2009 AP-B Exam

Problem B-1

Problem B-2

Problem B-3

Problem B-4

Problem B-5

Problem B-6

2009 AP Physics B

ENDProblem B-7

Grade Distributions

2009 Grade Distributions

14.9

5

18.6

4

27.2

3

18.3

2

20.9

1

62,702 Exams

Mean Grade = 2.86

2009 AP Physics B

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In an experiment, students are to calculate the spring constant k of a vertical spring in a small jumping toy that initially rests on a table. When the spring in the toy is compressed a distance x from its uncompressedlength L0 and the toy is released, the top of the toy rises to a maximum height h above the point of maximum compression. The students repeat the experiment several times, measuring h with objects of various massestaped to the top of the toy so that the combined mass of the toy and added objects is m. The bottom of the toy and the spring each have negligible mass compared to the top of the toy and the objects taped to it.

Physics B-1 (15 points)

2009 AP-B Exam

(a) 3 pointsDerive an expression for the height h in terms of m, x, k, and fundamental constants.

2kx21mgh

Energy .Cons

mg2kxh

2


1 pt. Conservation of Energy

1 pt. Correct Energy Expression

1 pt. Solving for h

2009 AP-B Exam

With the spring compressed a distance x = 0.020 m in each trial, the students obtained the following data for different values of m.

(b) i. 2 pointsWhat quantities should be graphed so that the slope of a best-fit straight line through the data points can be used to calculate the spring constant k ?


h1 vs. mor

m1 vs. hPlot

2 pt. Expression

h1vs. m

m1vs. h

2009 AP-B Exam

With the spring compressed a distance x = 0.020 m in each trial, the students obtained the following data for different values of m.

(b) ii. 2 pointsFill in one or both of the blank columns in the table with calculated values of your quantities, including units.

1/m (kg-1)5033252017

1/h (m-1)2.02.93.65.35.6


1 pt. Filling table with correct values.

1 pt. Correct Units.

2009 AP-B Exam

(c) 4 pointsOn the axes below, plot your data and draw a best-fit straight line. Label the axes and indicate the scale.

h(m)

0.5

0.4

0.3

0.2

0.1

0 10 20 30 40 50 60 1/m (kg1)


1 pt. Correctly plotting Points.

1 pt. Best Fit Straight Line.

1 pt. Correctly Scaling Axis.

1 pt. Correctly Labeling Axis.

2009 AP-B Exam

(d) 2 pointsUsing your best-fit line, calculate the numerical value of the spring constant.

0.5

0.4

0.3

0.2

0.1

0 10 20 30 40 50 60

h

1/m

h

1 m

m1hlopes

2

2

m 020.0

m/s 8.9 kgm 0107.0 2

N/m 524k


104010.042.0

kgm 0107.03032.0

mg2

kxh2

2x

g hm 2k

2x

g slope2k

1 pt. Calculating the Slope

1 pt. Correct Value for Spring Constant2009 AP-B Exam

(e) 2 pointsDescribe a procedure for measuring the height h in the experiment, given that the toy is only momentarily at that maximum height

Use a timer to measure the time the toy is in the air.Calculate the maximum height reached using this time.


2 pt. Correct, Complete Procedure

2009 AP-B Exam

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Two small objects, labeled 1 and 2 in the diagram above, are suspended in equilibrium from strings of length L. Each object has mass m and charge +Q. Assume that the strings have negligible mass and are insulating and electrically neutral. Express all algebraic answers in terms of m, L, Q, , and fundamental constants.


2009 AP-B Exam

(a) 3 pointsOn the following diagram, sketch lines to illustrate a 2-dimensional view of the net electric field due to the two objects in the region enclosed by the dashed lines.


1 pt. Field direction away from charges.

1 pt. Correct Curvature of Field Lines

1 pt. Zero field at point A

2009 AP-B Exam

(b) 2 pointsDerive an expression for the electric potential at point A, shown in the diagram at the top of the page, which is midway between the charged objects.


2

2

1

1r

kqr

kqV

rkQ2V

sinLkQ2

1 pt. Showing Field Contributions.

1 pt. Correct Expression Using Given Quantities

2009 AP-B Exam

r

sinLr

(c) 2 pointsOn the following diagram of object 1, draw and label vectors to represent the forces on the object.

T

mg

FE


1 pt. Correct Arrows.

1 pt. Correct Labeling of vectors.

2009 AP-B Exam

(d) 3 pointsUsing the conditions of equilibrium, write—but do not solve—two equations that could, together, be solved for and the tension T in the left-hand string.

T

mg

FE

EFsinT

mgcosT

2

2

r

kQ

22

sinL2

kQ


1 pt. TX = FE.

1 pt. TY = mg.

1 pt. Stating the Two Equations Using Given Quantities

mgcosT

22

sinL2

kQsinT

2009 AP-B Exam

sinL2r

r

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A metal rod of mass 0.22 kg lies across two parallel conducting rails that are a distance of 0.52 m apart on a tabletop, as shown in the top view above. A 3.0 resistor is connected across the left ends of the rails. The rod and rails have negligible resistance but significant friction with a coefficient of kinetic friction of 0.20. There is a magnetic field of 0.80 T perpendicular to the plane of the tabletop. A string pulls the metal rod to the right with a constant speed of 1.8 m/s.


2009 AP-B Exam

(a) 3 pointsCalculate the magnitude of the current induced in the loop formed by the rod, the rails, and the resistor.

RI

0.3

m/s 1.8m 0.52T 80.0 A25.0


RBLv

1 pt. Ohm’s Law

1 pt. Motional EMF 1 pt. Correct answer

2009 AP-B Exam

(b) 4 pointsCalculate the magnitude of the force required to pull the rod to the right with constant speed.

mgF kf 2m/s 9.8 kg 0.2220.0 N 0.43

BILFB m 0.52 A0.25T 80.0 N 0.10

Bf FFF N 0.10N 0.43 N 0.53


1 pt. Force of Friction

1 pt. Correct Magnetic Force

1 pt. Adding the Two Forces

1 pt. Correct answer

2009 AP-B Exam

(c) 3 pointsCalculate the energy dissipated in the resistor in 2.0 s.

PtE

t RI E 2 s .02 3.0 A0.25 2 J 0.38


1 pt. Power-Energy Relationship

1 pt. Electric Power (I2R)

1 pt. Correct Substitution

2009 AP-B Exam

(d) 2 pointsCalculate the work done by the string pulling the rod in 2.0 s.

vtd

s 2.0m/s 8.1d

m 6.3d

FdW

m 3.6N .540W

J 9.1W


1 pt. Correct Expression for Distance

1 pt. Correct Substitution for Force

2009 AP-B Exam

(e) 2 pointsCompare your answers to parts (c) and (d). Provide a physical explanation for why they are equal or unequal.

Answer (c) does not include work done by friction.Work done by friction dissipates energy.


1 pt. Work Done by Friction not Included

1 pt. Friction Dissipates Energy

2009 AP-B Exam

J 9.1W )d(J 0.38E )c(

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The cylinder contains 2.2 kg of water vapor initially at a volume of 2.0 m3 and an absolute pressure of 3.0 x 105 Pa. This state is represented by point A in the PV diagram below. The molar mass of water is 18 g, and the water vapor can be treated as an ideal gas.


2009 AP-B Exam

(a) 3 pointsCalculate the temperature of the water vapor at point A.

nRTPV

nRPVT

KJ/mol 8.31 mol 122

m .02 Pa 10x 0.3 33

K 590

kg/mol 10x 81

kg 2.2n 3 mol 122


1 pt. Ideal Gas Law1 pt. Correct Number of Moles


2009 AP-B Exam

kg/mol 10x 81 M

kg 2.2 m3

W

W

(b) 1 pointCalculate the temperature of the water vapor at point C.

nRPVT

KJ/mol 8.31 mol 122m .52 Pa 10x 0.4 33

K 980


1 pt. Correct Answer and Units

2009 AP-B Exam

The absolute pressure of the water vapor is increased at constant volume to 4.0 x 105 Pa at point B, and then the volume of the water vapor is increased at constant pressure to 2.5 m3 at point C, as shown in the PV diagram. mol 122n

(c) 3 pointsDoes the internal energy of the water vapor for the process A→B→C increase, decrease, or remain the same?

____Increase ____Decrease ____Remain the same

Justify your answer

Internal energy is proportional to temperature.


1 pt. Selecting Increase

2 pt. Correct Justification

2009 AP-B Exam

K 980

K 590

(d) 3 pointsCalculate the work done on the water vapor for the process A→B→C.

The area under the curve represents the work done on the water.

VPW 35 m .500 Pa 10x 0.4 J 10x 0.2 5


1 pt. Work Equals Area Under Curve

1 pt. Correct Numerical Answer and Units

1 pt. Negative Sign on Answer

2009 AP-B Exam

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Three objects of identical mass attached to strings are suspended in a large tank of liquid, as shown above.


2009 AP-B Exam

(a) 3 pointsMust all three strings have the same tension?____ Yes ____ No

Justify your answer.

The tension in each string depends on the weight and buoyant force on each object.The buoyant force on a submerged object depends on the object’s volume.


1 pt. Selecting No

2 pt. Correct Justification2009 AP-B Exam

Object A has a volume of 1.0 x 105 m3 and a density of 1300 kg m3 . The tension in the string to which object A is attached is 0.0098 N.

(b) 3 pointsCalculate the buoyant force on object A.

mg

T B

0mgBT

g Vmg TmgB

TVgB

N 0098.0m/s 9.8 m 10x 0.1 mkg 1300B 2353

N 12B


1 pt. Expression of Equilibrium

1 pt. Using Density and Volume

1 pt. Correct Answer

2009 AP-B Exam

(c) 2 pointsCalculate the density of the liquid.

Object A has a volume of 1.0 x 105 m3 and a density of 1300 kg m3 . The tension in the string to which object A is attached is 0.0098 N.

gVB L

VgB

L 23 m/s 8.9 m 5-10x 0.1

N 12.0

3kg/m 1200



1 pt. Correct Answer

2009 AP-B Exam

BN 12B

(d) 2 pointsSome of the liquid is now drained from the tank until only half of the volume of object A is submerged.Would the tension in the string to which object A is attached increase, decrease, or remain the same?

____ Increase ____ Decrease ____ Remain the same


Less liquid is displaced therefore the buoyant force is less

BmgT


1 pt. Selecting Increase


2009 AP-B Exam

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In a classroom demonstration, a beam of coherent light of wavelength 550 nm is incident perpendicularly onto a pair of slits. Each slit has a width w of 1.2 x 106 m, and the distance d between the centers of the slits is 1.8 x 106 m. The class observes light and dark fringes on a screen that is a distance L of 2.2 m from the slits.


2009 AP-B Exam

(a) 2 pointsCalculate the frequency of the light.

fc

cfm 10x 550

m/s 10x 3.09

8

Hz 10x 5.5 14


1 pt. Speed-Frequency-Wavelength

1 pt. Correct answer

2009 AP-B Exam

m/s 10x 0.3c

m 10x 5509

9

(b) 3 pontsCalculate the distance between two adjacent dark fringes on the screen.

dLmx

1m

dLx

m 10x .81

m 10x 505m .225

9

m 067.0


1 pt. Interference position

1 pt. Interference Separation


2009 AP-B Exam

= 550 nmL = 2.2 md = 1.8 x 106 m

The entire apparatus is now immersed in a transparent fluid having index of refraction 1.4.

(c) 2 pointsWhat is the frequency of the light in the transparent fluid?

Hz 10x 5.5f 14


2 pt. Frequency Does Not Change

2009 AP-B Exam

(d) 3 pointsDoes the distance between the dark fringes increase, decrease, or remain the same?

_____ Increase _____ Decrease _____ Remain the same

Explain your reasoning.

dLx

x is proportional to the wavelength nadthe wavelength decreases in the fluid.


1 pt. Selecting Decrease

2 pt. Correct Reasoning

2009 AP-B Exam

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A photon of wavelength 250 nm ejects an electron from a metal. The ejected electron has a de Broglie wavelength of 0.85 nm.

(a) 3 pointsCalculate the kinetic energy of the electron.

2mvK

2

mvh

mhv

2mhm

2

2

2

m2

hK

2931

234

m10x .850kg10x 11.92

sJ 10x 63.6

J 10x 3.3 19


1 pt. Correct Substitution of wavelength for Velocity

1 pt. Correct Substitution of Planck’s Constant

1 pt. Correct Substitution of Electron Mass

2009 AP-B Exam

(b) 3 pointsAssuming that the kinetic energy found in (a) is the maximum kinetic energy that it could have, calculate the work function of the metal.

A photon of wavelength 250 nm ejects an electron from a metal. The ejected electron has a de Broglie wavelength of 0.85 nm.

hfK

Khf Khc

J 10x 3.3m10x 502

m/s 10x 3.0 sJ 10x 63.6 199

834

J 10x 7.4 19


1 pt. Photoelectric Effect

1 pt. Correct Substitution of Photon Wavelength

1 pt. Correct Substitution of (hc)

1 pt. Correct Units in Parts (a) and (b)2009 AP-B Exam

(c) 3 pointsThe incident photon was created when an atom underwent an electronic transition. On the energy level diagram of the atom below, the transition labeled X corresponds to a photon wavelength of 400 nm. Indicate which transition could be the source of the original 250 nm photon by circling the correct letter.


Emission of the original photon means the atom goes to a lower energy level. Energy is inversely proportional to wavelength.

hcE


1 pt. Selecting Correct Transition


2009 AP-B Exam

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2009 AP-B Exam