2003 ap physics workshop, ted vittitoe. problem b-1 problem b-2 problem b-3 problem b-4 problem b-5...

2003 AP Physics Workshop, Ted Vittitoe

Problem B-1

Problem B-2

Problem B-3

Problem B-4

Problem B-5

Problem B-6

Problem B-7


Problem B-1 (15 points)A rope of negligible mass passes over a pulley of negligible mass attached to the ceiling, as shown. One end of the rope is held by Student A of mass 70 kg, who is at rest on the floor. The opposite end of the rope is held by Student B of mass 60 kg, who is suspended at rest above the floor.


(a) On the dots below that represent the students, draw and label free-body diagrams showing the forces on Student A and on Student B.

A

B

gmA

T

T gmT B

gmBN

NTgmA


(b) Calculate the magnitude of the force exerted by the floor on Student A.

0F

gmNT A

gmgmN BA

106070N

gmmN BA

A

gmA

T

NgmT B

N100


Student B now climbs up the rope at a

constant acceleration of 0.25 m/s2 with respect to the floor.

(c) Calculate the tension in the rope while Student B is accelerating.

amF BB

amgm'T AA

gmam'T AA

gam'T A 1025.060 N615


Student B now climbs up the rope at a

constant acceleration of 0.25 m/s2 with respect to the floor.

(d) As Student B is accelerating, is Student A pulled upward off the floor?

The tension in the rope must exceed the weight (700 N) of Student A for him/her to be pulled off the ground.

Justify your answer.

No


Student B now climbs up the rope at a constant acceleration of 0.25 m/s2 with respect to the floor.

(e) With what minimum acceleration must Student B climb up the rope to lift Student A upward off the floor?

When T = 700 N

amF BB

amgmT AA

A

Am

gmTa

60

1060700 2m/s 67.1


Problem B-2 (15 points)A circuit contains two resistors (10 and 20 ) and two capacitors (12 F and 6 F) connected to a 6 V battery, as shown in the diagram. The circuit has been connected for a long time.


(a) Calculate the total capacitance of the circuit.

Capacitors is series:

21

21CC

CCC

612612

F 4


(b) Calculate the current in the 10 resistor.

Kirchhoff’s loop rule:

0IRIRV 2010B

2010

BRR

VI

20106

A 20.0


(c) Calculate the potential difference between points A and B.

The voltage between points A and B is the same as

the voltage across R20.

2020R IRV 2020.0 V 0.4


(d) Calculate the charge stored on one plate of the 6 F capacitor.

VQ

C

CVQ V 4F 4 C 16


(e) The wire is cut at point P. Will the potential difference between points A and B increase, decrease, or remain the same.'?

____increase ____decrease ____remain the same

Justify your answer.

In a steady state, the capacitors represent a break in the circuit between points A and B. Cutting the wire a point P is just another break and will have no effect on the potential difference between points A and B


Problem B-3 (15 points)A rail gun is a device that propels a projectile using a magnetic force. A simplified diagram of this device is shown above. The projectile in the picture is a bar of mass M and length D, which has a constant current I flowing through it in the +y-direction, as shown. The space between the thin frictionless rails contains a uniform magnetic field B, perpendicular to the plane of the page. The magnetic field and rails extend for a distance L. The magnetic field exerts a constant force F on the projectile, as shown.


Express all algebraic answers to the following parts in terms of the magnitude F of the constant magnetic force, other quantities given above (M, D, I, B, L) , and fundamental constants.


(a) Determine the position x of the projectile as a function of time t while it is on the rail if the projectile starts from rest at x = 0 when t = 0.

2at

tvx2

o

M2Ft2

MF

a

0vo

2t

MF

t0x2


(b) Determine the speed of the projectile as it leaves the right-hand end of the track.

Work/Energy Theorem

KW

2Mv

FL2

MFL2

v


(c) Determine the energy supplied to the projectile by the rail gun.

FLW


(d) In what direction must the magnetic field B point in order to create the force F ?

+Z direction

The magnetic force on a current-carrying conductor

Explain your reasoning.

Rule)-Hand-(Right BIDF


(e) Calculate the speed of the bar when it reaches the end of the rail given the following values.

B = 5 T L = 10 m I = 200 A M = 0.5 kg D = 10 cm

MFL2

v

MIDLB2

v

5.05101.02002

m/s 63

IDBF


You have an optical bench, which is a long straight track as shown. Objects in holders can be attached at any location along the bench. In addition to the concave mirror and the lit candle in holders, you also have the following equipment.

convex mirror in holder concave lens in holder convex lens in holder meter stick ruler screen in holder

Problem B-4 (15 points)In your physics lab, you have a concave mirror with radius of curvature r = 60 cm. You are assigned the task of finding experimentally the location of a lit candle such that the mirror will produce an image that is 4 times the height of the lit candle.


(a) Briefly list the steps in your procedure that will lead you to the location of the lit candle that produces the desired image. Include definitions of any parameters that you will measure.

Place the concave mirror at one end of the optical bench (x = 0).Place the candle 60 cm from concave mirror and adjust theposition of the screen until you get a sharp image.. Move the candle slowly toward from the mirror while adjusting theposition of the screen to keep a sharp image. Use the rulerto measure the height of the candle flame and its image.Continue adjusting the position of the candle until it imageis 4 times larger than the flame.


(b) On the list of equipment place check marks beside each additional piece of equipment you will need to do this experiment.

____convex mirror in holder ____concave lens in holder ____convex lens in holder ____meter stick ____ruler ____screen in holder


(c) On the scale below, draw a ray diagram of your lab setup in part (a) to show the locations of the candle, the mirror, and the image.

150 cm

image37 cm

0mirror

object


____real ____upright ____ larger than object

____virtual ____ inverted ____smaller than object

(d) Check the appropriate spaces below to indicate the characteristics of your image.


(e) You complete your assignment and turn in your results to your teacher. She tells you that another student, using equipment from the same list, has found a different location for the lit candle. However, she tells both of you that the labs were done correctly and that neither experiment need be repeated. Explain why both experiments can be correct.

Lenses had different focal lengths


Problem B-5 (10 points)A cylinder with a movable piston contains 0.1 mole of a monatomic ideal gas. The gas, initially at state a, can be taken through either of two cycles, abca or abcda, as shown on the PV diagram above. The following information is known about this system.

J 75WJ 450UU

path curved the alongJ 201Wpath curved the alongJ 685Q

cbaba

acac


(a) Determine the change in internal energy, Ua - Uc, between states a and c.

J 75WJ 450UU


cbaba

acac

TncU v

TR23

nU

271722315.8

23

1.0U J 625


(b) i. Is heat added to or removed from the gas when the gas is taken along the path abc ?

____added to the gas ____ removed from the gas

J 75WJ 450UU


cbaba

acac

ii. Calculate the amount added or removed.

nRpV

T

nRTpV

K 271TK 361TK 722T

cba

bcababc QQQ bcpabvabc TncTncQ

90361315.81.0Q25

23

abc

bc25

ab23

abc TRnTRnQ bc2

5ab2

3abc TTnRQ

J 637


(c) How much work is done on the gas in the process cda?

345 m10x5.2Pa 10x6W

dad VpW

J 150


(d) Is heat added to or removed from the gas when the gas is taken along the path cda?

____added to the gas

____removed from the gas

In process cd: Heat must be added to increase the internal energy

In process da: Heat must be added to do work and also to increasethe internal energy

Explain your reasoning.


Problem B-6 (10 points)A diver descends from a salvage ship to the ocean floor at a depth of 35 m below the surface. The density of ocean water

is 1.025 × 103 kg/m.

(a) Calculate the gauge pressure on the diver on the ocean floor.

ghp

351010 x 025.1p 3Pa 10 x 52.3 5


(b) Calculate the absolute pressure on the diver on the ocean floor.

ghpp o

351010 x 025.110 x 013.1p 35Pa 10 x 53.4 5


The diver finds a rectangular aluminum plate having dimensions 1.0 m × 2.0 m × 0.03 m. A hoisting cable is lowered from the ship and the diver connects it to the

plate. The density of aluminum is 2.7 × 103 kg/m( Ignore the effects of viscosity.

(c) Calculate the tension in the cable if it lifts the plate upward at a slow, constant velocity.

BwT

gmw Al gVB ww

VgVgT wAl

gVw Al

VgT wAl 8.906.010x 1.02510x 2.7 33 N 985


The diver finds a rectangular aluminum plate having dimensions 1.0 m × 2.0 m × 0.03 m. A hoisting cable is lowered from the ship and the diver connects it to the plate. The density of aluminum is 2.7 × 103 kg/m(Ignore the effects of viscosity.

(d) Will the tension in the hoisting cable increase, decrease, or remain the same if the plate accelerates upward at 0.05 m/s2?

____increase ____decrease ____remain the same


Problem B-7 (10 points)Energy-level diagrams for atoms that comprise a helium-neon laser are given above. As indicated on the left, the helium atom is excited by an electrical discharge and an electron jumps

from energy level Eo to energy level E2. The helium atom

(atomic mass 4) then collides inelastically with a neon atom (atomic mass 20), and the helium atom falls to the ground state, giving the neon atom enough energy to raise an electron from

Eo' to E2'. The laser emits light when an electron in the neon

atom falls from energy level E2' to energy level El'.2003 AP Physics Workshop, Ted Vittitoe

(a) Calculate the minimum speed the helium atom must have

in order to raise the neon electron from Eo' to E2'.E'EK

J 10x 3.306 18J 10x 3.298 18

o2'o

'2

2He EEEE2

vm

He

o2'o

'2

m

EEEE2v

72

1818

10x 66.14

10x 3.29810x 3.3062

m/s 1,550v 2003 AP Physics Workshop, Ted Vittitoe

(b) Calculate the DeBroglie wavelength of the helium atom when it has the speed determined in (a).

HeHevmh

p

HeHevmh

155010x 1.664

10x 6.6327

34m 10x 6.44 11


(c) The excited neon electron then falls from E2' to El' and

emits a photon of laser light. Calculate the wavelength of this light.

J 10x 3.306 18

J 10x 2.992 18

hc

E

Ehc

8181

25

10x 2.99210x 3.306

10x 1.99 m 10x 34.6 7


(d) This laser light is now used to repair a detached retina in a patient' s eye. The laser puts out pulses of length 20 × 10-3 s that average 0.50 W output per pulse. How many photons does each pulse contain?

tE

P t

hcn

hcPt

n

52

7

10x 99.1

10x 6.3402.050.0 photons 10x 19.3 16


END


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