Spring 2009

HOMEWORK

All problems listed are from College Physics, by Knight, Jones, and Field.The notation followed is C.NN where C is the chapter number and NN is the problem number. Hence 5.4 stands for 4th problem from chapter 5.

INSTRUCTIONS

Complete instructions on how to go about solving the homework are given in this section of the syllabus.

We will select and grade in detail two problems from every homework; each of the two problems are worth 5 points each.The problems graded in detail are marked in bold red.Often, I may suggest work problems that may help students to better understand some concepts.  These problems are not due in class or will not be graded, although it would be extremely beneficial to work through them. These solutions to these problems will be put up on the website. These problems are marked green italics. The rest of the problems (are graded out of 2 points each.  An correct solution gets 2 points, a valiant attempt "almost there" gets 1.5 points, while a good attempt (right method with the correct equations, correct picture) could get 1 point, some attempt gets 0.5 points.

Some of the problems might have extra parts and these are mentioned at the end of the table. But you can access them by clicking on the link adjacent to the problem.

If you are not doing well on the homeworks consistently, then something is not right and needs to be fixed. This can only happen if you talk to us. The earlier the better.

14.45

For the graph shown in figure P14.45, assuming a mass of 2 kg, SKETCH the velocity-time, acceleration-time, Force time graphs. Also SKETCH the kinetic energy, potential energy and the total energy in the one graph.

Bungee

The Guinness Book of World Records states the highest commercial bungee jump is off of Macau Tower (click on "bungy jump" below), Macau SAR China. This jump takes place from a platform at the Observation Deck Level of the tower, and the height from the platform to the floor is 233 metres (760 ft). The jump at Macau Tower will take its guests on a free fall at a speed of up to 200km/h for the ultimate extreme journey! Plunging from a platform 233m high, challengers will experience a 4-5 second freefall before stretching the 50 meter bungy cord nearly four times its unloaded length and rebounding when the person's head is approximately some meters (h) above meters above the ground. Using a guide cable system, bungy jumpers will be able to safely experience a few rebounds before slowly landing onto a specially designed airbag. Assuming that the height of the person is 5' 5" and she weighs 130 pounds. The bungee cord is tied to her ankle, which is 5 inches above (when standing upright) bottom of the heel. a)Assuming the center of gravity to be at the center of the person, find the spring constant of the cord (assume it is constant throughout the fall). b)) How far above the ground does the person's head come to rest momentarily? c) How fast was the person moving when the cord was stretched by 50 m?

14.54

This is a classic problem. Although, this is a PHYS 122 class, you will need to use the concept of conservation of momentum from PHYS 121. Physics does not have boundaries of courses. This is also true for your MCATs or PCATs. But let us help you get started. When two objects collide, the linear momentum of the system p=mv is conserved. If the system contains two objects then m1v1_initial +m2v2_initial=m1v1_final+m2v2_final. When objects stick to each other, the energy during collision is not conserved. (the converse is not always by the way). But once the collision is done and the bulledt and mass begin to move, you just have gravity and spring force acting on the system and these forces are conservative.

D1

Standing at a crosswalk, you hear a frequency of 560 Hz from a siren of an approaching ambulance. After the ambulance passes, the observed frequency of the siren is 480 Hz. Determine the ambulance's speed from these observations.

Instructions for chapter 18

We will not use accurate ray tracing to get answers to a lot of problems, but use equations and rough sketches to arrive at answers. So use the lens formulas discussed in class to solve these problems quantitatively. Your diagrams do not have to be accurate but good sketches as discussed in class. It is a good idead to draw all the 6 cases for a convex lens before you start this homework. The equation to use would be the lens equation 1/s+1/s'=1/f. Also remember that since the main focus contributing to a diverging (concave lens is on the virtual side, f is negative). For a convex converging lens the main focus is on the real side (since the rays converge in reality to the focus), Hence f for convex lenses is +.

Instructions for problem list.

This task can get you extra credit worth 1.5 % of the course which is roughly equivalent to 1.5 homeworks. But think very carefully before deciding to attempt this. It might be a waste of your time. You have to answer all these problems (solutions are already posted) from scratch. You have to explain your steps and explain the physics behind the steps. The focus should be on explaining the concepts, not to write lines to fill up space. Results must be interpreted through explanations. You have to draw pictures where necessary

You will not get any credit if

• not explain concepts
• not draw diagrams

Advantage of doing this task is that you will recognize problems in the exam from the previous material IMMEDIATELY! but is it worth the time you will spend? That is your call. THIS IS DUE JUST BEFORE THE EXAM. It will not be accepted after 19th.

HW3 Chapter 14
14.20 a) 0.50s  b) 5.5cm  c) 70cm/s  d) 0.049J
14.26 7.5m
14.42 a) 0.17kg  b) 0.57m/s
14.46 You must show your steps. Giving the answer gives it away.

HW4 Chapter 14
14.18 5.5N/m
14.62 a) 9.5N/m  b) 0.50m/s  c) 2.9s

HW5 Chapter 15

15.14)  a) 19.7Hz b) 2.33m c) 46m/s
15.26)  6.2*10^-9 W
15.32) 3.2*10^-3w/m^2. B) simple calculation based on part a.
15.38) a)431Hz b) 429Hz
15. 58 y(x,t)=(0.1 mm) Cos[ 2 pi(x/2m – t/0.005s)]

15.70 around 100 m/s (do it exactly).

HW6 Chapter 16
15.72 a) 19.7Hz b) 2.33m c) 46m/s
16.14 a)24m/s b)wavelength=2/3m
16.28 f1=6700Hz

HW7 Chapter 14
14.54 a) 500m/s b) No
Chapter 16
16.40 65Hz
16.52 a) an open-open tube  b) 1.32m
16.56 26cm, 56cm, and 85cm
Q18 D
Q20 B

HW8 Chapter 18
18.8 9.0 cm
18.10 a) they are parallel  b) they are parallel
18.12 31.3°

HW 9

18.20. 3.0 degrees
18.18. 22.3 degrees

18.58 18°
18.26 s’=20cm, inverted and real
18.30 s’=-6cm, upright and virtual
18.68 s’=-30cm, height=3.0cm
18.64 s’=-40cm, height=10cm, upright and virtual

19.38 two, both inverted, height = 8.0cm at 160cm from lens, and 0.5 cm tall at 40 cm from the lens
19.42 s’ = -4.5cm, height = 1.0cm, inverted and virtual
19.40 s’ = 49cm, height = 4.6cm
19.46 1.0m
19.20 -0.33D

HW13 Chapter
19.44 66.7cm
19.16 2.8mm 22mm
19.28 a)20 b)8.0 mm
19.24  W,C,B=M,J
16.30 0.25m

HW14 Chapter
16.60  minima will occur at distances of 2.98 m, 5.62 m, and 17.88 m.
16.62  a)690Hz b)1370Hz
16.10  40m/s

HW15 Chapter 17
17.24 a) 1.33  b) 87 nm
17.28 0.20 mm
17.30 4.0 mm
17.32 895 nm
17.42 a) 1.2 mm  b) 1.60 mm
17.46 4

HW16 Chapter 17 & 20
17.54 1.6 μm
20.14 0 N
17.60 a) 473 nm  b) 406 nm, 568 nm  c) blue, yellowish green
20.22 36 kN/C, 18 kN/C, 18 kN/C

HW 17

20.26.  3.3 * 10^6 N/C, downward.
20.52.  x = -2.4 cm.  Yes.
20.24.  E = 2500 N/C, to the right.

HW 18

20.64.  750 nC.
21.4.  1000 eV.  1.60 * 10^(-16) J.  1.9 * 10^7 m/s.
21.16.  +1400 V.

HW19 Chapter 21
21.12 a) right  b) 100 kN/m  c) 150 eV (or 2.4×10^(-17) J )
21.18 a) A  b) 70 V
21.54 0 V
21.50 a) x = ±Infinity  b) x = 0, ±Infinity

HW21

22.12 Junction 1: 5 A = 3 A + i1 or i1 = 2 A
Junction 2: i1 = iB + 1 A or iB = i1 – 1 A = 1 A
Junction 3: 3 A = i2 + 2 A or i2 = 1 A
Junction 4: 1 A + i2 = iC or iC = 1 A + i2  = 2 A

22.20 0.04 ohm
23.10  11ohm,9ohm

HW 22

22.46 1.8m,190
23.52 54.5ohm
23.60

 Resistor Potential difference (DV) Current (A) 4.0 W 8.0 2.0 6.0 W 8.0 1.3 8.0 W 8.0 1.0 Bottom 24 W 8.0 0.33 Right 24 W 16 0.67

23.24

 Resistor Potential difference (V) Current (A) 3 W 4 W 48 W 16 W 6 6 6 6 2 1.5 0.13 0.38

HW23 Chapter 23
23.32 20 μF, in parallel
23.34 37 μF
23.36 2.0 ms
23.39 6.9 ms
23.40 a) 18 μC, 180 mA  b) 11 μC, 110 mA  c) 2.4 μC, 24 mA
23.70 a) 80 μC  b) 0.23 ms

HW24 Chapter 24
24.6 a: 0.20 mT to the right  b: 0.40 mT to the right  c: 0.20mT to the right
24.8 52 μT
24.22 a) 5.7×10^(-13)N to the +y direction  b) 0 N
24.32 0.13 T
24.34 56 N

HW27 Chapter 25
25.4 a) 1.1 A  b) 0.24 N to the left
25.12 a) 3.9 mV, 39 mA, clockwise  b) 3.9 mV, 39 mA, clockwise  c) 0 mV, 0 mA
25.16 2.3 T/s increasing
25.18 0.46 A
25.58 a) 0.63 mN  b) 0.31 mW  c) 13 mA  d) 0.31 mW

HINTS

HW3 Chapter 14
14.20 Can you find spring constant from mass and frequency? It may be easier to find total energy prior to amplitude and maximum speed.
14.31 Recall the definition of period, what is the period for a sinusoidal function? To find the length, you may need the answer of (b), and notice that it is a uniform solid rod rather than a simple pendulum. (Read example 14.9 once more may help!)
14.42 You may find frequency first.
14.45 To draw a graph for (b), can you find out the new amplitude and frequency due to the change of mass? You may need Equation 14.18 for additional parts.
14.46 To draw graphs for (a) and (b), you need "maximum velocity" and "frequency". You have to draw the dependence of kinetic energy, potential energy and total energy in the same graph. You know how the X and V graphs look. Potential energy and Kinetic energy are a function of X and V, so you can arrive at that. Graph of E is simple! (Why?).
14.47 To find the ratio kA/kB, you may need the ratio of mass and the ratio of frequency.
14.55 Try to move the block by x and draw a free body diagram. From the relation between F and x, you may find out the "effective spring constant" for this problem. Or, you can try to divide the block into two from the middle and see if you move all these blocks by x, how will they move accordingly? Do they push each other?

HW4 Chapter 14
Bungee: Energy is conserved. So you can compare it at different points. But remember that the X in the potential energy of spring is the amount by which the spring is stretched or compressed. Part c, you have to calculate the velocity when the cord is stretched by 50 m. So total length of cord

HW5 Chapter 15
15.5 set up 2 formulas for distance,time and speed.
15.14 check definition.
15.14 same as 15.14
15.17 check definition.
15.29 set up 2 formulas for intensity,power and distance
15.32 same as 15.29
15.37 doppler effect.
15.47 what is the relation of the tension of two ropes? Length and time?
15.57 check definition.
15.58 same as 15.57
15.70 doppler effect. To decrease frequency, should the bat fly away from or to you?is 100 m at this point.
14.18 Find frequency first.
14.27 Notice that g is not always 9.8m/s^2.
14.35 You may want to draw the amplitude-time lines first; your graph will bounded by them.

HW6 Chapter 16
15.72. use concept of relative velocity.
16.3 pulse moves. When they meet, they add up.
16.9 start from finding wavelength of standing wave
16.14 relations of successive frequencies.
16.17 string fixed at ends forms standing waves.set up 2 formulas for f,wavelength and speed.
16.28 which type is ear canal belongs to?refer to figure 16.19

HW7 Chapter 16
16.4 Pay attention to each characteristic point, and you can get the graph by connecting these points.
16.40 What's the relation between these two frequencies? What is the value m for each frequency?
16.47 You may need to calculate the linear mass density. What's the area for the cross-section?
16.52 Simplify the ratio of these frequencies; what can you observe?
16.55 It is similar to 16.52, but it asked in a different way. The air temperature can be used to find sound velocity.
16.56 Find all the possible length for the tube lower than 1m. What kind of tube is it?

HW8 Chapter 18
18.7 Where is the image of O?
18.8 You may need the geometry of the diagram to solve this problem.
18.10 You can draw the reflected rays and calculate the angle between outgoing and incoming rays.
18.12 Notice that the light seen by the diver is already refracted.
18.15 When the light strike the surface of the water, it will change its direction, and the length of shadow will also change accordingly.

18.20. Different indeces of refraction will result in different refraction angles. What do you get when you use the smaller n? What about the bigger n? What does that tell you about the spread? Make sure you read the problem carefully and draw a diagram of the situation.
18.18. If you use the equation given in the book, make sure you are clear which one is n1 and which is n2.
18.21. This is similar to #20. As we saw, we got different angles for different colors. Draw a diagram to figure out how far apart the light rays are. See figure 18.27 for the indeces of refraction.
18.51. Break this problem up into two refractions.
18.58 You will need to use Snell's law twice. Use the properties of triangle to find the angle relationship between the refracted angle of the first refraction and incident angle of the second one.
18.59 What is the angle relationship between the refracted angle of the first refraction and α?

19.38 Notice that there is a given relationship between s and s’ instead of given either s or s’. With this relationship and thin-lens formula, you can solve for both s and s’. Pay attention to units.
19.41 You can find the location of the image of the first lens and this becomes the object for the second lens.
19.42 Similar to 19.41
19.40 Similar to 19.41
19.46 What are the refractive powers of these lenses?
19.19 What lens does a farsighted person need? How should we modify their near point?
19.20 What lens does a nearsighted person need? How should we modify their far point?

19.22  formula of angular size
19.44 thin lens formula (1/s+1/s’=1/f)
19.16 The f-number is related to the focal length and diameter of the lens by?
19.17 same as 19.16
19.28 Formula application
19.29 relation of s and f0
19.24  relations of lens power and focus?
19.25 Formula application
19.31 magnification of a telescope in terms of the focal lengths of the two lenses.
19.32  relation of angle and distance?
19.47 Formula application. Use the tables we generated in class.
16.30 Both speakers are emitting along x-axis. Normally we consider interference at a particular point. So wherever we consider the interference the |d2-d1| is the same!
16.31 think about the difference between their path lengths
16.33 in phase or out of phase? Use the swimming pool example we discussed in class.

16.60  calculate path difference. The distance between speakers, d1, and d2 form a right triangle – Pythagoras..
16.59 Path difference is simpler since both speakers are along the x axis. Ignore the distance between speakers in the y direction as sound waves are pretty large.
16.62 same as 16.60
16.10  wavelength=?
16.11 same as 16.10
16.9  what is number of mode?

16.7    draw snapshot of each second and observe the  y position of x=

HW15 Chapter 17
17.15 What is the spacing d of the grating?
17.17 What is the spacing d of the grating? Don’t assume θ is small here; how can you find θ?
17.19 Try to find θ first. How many m’s are possible? Don’t assume small θ.
17.24 See example 17.5
17.25 What is the condition that a wave undergoes a phase change?
17.28 What are the positions of the first and second minima? What about the distance between them?
17.41 There are two different mode m and two different wavelength λ at the same position y. What is the relationship between them?
17.42 Which will change when the water is drained out of the tank, wavelength, slit spacing or the distance between the slit and the screen?
17.51 Notice that the distance between the grating and the screen is 1.0 m, is it appropriate to assume small angle?

HW16 Chapter 17 & 20
17.54 How can you calculate the angle θ? Is the small angle approximation valid here?
20.9 Recall Newton’s third law.
20.14 Consider all the sources that will contribute to the total electric force.
20.23 The electric field is a vector at any assigned points. How could you find the strength and the direction? Recall that in a vector graph, we use “length” to represent the magnitude, and they are “proportional” to each other.
17.60 Here we set the range of visible light to be 400 ~ 700 nm, and notice that eyes are most sensitive to wavelength of about 555 nm and the sensitivity drops when the wavelength is very different from this value.
20.22 Similar to 20.23.

HW 17

20.26.  Draw a free-body diagram.  What forces are there that you have to balance?
20.52.  You only have to look at positions on the x-axis; that is, positions that have the coordinates (x,0).  Also, it helps to split things up into three regions: x < 0, between x = 0 and x = 1, and x > 1.  In each region, look at the force due to the positive charge and to the negative charge.  Where do these forces cancel?
20.63.  Remember back to the chapter on springs, and think about how to find k.  Then, what forces come into play?
20.65.  Draw a free-body diagram (look back at the chapter on pendulums if you need to).  What forces balance each other?
20.24.  You can use symmetry to make this problem a little easier.  Think about what the electric field from the top charge looks like, and compare that to the electric field from the bottom charge.  Does anything cancel out?  Remember that the electric field is a vector, so directions matter.
20.49.  Again, use symmetry to make this problem MUCH easier.  Think about what you did in problem 24, where some things canceled out.

HW 18

20.64.  Focus on one ball, and consider how the other ball affects it.  How is this similar to problem 20.65, and how is it different?
21.4.  Remember conservation of energy.  Note that the particle is accelerated from rest.
21.16.  Electric potential is a scalar.  How do scalars add?
20.67.  Identify each of the terms in the equation, and figure out what they refer to.  From there you can construct a problem, and then solve.

HW19 Chapter 21
21.12 Recall the definition of the potential and the relationship between electric potential and field.
21.18 Similar with 21.12.
21.23 How to read an equipotential diagram?
21.54 You need to find from the geometry that the distance between the charges and the point.
21.21 What is the relationship between electric potential and field?
21.55 Similar to 21.54.
21.50 If you have problems plotting those graphs, you can try to plot it by Excel first to see the relationship: assign the x values and calculate the y values by the equation and plot the graph. Notice that Excel cannot plot a value of ± infinitiy, so you must judge yourself in the end.If you look at the answer, the field is zero only at infinities. Why are we not getting a solution for any other point on the x axis. How is it different from the example done in class?

HW21

22.11 sum of current in =sum of current out
22.20 relation of resistance with length
23.10 series or parallel?

23.11 series or parallel?

HW22

22.35 think about what is the unit for joule?
22.46 use resistance formula with length and area.
23.17 There are parallels inside parallels so identify parallel one by one, and solve for the effective resistance
23.52  solve effective resistance one segment by one segment and put them together last.
23.60 same as 23.52.
23.21 use  Kirchhoff law. You should set up 2 formulas
23.23 same as 23.17 and 23.21

HW23 Chapter 23
23.34 Notice the difference between the formulae for capacitors and resistors in parallel or in series
23.35 Similar to 23.34.
23.37 To charge capacitor to 87% in 8.0s, what is the time constant?
23.39 How can you find the time constant?
23.40 What’s the relation between Q and V? How can you find Q as a function of time from the relationship mentioned above?
23.69 What’s the time constant for this circuit? Is the current in the main loop the same as the current in the 8.0 Ω resistor?
23.70 After the switch has been closed for a very long time, there is no current flowing through the rightmost branch (why?). After the switch is opened, there is no current flowing through the 60 Ω resistor (why?).

HW24 Chapter 24
24.5 Pay attention to the direction of the magnetic field.
24.6 By symmetry, the y component can be easily decided without any calculation. You need to use trigonometric functions to find the x component.
24.15 You can simplify this situation to one straight wire and one circular loop.
24.8 You need to use trigonometric functions to find the distance from the points to the wires. Pay attention to the direction of the magnetic field.
24.9 You may set the point to be (x, 0), but you need to find the region the point belong to (either x < -2cm, -2cm < x < 2 cm, x > 2 cm) by observing the direction first.
24.22 You need to find the direction of the force by the right-hand rule.
24.23 Similar to 24.22, notice that the charge is negative now.
24.34 Similar to 24.22.

HW27 Chapter 25
25.4 You can decide the direction of the force intuitively by Lenz’s law.
25.7 You can assign the direction of the area arbitrarily, but your answer should be consistent with this assignment.
25.12 The direction of the current can be decided by Lenz’s law.
25.53 By Faraday’s law, you just need to decide the changing rate of the flux. Which one is changing in this question, B or A? The direction of the current can be decided by Lenz’s law.
25.18 What is the direction of the induced current? From this you can get the induced emf, is it in the same or opposite direction as the applied voltage?
25.48 You don’t need to include the detailed reading of the ammeter (in fact, you can’t). Instead, you need to explain your sketch in detail in “approaching”, “stationary”, and “leaving” steps.
25.58 Similar to 25.4.