m L = 1.56 m L = 0.248 m
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Solution: This question is related to the previous question about the period of the pendulum. We can solve for L = T2g/(2 π)2. After substitution, we find L = 0.248 m.

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PHYS 101 Exams
UIUC
Instructor
Unit 3: Homework / Homework / Homework / Schulte, Elaine

Student

Homework: Hour Exam 3
Deadline: 100% until Thursday, November 21 at 8:00 AM

Problems Print Assignment View
Standard Exercise

The Hydraulic Lift
1 2 3 4

The Mass and The Spring

Standard Exercise

The Pendulum

Standard Exercise

The Hydraulic Lift

Standard Exercise

Archimedes and the King's Crown

Standard Exercise

The Garden Hose

Standard Exercise

The Guitar String
To work on your car you use a hydraulic lift as shown in the diagram. It confines a fluid with ρ = 1.81 kg/m3. Your car has mass Mcar = 739 kg . The lift piston has mass Mpiston = 171 kg. The input piston (on the left) is massless and has an area of 2.54 m2. The lift piston (on the right) has an area of 2.18 m2.
Standard Exercise

Standard Exercise

The Intense Speakers

1) In Figure 1 the piston bases are at the same height. How are the pressures on lift side and the input side related? Plift = Pinput Plift < Pinput Plift > Pinput
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The Speeding Car

Standard Exercise

Heating a Metal Strip

Solution: This is a question of Pascal's Principle. Remember that F1/A1 = F2/A2. Thus Plift = Pinput.

Standard Exercise

Compressing a Gas

2) The lift piston base and the input piston base are at the same height. What force is required to maintain this system? Finput Finput Finput Finput Finput
Submit

= = = = =

7650 N 10400 N 8460 N 6220 N 1960 N
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Solution: We can use Pascal's Principle to solve for the input force using F1/A1 = F2/A2. We can solve for the force Finput = FliftA1/A2. We know the areas we need to know the force on the lift side, which is just the weight of the car Flift = (739 kg)(9.8 m/s2). After substitution, we find Finput = 7650 N.

3) Now you would like to lift the car Δ h = 1.9 m from its current position. How does the work done by the input piston relate to the work done by the lift piston? Winput < Woutput Winput = Woutput Winput > Woutput
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Solution: One side of the lift cannot do more work than the other side of the lift. Therefore, Winput = Woutput.

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4) How far must you push the input piston down to lift the car Δ h = 1.9 m? hinput = 1.6 m hinput = 0.8 m hinput = 8 m
Submit Hide Solution

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Solution: In order to move the car a distance Δ h = 1.9 m we must shift a volume ΔV = AliftΔ h. The same volume of liquid must have been pushed from the small piston: ΔV = AinputΔ hinput. After some algebra we find hinput = AliftΔ h/Ainput. After subsitiution we find hinput = 1.6 m.

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PHYS 101 Exams
UIUC
Instructor
Unit 3: Homework / Homework / Homework / Schulte, Elaine

Student

Homework: Hour Exam 3
Deadline: 100% until Thursday, November 21 at 8:00 AM

Problems Print Assignment View
Standard Exercise

Archimedes and the King's Crown
1 2

The Mass and The Spring

Standard Exercise

Archimedes has been tasked with finding out if the King's crown is really gold. Let's use Archimedes' Principle to see if we can help him figure it out.

The Pendulum

Standard Exercise

1) How can Archimedes' Principle help solve this problem? The crown's mass and displaced volume will tell us the density of the crown. The atmospheric pressure will cause the crown to sink. Archimedes Principle only works for objects that float.
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The Hydraulic Lift

Standard Exercise

Archimedes and the King's Crown

Solution: Archimedes' Principle relates the displaced volume of a fluid to the mass of the object displacing the fluid.

Standard Exercise

The Garden Hose

Standard Exercise

The Guitar String
2) You weigh the King's crown. Its mass is mcrown = 1.78 kg. How much water should it displace if it is solid gold (ρgold = 19.3 g/cm3)? Vcrown = 0.092 cm3 Vcrown = 92 cm3 Vcrown = 3.4 × 104 cm3 Vcrown = 34 cm3 Vcrown = 280 cm3
Submit Hide Solution
Standard Exercise Standard Exercise Standard Exercise

The Intense Speakers

The Speeding Car

Solution: For this problem, we need to remember that V = m/ρ. We know the mass of the crown and the density of gold. After substitution we find: Vcrown = 92 cm3. Remember to watch the units!

Heating a Metal Strip

Standard Exercise

Compressing a Gas

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PHYS 101 Exams
UIUC
Instructor
Unit 3: Homework / Homework / Homework / Schulte, Elaine

Student

Homework: Hour Exam 3
Deadline: 100% until Thursday, November 21 at 8:00 AM

Problems Print Assignment View
Standard Exercise

The Garden Hose
1 2 3 4

The Mass and The Spring

Standard Exercise

The Pendulum

Standard Exercise

The Hydraulic Lift

The diagram shows two attached garden hoses. Hose 1 has a cross-sectional area A1 = 1.84 cm2. Hose 2 has a crosssectional area A2 = 3.84 cm2. Water (ρ = 1.0 g/cm3) flows through the hoses.

Standard Exercise

Archimedes and the King's Crown

1) Bernoulli's Equation is a statement about conservation of energy: True False
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Standard Exercise

The Garden Hose

Standard Exercise

The Guitar String

Solution: True, Bernoulli's Equaiton is a statement about energy conservation.
Standard Exercise

The Intense Speakers

2) The water in hose 1 has a velocity v1 = 2.7 cm/s. What is the velocity v2 of the water in hose 2? v2 v2 v2 v2 v2 = = = = = 5.6 cm/s 6.5 cm/s 1.3 cm/s 0.26 cm/s 2.6 cm/s
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Standard Exercise

The Speeding Car

Standard Exercise

Heating a Metal Strip

Submit

Standard Exercise

Solution: Continuity demands that A1v1 = A2v2. Since we know the cross-sectional areas of the two hose sections, and v1 = 2.7 cm/s, we can solve for v2 = 1.3 cm/s.

Compressing a Gas

3) What is the change in pressure between hose 1 and hose 2? ΔP = 0.7 Pa ΔP = 0.093 Pa ΔP = 0.28 Pa
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Solution: From Bernoulli's Equation we know that P1 - P2 = (1/2)ρ(v22 - v12). After substitution (be careful of units) we find: ΔP = 0.28 Pa.

4) The pressure in hose 1 is P1 = 5.88 Pa. If you put a plate of the same area as hose 2, Aplate = 3.84 cm2, at the end of of hose 2, what force would the plate experience from the water? F2 = 10 N F2 = 22 N F2 = 46 N
Submit Hide Solution

Solution: For this problem we need to remember F = PA . We can now solve by direct substitution: F2 = 22x104 N (note error).

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PHYS 101 Exams
UIUC
Instructor
Unit 3: Homework / Homework / Homework / Schulte, Elaine

Student

Homework: Hour Exam 3
Deadline: 100% until Thursday, November 21 at 8:00 AM

Problems Print Assignment View
Standard Exercise

The Guitar String
1 2 3 4

The Mass and The Spring

Standard Exercise

An E guitar string of length 70 cm is fixed at both ends. Its fundamental frequency (frequency of the fundamental harmonic) is f = 330 Hz.

The Pendulum

Standard Exercise

1) What is the wavelength of the fundamental oscillation of this string? λ λ λ λ λ = = = = = 35 cm 70 cm 105 cm 140 cm 175 cm
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The Hydraulic Lift

Standard Exercise

Archimedes and the King's Crown

Submit

Standard Exercise

The Garden Hose

Solution: The wavelength of the fundamental mode is twice the length of the string: λ = 140 cm.
Standard Exercise

The Guitar String

2) What is the velocity of a wave travelling in the string? v = 200 m/s v = 462 m/s v = 684 m/s
Submit Hide Solution

Standard Exercise

The Intense Speakers

Standard Exercise

The Speeding Car

Solution: The speed of a wave is v = fλ. From direct substitution we get: v = 462 m/s.
Standard Exercise

Heating a Metal Strip

Standard Exercise

3) The string is retuned. The new tension is T' = 4T. What is the new fundamental frequency of the string, f'? f' f' f' f' f' = = = = = f/4 f/2 f 2f 4f
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Compressing a Gas

Submit

Solution: The frequency of a wave is proportional to the square root of the tension. Therefore, if the new tension is 4 times large, the frequency must be 2 times larger.

4) The string is replaced with a new string. The new string has the same length (70 cm) and tension T. It has four times the mass, M'' = 4M. What is the new fundamental frequency of the string, f''? f'' f'' f'' f'' f'' = = = = = f/4 f/2 f 2f 4f
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Submit

Solution: The frequency of a wave is inversely proportional to the square root of the mass of the string. Therefore, if the mass of the string is 4 times as large as the original, the frequency of the string must be half as large as the original.

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PHYS 101 Exams
UIUC
Instructor
Unit 3: Homework / Homework / Homework / Schulte, Elaine

Student

Homework: Hour Exam 3
Deadline: 100% until Thursday, November 21 at 8:00 AM

Problems Print Assignment View
Standard Exercise

The Intense Speakers
1 2

The Mass and The Spring

Standard Exercise

You are standing 14.5 m away from a speaker and measure a loudness of 73 dB.

The Pendulum

1) If you measure the sound 29 m from the speaker, what intensity, I', would you measure compared to the original intensity, I? I' = I/2 I' = I/4 I' = I/16
Submit Hide Solution

Standard Exercise

The Hydraulic Lift

Standard Exercise

Archimedes and the King's Crown

Solution: The intensity of sound drops off as 1/r2, so if you move twice the distance from your starting position, the intensity of the sound will be 4 times smaller.

Standard Exercise

The Garden Hose

Standard Exercise

The Guitar String
2) Your friend stacks a second, identical speaker on top of the first. It plays at the same intensity. You measure the loudness at the original position, 14.5 m from the speakers. What is the new level of loudness you measure? 80 dB 74 dB 87 dB
Submit Hide Solution

Standard Exercise

The Intense Speakers

Standard Exercise

The Speeding Car

Solution: This question was removed from grading.
Standard Exercise

Heating a Metal Strip

Standard Exercise

Compressing a Gas

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PHYS 101 Exams
UIUC
Instructor
Unit 3: Homework / Homework / Homework / Schulte, Elaine

Student

Homework: Hour Exam 3
Deadline: 100% until Thursday, November 21 at 8:00 AM

Problems Print Assignment View
Standard Exercise

The Speeding Car
1

The Mass and The Spring

Standard Exercise

The Pendulum
1) At what speed, vs, must a car drive towards a stationary observer so that the frequency heard by the observer, fo, is twice that emitted by the source, fs, i.e. fo = 2fs? The speed of sound is v = 330 m/s. vs vs vs vs vs = = = = = 100 165 187 212 375 m/s m/s m/s m/s m/s
Hide Solution

Standard Exercise

The Hydraulic Lift

Standard Exercise

Archimedes and the King's Crown

Submit

Standard Exercise

Solution: This is a question on the Dopler Effect. Remember that the frequency of a wave from a moving source is f = fs(vsound - vobserver)/(vsound - vsource). Now we need to get the signs of the source velocity right. The observer is not moving in this problem, so vobserver = 0 m/s. The source is moving toward the observer. This causes the sound wave to move faster than the speed of sound. So the vsource term must be negative to make the overall sign positive. Thus, f = fs(vsound)/(vsound + vsource). Solving for vs and substituting we find: vs = 165 m/s.

The Garden Hose

Standard Exercise

The Guitar String

Standard Exercise

The Intense Speakers

Standard Exercise

The Speeding Car

Standard Exercise

Heating a Metal Strip

Standard Exercise

Compressing a Gas

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PHYS 101 Exams
UIUC
Instructor
Unit 3: Homework / Homework / Homework / Schulte, Elaine

Student

Homework: Hour Exam 3
Deadline: 100% until Thursday, November 21 at 8:00 AM

Problems Print Assignment View
Standard Exercise

Heating a Metal Strip
1

The Mass and The Spring

Standard Exercise

The Pendulum
1) You heat a metallic strip from 275 K to 1873 K. If at 275 K its length is 1.35 m and the coefficient of linear expansion is α= 17 x 10-6 K-1, what is the length of the strip at 1873 K? l = 0.675 m l = 1.39 m l = 2.02 m
Submit Hide Solution
Standard Exercise

The Hydraulic Lift

Standard Exercise

Archimedes and the King's Crown

Solution: Recall: for thermal expansion Δl = αΔT L. We can find the final length by direct substitution and remembering that l = L+Δl. We find l = 1.39 m.

Standard Exercise

The Garden Hose

Standard Exercise

The Guitar String

Standard Exercise

The Intense Speakers

Standard Exercise

The Speeding Car

Standard Exercise

Heating a Metal Strip

Standard Exercise

Compressing a Gas

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PHYS 101 Exams
UIUC
Instructor
Unit 3: Homework / Homework / Homework / Schulte, Elaine

Student

Homework: Hour Exam 3
Deadline: 100% until Thursday, November 21 at 8:00 AM

Problems Print Assignment View
Standard Exercise

Compressing a Gas
1

The Mass and The Spring

Standard Exercise

The Pendulum
1) We use a piston to compress 86 ml of a gas at a pressure of 92 Pa to a new volume of 17 ml at constant temperature. What is the new pressure of the gas? P P P P P = = = = = 80.4 Pa 465 Pa 15.9 Pa 17 Pa 498 Pa
Hide Solution
Standard Exercise

Standard Exercise

The Hydraulic Lift

Standard Exercise

Archimedes and the King's Crown

Submit

Solution: This is a problem of the Ideal Gas Law. At constant temperature P1V1 = P2V2. We can make use of this relationship to solve for P2 and we find: P = 465 Pa after substitution.

The Garden Hose

Standard Exercise

The Guitar String

Standard Exercise

The Intense Speakers

Standard Exercise

The Speeding Car

Standard Exercise

Heating a Metal Strip

Standard Exercise

Compressing a Gas

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