Phys 261 Final
(Exp 2)"1/3" rule to determine the uncertainty ∆x
Error is 1/3 of the smallest unit (Ex: ruler in mm, error=1/3mm)
(Exp 8)# harmonic=
# of antinodes
(Exp 8)n=
# of antinodes
(Exp 7)amplitude x0=
(A0/2)/(sqrt((f^2/(Q^2*f0^2))-((f^2/f0^2)-1)^2) A0=drive amplitude
(Exp 5)Make a sketch that shows how the period of the rotating mass varies with the radius of the masses orbit
(look at graph in exp) period reduces as radius increases, steep at first then levels off
(Exp 6)percentage error for small angle approximation
(sin(theta)-theta)/sin(theta) * 100 ***theta is in radians
(Exp 4)Acceleration vs time
(v2-v1)/(t2-t1)
(Exp 4)Velocity vs time
(xf-x0)/(tf-t0)
(Exp 4)some external forces that cannot be completely eliminated exp 4
-drag -small tilts -residual tilt
(Exp 6)Suppose a pendulum bob is swinging with an amplitude Θo = 0.1 radians and a frequency ω0 = 2π radians/sec. The angle the pendulum's string makes with the vertical direction can be written as Θ = Θo cos (ωot). Use the spreadsheet to compute Θ at times = 0, 0.1, 0.2, 0.3,..., 1.9, 2.0 seconds and then plot Θ versus t.
-plug in given times into the eqn to get amplitude values -plot amplitude and time points on a plot
(Exp 6)Is a calibration error in the timer a systematic or random error in determining g? Can you overcome this by making more measurements with the same timer?
-systematic error -no, same error for all measurements
(Exp 9)How precisely can you measure temperature in the Charles law apparatus? How precisely can you measure the pressure?
.01 degrees Celsius .01 kPa DeltaT=0.003*T+0.2 DeltaP=Pavg/500
(Exp 7)The phase θ is equal to (blank) for f=0
0
(Exp 2)The smallest increment the scale can display is 0.1 g and thus the uncertainty ∆M in a measurement of mass would be about
0.033 g
(Exp 4)A χ-dist value between (blank) is indicative of statistical agreement or a good fit.
0.05 and 0.95
(Exp 2)reduced χ2 should equal (blank) for good fit
1
(Exp 1)Before the lab template will let you exit from EXCEL, according to step 21, you must...
1) enter your name in the designated area of the spreadsheet 2) enter your section number in the designated area of the spreadsheet 3) save the file using the gray save button in the body of the spreadsheet
(Exp 5)the large gear wheel at the top of the apparatus reduces the rotation rate by about a factor of 27 so that the period of the mass will be only about
1.8 Hz
(Exp 7)To what uncertainty can the drive frequency be determined in this experiment?
1/3 mHz
(Exp 7)The phase θ is equal to (blank) for f >>f0
180
(Exp 9)What is room temperature on the Celsius temperature scale, approximately?
21.1 Degrees Celsius
(Exp 8)Sketch the shape of the string when it is excited in the third harmonic.
3 anti nodes and 4 nodes
(Exp 5)3000 rpm is 50 revolutions per second or
50 Hz
(Exp 6)One radian is equal to how many degrees?
57.3 degrees (180/pi)
(Exp 7)Suppose the drive frequency f equals the resonance frequency fo. What is the phase difference θ between the position of the drive and the mass?
90 degrees
(Exp 6)∆g pendulum
=2*g/a*∆a
(Exp 2)χ2
=∑((xi-xtheory)/∆xi)^2
(Exp 3)Sonic ranger
A loudspeaker emits a brief pulse of sound that reflects off a screen attached to the cart. The reflected sound returns to the speaker, where it is detected by means of a microphone.
(Exp 9)Use the thermometer to accurately measure room temperature and estimate the uncertainty in this measurement. Be sure to give proper units.
About 20 degrees CelsiusUncertainty:Using Charles Law Apparatus: deltaT=0.003*T+.02Using thermometer: deltaT=0.5 or 0.25 of smallest division
(Exp 8)for a given tension does the wave speed depend on the frequency?
As the frequency increases, the wave speed increases
(Exp 9)Without using a thermometer, how can you establish a temperature of 100 °C?
Boil water
(Exp 7)Make a sketch, which shows how the amplitude depends on frequency
Cusp
(Exp 4)How can it happen that when two carts collide in this experiment that the total momentum of the two carts is not conserved?
External forces are not conserved
(Exp 3)Force of cart
Fx = Mgsin(θ)
(Exp 2)Degrees of freedom (v)
N-α (where N is the number of measurements and α is the number of fitting parameters used to find the theoretical value from the data)
(Exp 9)P1V1=
P2V2
(Exp 9)Using the Charles' law apparatus, a student finds pressures of 760, 840, 950 mm of Hg at temperatures of 26 °C, 57 °C, and 100 °C respectively. Use the spreadsheet to make a plot of P versus T and find the slope of the resulting straight line. Does the data agree with Charles's law? Briefly explain.
Plot in excel. Linear relationship-->P=C*T
(Exp 9)Explain how you can use the Charles' Law apparatus to determine the absolute zero temperature.
Plotting temperature vs pressure yields a linear line. The y intercept of the line would be the slope multiplied by absolute zero.
(Exp 7)Explain how you could measure the Q of the resonance in this system?
Record the oscillations, find f0 by finding the period and taking the inverse (1/period), find the damping time (td, time where amplitude is 1/3 max amplitude), then plug into equation: Q=2pif0*td/2
(Exp 7)Suppose that you wanted to decrease the resonance frequency of the system, what could you do?
Reduce the mass
(Exp 9)Using the Boyle's law apparatus, a student finds volumes of 40, 30, 20, and 15 cm3 at pressures of 7.5, 10, 15, and 20 lb/in2 . Use the spreadsheet to make a log-log plot of P versus V and find the slope of the resulting straight line (hint: plot the log of P versus the log of V rather than using the spreadsheets log plotting option.). Does the data agree with Boyle's law? Briefly explain.
Slope=-1So exponential equation has exponent of -1 which is the same as 1/(base of exponent). This correlates to V'=Cb(1/Pavg)-V0V as function of P:V=(nRT)/P
(Exp 7)Make a sketch, which shows how the phase depends on frequency.
Slope=0, then sharp incline, then slope=0
(Exp 6)Period of oscillation
T=2π/ω=2π*sqrt(L/g)
(Exp 8)A student measures wave speeds of 5 m/s, 7 m/s, 10 m/s and 15 m/s for tensions of 1 N, 2 N, 4 N, and 9 N respectively. Use the spreadsheet to make a log-log plot of the wave speed versus the tension. Also find the slope of the resulting straight line.
Take log of both variables. Plot. Add trendline with equation. log(v)=0.5*log(T)-0.5*log(density)
(Exp 6)Why is it important to keep the angle small in this experiment?
The angle must be small for the period eqn to be valid, if the angle is small theta=sin(theta), this equivalence is used to derive the period
(Exp 1)A cell in an Excel spreadsheet contains $A$5. What does it mean?
The cell is fixed
(Exp 7)Suppose that you wanted to increase the quality factor Q of the system, what could you do?
The mass could be increased.
(Exp 4)What is the physical source of the change of sign in v2 - v1 in your plot in Part C?
The source of change is due to drag and small tilts.
(Exp 9)What does "absolute zero temperature" mean?
The temperature at which the pressure of an ideal gas would be zero (0 Kelvins)
(Exp 4)Two carts collide and bounce off each other. If there are no external forces acting on the system, which of the following is true:
The total kinetic energy can change during the collision but the total momentum of the carts must be the same before and after the collision
(Exp 6)What effect does the weight of the bob have in this experiment?
The weight provides a restoring force on the pendulum. It increases tension but does not affect frequency, period, or length. The bob is pulled down by the same gravitational force, no matter what mass the bob has. Thus, motion is independent of the mass.
(Exp 8)y = ax^n is equivalent to
log(y)=log(a)+nlog(x)
(Exp 4)Perfectly inelastic eqn
m1v1+m2v2=(m1+m2)vf
(Exp 2)Using the ruler, and without using the vernier calipers, estimate how precisely you can measure the length of one of the sides of one of the blocks.
To the nearest mm with an error of 1/3mm
(Exp 8)How is the spacing between nodes of a standing wave related to the wavelength?
Wavelength=2*spacing between two nodes
(Exp 4)Explain how the optical picket fence works and how this system can find the velocity of the cart.
When the cart moves through an optical gate, the dark parts of the picket fence block the sensor beam. The gates keep track of when the light intensity changes, and then use the known distance between the pickets to find the speed of the cart.
(Exp 4)below 0.05 indicates
a disagreement between values.
(Exp 7)In this lab a periodic force is applied to the cart using:
a spring that is attached to a speaker
(Exp 6)T=
a*L^b
(Exp 3)a0 vs height
a=gh/L g=L*(slope of a vs height)
(Exp 4)Above 0.95 is too high and can indicate
an overestimation of the uncertainties
(Exp 5)linear speed(v)=
angular speed(ω)*r
(Exp 2)Determining if values are consistent
are within 2 error bars from the accepted value
(Exp 3)acceleration of cart
ax=gsin(θ)
(Exp 5)Percent difference equation
known-experimental/known x 100
(Exp 4)Inelastic and inelastic eqn(conservation of momentum)
mAvA+mBvB=mAvC+mBvD
(Exp 3)The ranger measures the position by...
emitting an ultrasonic pulse
(Exp 8)With a total mass of 200 gm hanging on the end of the string, measure the frequency of the fundamental.
f=(1/2*L)*(sqrt(T/mu))
(Exp 7)What is the quality factor Q?
fres=f0*sqrt(1-(2*Q^2))
(Exp 6)The forces on the mass on the pendulum are due to
gravity and the tension T in the string
(Exp 2)"two-sigma rule"
if your data point is no more than two error bars from the accepted value then the disagreement is not significant
(Exp 6)If you make a pendulum 3 times longer, then its period of oscillation will...
increase by a factor of the square root of 3
(Exp 2)Random errors
involve errors in measurement due to random changes or fluctuations in the process being measured or in the measuring instrument.
(Exp 2)Illegitimate errors
involve making gross mistakes in the experimental setup, in taking or recording data, or in calculating results.
(Exp 2)systematic error
is a repeated and consistent error that occurs in all of your measurements due to the design of the apparatus
(Exp 2)sampling error
is a special kind of random error that occurs when you make a finite number of measurements of something which can take on a range of values
(Exp 7)the phase changes most rapidly when the drive frequency f
is near the resonance frequency (1.5 Hz in this case) and that the change is more rapid for larger Q
(Exp 2)Density consistent value
measured and accepted density should differ by no more than twice the uncertainty.
(Exp 1)What is the Solver used for? (pick the best answer)
minimizing or maximizing a cell by varying other cells
(Exp 9)PV=
nRT
(Exp 4)momentum eqn
p=mv
(Exp 3)x vs t plot for the cart
parabolic
(Exp 1)Which type of chart in EXCEL will actually plot the point at its Cartesian coordinates?
scatter chart
(Exp 6)small angle approximation
sin(theta)=theta
(Exp 6)∆L=
sqrt(2)*∆y
(Exp 2)estimate
sum of values/# of values
(Exp 5)radius of orbit eqn
tan(theta)=(r-r0)/(sqrt(L^2-(r-r0)^2)
(Exp 5)What provides the vertical force to balance the force of gravity on the pendulum bob?
tension in the string
(Exp 4)The fact that momentum is a vector means that you will need to keep track of both
the direction and magnitude of the momentum of each object in order to find the total momentum
(Exp 4)Elastic Collision -
the objects bounce off each other and the total kinetic energy before the collision is the same as after the collision. For such a collision the total momentum will not change and and the total kinetic energy will not change
(Exp 4)Inelastic Collision -
the objects bounce off each other but the total kinetic energy before the collision is different from that after the collision. Although the total kinetic energy will change, the total momentum will not change
(Exp 6)Why should the period be independent of the mass
the period is only dependent on L and g. Acceleration due to gravity is constant regardless of the mass.
(Exp 6)period
the time for one swing.
(Exp 4)Perfectly Inelastic Collision
the two objects collide and stick together resulting in the maximum kinetic energy being lost, total momentum unchanged
(Exp 1)To run a macro in EXCEL, you may need to first click on.....?
the view tab and then click on the macro button.
(Exp 3)tilt angle of the air-track
theta= invsin(added height/length of track)
(Exp 7)phase difference
theta=arctan((1/Q)((f*f0)/(f0^2-f^2)))
(Exp 8)fundamental mode velocity eqn
v = 2fL
(Exp 8)fundamental frequency=
v/(2*L)
(Exp 3)vtheory=
v0+a*t
(Exp 3)If it takes a time interval ∆t for the sound to leave the speaker and return, then the distance to the cart must be...
x = 0.5*s0*∆t where so = 330 m/s
(Exp 3)xtheory=
x0+v0*t+0.5*a0*t^2
(Exp 3)position of cart vs time
x=0.5gsing(theta)*t^2*v0*t+x0
(Exp 4)What is the maximum height y that the pendulum can reach in this experiment?
y0 + L
v(wave propagation speed)=
λ f
(Exp 5)period eqn
τ=2πsqrt((rsqrt(L^2-(r-r0)^2))/g*(r-r0)) L=length r=radius of orbit τ=period
(Exp 2)reduced χ2 eqn
χ2/v
(Exp 2)Density error
∆ ρ =ρ sqrt((∆V/V)^2 + (∆M/M)^2)
(Exp 6)∆ τ avg=
∆ τ/sqrt(N)
(Exp 2)Volume error
∆V =V*sqrt((∆c/c)^2 + (∆b/b)^2 + (∆a/a)^2)
propagation of errors equation
∆f=sqrt(sum((df/dx)*∆x)^2))
(Exp 2)Mean error
∆〈x〉=∆x/sqrt(N)
