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P185 Lab Manual (Drum) Revised 4/24/15
Orange Coast College
Physics 185 Lab Manual
ContentsSubjectPage
Lab 1Galileo and the Pendulum2
Lab 2Free-fall5
Lab 3 Understanding Motion8
Lab 4Force Vectors11
Lab 5Newton’s 2nd Law12
Lab 6Forces and Collisions14
Lab 7Energy Conservation15
Lab 8Momentum and Collisions19
Lab 9Buoyancy21
Lab 10Heat and Temperature24
Lab 11Simple Harmonic Motion27
Lab 12Resonance31
Lab 13Statistics34
Lab 14Velocity of Sound33
Lab 15Cannonball Range37
Lab 16Fluid Flow41
Lab 17Moment of Inertia45
Lab 18Error Analysis47
Appendix48
Lab 1: Galileo’s PendulumName: ______
1. Period and amplitude
Find the period of a pendulum for various amplitudes.
Table 1.1 Period vs. Amplitude
() / # of Osc. / Total ttrial 1 / Total t
trial 2 / T
2
4
6
8
10
15
20
30
40
50
60
1.2Graph T() with the y-axis starting at 0.
Graph T()with the y-axis covering just the range of your data.
In your report, discuss the validity of Galileo’s hypothesis based on your evidence.
2. Finding g with a pendulum
2.1For one small (<5) amplitude, find T for two trials of 100 oscillations each.
() / N / Total tTrial 1 / Total t
Trial 2 / T
100
2.2Re-write the equation to find g.
Length of string: ______Diameter of ball: ______
Total length d: ______Period T: ______
Experimental g: ______Theoretical g: ______
Error Analysis: Determining basic errors
List all measured quantities and the measuring instrument. Include units.
List the errors on each quantity. Briefly indicate how you determined the errors.
Quantity& Instrument / Errors / How determined
t / Read.
Cal.
Other
/ Read.
Cal.
Other
L / Read.
Cal.
Other
D / Read.
Cal.
Other
Lab 2: Free-fall Name: ______
Position and speed vs. time
Find the time for the ball to drop various distances.
For h = 5 to 35 cm, take a data point every 5 cm.
For h = 40 to 70 cm, take a data point every 10 cm.
For h = 80 to 120 cm, take a data point every 20 cm.
Table 2.1 Position vs. time
x / t1 / t2 / tAVG / x / t / v / t1/22. Analyzing the data
2.1Make four graphs:
(1) Graph v(t) using Excel and a linear fit line
(2) Graph x(t2) using Excel and a linear fit line
(3) Graph x(t) using Excel and a power fit line
(4) Graph x(t) using Data Studio and a power fit line
Print each graph. For each graph,
- Write the equation you expect from the theory of kinematics.
- Write the equation of the computer-generated fit line to your data.
- Circle each number or variable in the kinematic equation and draw a line to the corresponding quantity in the computer equation.
- Calculate the value of “a”. Find your average “a” and compare to the book value.
V(t) / Kinematic Equation / Value for a
Computer Equation
x(t2) / Kinematic Equation / Value for a
Computer Equation
x(t) / Kinematic Equation / Value for a
Computer Equation
x(t) / Kinematic Equation / Value for a
Computer Equation
Questions
1.Is the acceleration constant? How do you know?
2.Is the object in “free fall?” How do you know?
Error Analysis: Determining basic errors
List all measured quantities and the measuring instrument. Include units.
List the errors on each quantity. Briefly indicate how you determined the errors.
Quantity& Instrument / Errors / How determined
t / Read.
Cal.
Other
x / Read.
Cal.
Other
Lab 3: Understanding MotionName: ______
1. Position graph
Get the motion sensor set up and working properly. Pull up the position-match graph.
DO NOT PRACTICE FOR THE FIRST TRY.
- Make ONE trial where you match your movement to the graph.
- Print out this trial.
- Delete the graph.
- Let the next person try.
When everyone in the group has printed their trial, sit down and analyze your graph. Look at the graph and circle regions where your graph doesn’t match the red line. Explain why the two graphs don’t match. Be as specific as possible.
1.2When everyone is finished with part 1.1, make more trials to match the graph.
- Make several trials to you match your movement to the graph. Keep going until you have one you think is a good fit.
- Delete all the graphs but your best.
- Print out this trial.
- Delete the graph.
- Let the next person try.
2. Velocity graph
2.1This procedure is exactly the same, but using the velocity-match graph.
Questions
1.Which graph, x(t) or v(t), was smoother. Why?
2.Which one was easier to match? Why?
Lab 4: Force VectorsName: ______
1. Theory
- For an object in equilibrium,
2. Two forces
2.1Put two hangers on the table: 100 g for m1 at 0 and an empty hanger for m2 at 180.
Find the range for m2 at equilibrium. MMIN = _____ g mMAX = _____ g
3. Three forces
3.1Put three hangers on the table: 100 g for m1 at 0, 200 g for m2 at 160 and an empty hanger for m3.
What mass and angle on the third hanger do you predict will create equilibrium? Draw a free-body diagram and find the vector components; do not use any other method. Check your prediction with the instructor before hanging any weights.
PREDICTED = ______MEASURED = ______difference ______
mPREDICTED = ______mMEASURED = ______% difference ______
4. Three forces
4.1Put three hangers on the table: 100 g for m1 at 0, 150 g for m2 at 140 and an empty hanger for m3. Find the mass and angle for m3 by trial and error.
M3 = ______3 = ______
Now use vector algebra to find the magnitude of the net force. Draw a free-body diagram and show all your work.
Lab 5: Newton’s 2nd LawName: ______
1. Predicting acceleration
1.1A cart on a frictionless track is attached to a weight. The
cart’s mass is M and the weight’s mass is m.
Draw two free-body diagrams: one for the cart and one for the weight. Don’t include friction or air resistance.
Write FNET = ma for the cart in terms of M, m, g, and the tension T.
Write FNET = ma for the hanging weight in terms of M, m, g, and T.
Solve for a.
2. Measuring F and a
2.1You instructor will explain how you will measure a.
For each of the weights in the table below, find your expected acceleration and then measure a.
Table 2.1 Acceleration for Different Weights
m (kg) / aEXPECTED / aMEASURED / % Difference.050
.100
.150
.200
3.Inclined plane
For the cart going uphill draw a free-body diagram; include friction.
Write an equation for a for the cart going uphill. Assume uphill is positive.
For the cart going downhill draw a free-body diagram; include friction.
Write an equation for a for the cart going downhill. Assume downhill is positive.
We want to find f by measure a. For the two equations you wrote, solve for f in terms of aUP and aDOWN.
Set up an inclined plane. Measure a both up the ramp and down the ramp. Use this data to estimate the force of friction on the cart.
Lab 6: Forces and CollisionsName: ______
1. Collisions
Cart A collides with cart B. Sensors measure the forces during the collision.
In the table, various combinations of bumper, mass, and motions are given. Cart A always moves to the right initially. Fill in the “Predicted” column with a >, =, or < symbol.
Table 1.1 Forces in Collisions
Bumper / Mass / BMoves / FA ? FB
Pre-dicted / Maximum F / Mea-
sured
>, <. = / Impulse / Mea-
sured
>, <. =
FA / FB / IA / IB
Magnetic / A = B / Left
A = B / Stop
A B / Left
A B / Over-take
Spring / A = B / Left
A = B / Stop
A B / Left
A B / Over-take
Clay / A = B / Left
A = B / Stop
A > B / Left
A > B / Over-take
Lab 7: EnergyName: ______
1. Definitions
- The formulas for kinetic energy (KE) and potential energy (PE) are:
1.1Open DataStudio
1.2Write a formula expressing PE in terms of m, g, and x:
2. Energy
2.1On the left-hand graph below, draw a plot of what you expect a graph of
the PE to look like as the cart goes up and down the track.
On the right-hand graph below, draw a plot of what you expect a graph of
the KE to look like as the cart goes up and down the track.
Graph 2.1: PE and KE of a Coasting Cart
2.2Find : ______
Weigh your cart. m: ______(kg)
2.3Get a good run for position vs. time. Check with your instructor. Erase all but the best run.
2.4Your instructor will show you how to use the calculator function.
- To graph PE, click on the calculator icon and enter the formula for PE.
- To graph KE, click on the calculator icon and enter the formula for KE.
- To graph E, click on the calculator icon and enter the formula for E.
2.3Draw graphs of PE and KE on graph 2.1 using solid lines. How are the two graphs different? Explain any differences in your lab report.
Print out your graphs of PE, KE, and total E.
2.4Find the total energy for the beginning and end of the run.
EINITIAL ______JEFINAL ______J
What % of the original energy was lost? Where did it go?
3. Spring
3.1Set up a hanging spring. Obtain a graph of y(t) for the mass as it oscillates.
Create a graph of kinetic energy vs. time.
Create a graph of GPE vs. time.
Create a graph of EPE vs. time.
Create a graph of total energy vs. time.
Error Analysis: Combining Errors
Find the uncertainties on “m” and “v” for two different trials. Express each uncertainty as both an absolute number and a relative number.
To change between % to absolute for a measurement of “x” use:
Find the total error on each measurement.
To find the total error use:
Quantity / READAbs % / CAL
Abs % / OTHER
Abs % /
Abs %
Lab 8: Conservation of MomentumName: ______
1. Collisions
In this lab we will measure the momentum of colliding carts.
Magnetic bumpers: 1. Equal mass cars, one car at rest.
2. Equal mass cars, both cars in motion.
3. Unequal mass cars, both cars in motion.
Clay bumpers:4. Equal mass cars, one car at rest.
5. Equal mass cars, both cars in motion.
6. Unequal mass cars, smaller car at rest.
“Explosion:”7. Equal mass cars.
- Unequal mass cars.
In your lab report, you will want to include the following:
- Was momentum conserved in all cases, according to your data?
- When was kinetic energy conserved, according to your data?
- Was the percent difference always a reliable measure? If not, what else would you use to compare initial and final states?
Anaylsis
Analysis: Using the percent difference formula
If two momentums are opposite and almost equal, or both zero, you will get a total momentum of nearly zero. Using the percent error formula will give you a meaningless number in this case. Consider comparing the absolute values or using some other method to decide if momentum is being conserved.
Analysis: Kinetic Energy
Under what conditions do you expect KE to be conserved? Partially conserved?
Error Analysis: Combining Errors
To change between % to absolute for a measurement of “x” use:
Find the total error on each measurement.
To find the total error use:
Quantity / READAbs % / CAL
Abs % / OTHER
Abs % /
Abs %
Quantity / READ
Abs % / CAL
Abs % / OTHER
Abs % /
Abs %
Lab 9: BuoyancyName: ______
1. Theory
1.1The theoretical buoyant force is given by
- ρ = 1000 kg/m3 for water
- g = 9.8 m/s2
- V is the volume of the object in m3
To measure the buoyant force, compare the weight of an object in and out of the water:
The volume for various shapes is
For this lab, use meters, kilograms, and newtons.
2. Predicting Buoyancy
2.1For each object, measure the dimensions and calculate V and FB.
Table 2.1 Theoretical Buoyant Force
Object / Dimensions (m) / V (m3) / FB (Theory) (N)3. Measuring Buoyancy
3.1Calibrate your force sensor. Your instructor will explain this.Find the buoyant force of various objects. Compare to the predictions.
Table 3.1 Measured Buoyant Force
Object / WIN (N) / WOUT (N) / FB (Measured)Table 3.2 Summary
Object / FB (Theory) / FB (Measured) / % Diff4. Capacity of a boat
4.1Find the maximum buoyant force the water could exert on your “boat” (really it’s a tuna can). Show your work on a separate sheet.
Use this to predict the maximum load of your boat.
4.3Load up your boat until it sinks. How much could it hold?
Predicted Capacity: ______Measured Capacity: ______
Error Analysis: Propagationby Substitution; Comparing Numbers Using Errors
For a sphere, find the error on D. For a cylinder, find the errors on D and L.
Use only absolute errors.
To find the total error use:
Quantity and Value / READ / CAL / OTHER / DSphere=
DCylinder=
LCylinder=
Find the largest and smallest possible value for eachquantity.
Quantity / Max Value / Min ValueDSphere=
DCylinder=
LCylinder=
Find the largest and smallest possible value for eachquantity.
Quantity / Max Value / Min ValueVSphere=
VCylinder=
Express Vin “” notation
VSphere = ______± ______
VCylinder = ______± ______
Lab 10: Specific Heat & Abs. ZeroName: ______
1. Theory
Heat energy (Q) is related to temperature by
- The ideal gas law is , T in kelvins.
2. Specific Heat of a Metal
2.1Weigh out a metal sample in a cup. Add about 200 cc of hot water. Find c.
Metal / Aluminum / Copper / Iron / LeadAmount / 200 g / 500 g / 500 g / 800 g
Metal / mMETAL / MWATER / TINITIAL / TFINAL
Metal / c / cBOOK / % Diff
3. Constant-volume Thermometer
3.1Graph P vs. T. Graph your data. Draw a fit line and extend it back to P = 0. At what T does P = 0? What is the significance of this?
Table 3.1 Pressure of air at different temperatures
T (C) / P (kPa)Error Analysis: Propagationby Substitution; Comparing Numbers Using Errors
For a sphere, find the error on r. For a cylinder, find the errors on r and h.
If you have a relative error, convert it to an absolute error.
Quantity and Value / READ / CAL / OTHER / Find the largest and smallest possible value for eachquantity.
Quantity / Max Value / Min ValueFind the largest and smallest possible value for eachquantity.
Quantity / Max Value / Min ValueExpress FB in “” notation
FB,S = ______± ______
FB,C = ______± ______
Compare this value of I to the theoretical calculation. Are the two values comparable within the stated uncertainty?
Lab 11: Simple Harmonic MotionName: ______
1. Static stretching and Hooke’s Law
Find the stretching distance as a function of force.
Table 8.1 Stretching vs. Force
m (kg) / X (m) / x (m) / F (N)0
2. Period of oscillation
2.1Find the period of oscillation for various masses. Leave “M” blank for now.
Table 8.2 Period vs. m
m (kg) / # of Osc. / Total t (s)trial 1 trial 2 / T (s) / M (kg)
.100
.150
.200
.250
.300
.350
.400
.450
.500
3. Analysis
3.1The period “T” is related to m and k by where m is the moving mass and m’ is the effective mass of the spring.; m’ is not the same as the spring’s actual mass. Re-write this to get m(T2):
Plot F(x). Write the theoretical relationship in table 8.3 and find k.
Make a plot of m(T2). Write the theoretical relationship in table 8.3 and find k.
The effective oscillating massis M = m + m’. Fill in the last column of table 8.2.
Make a graph of T(M). Write the theoretical relationship in table 8.3 and find k.
Table 8.3 Fit-line Analysis
F(x) / Theoretical Equation / Value for kComputer Equation
m(T2) / Theoretical Equation / Value for k
Computer Equation
T(M) / Theoretical Equation / Value for k
Computer Equation
What fraction of the spring’s mass is its effective mass? m´/mSPRING = ______
4. Effective mass of a vibrating rod
4.1 Find the period of oscillation for various masses at the end of a rod.
Table 8.4 Period vs. m
M (kg) / # of Osc / Total t (s)trial 1 trial 2 / T (s)
Make a plot of m(T2). Use a fit line to find the slope and intercept. Include units.
Slope: ______Intercept: ______
kDYNAMIC: ______m’: ______
What fraction of the rod’s mass is its effective mass? m´/mROD = ______
Error Analysis: Propagationby Substitution; Comparing Numbers Using Errors
Write the formula for “k” in terms of “T,” “m,” and “m´”
Pick one data point and find the errors on T,” “m,” and “m´.” If you have a relative error, convert it to an absolute error.
Quantity and Value / READ / CAL / OTHER / T =
m =
m´ =
Find the largest and smallest possible value for eachquantity.
Quantity / Max Value / Min ValueT
m
m´
Express “k” in “” notation k = ______± ______
Compare kSTATIC to kDYNAMIC using this uncertainty. Are the two values comparable within the stated uncertainty?
Lab 12: String ResonanceName: ______
1. Theory
Everything has one or more natural frequencies of vibration and will resonate at these frequencies.
2. Resonances and nodes
2.1Set L to 1 m. Put a mass of 200 g on your string. Find the first fiveresonant frequencies. For each resonance measure and calculate the wave speed. Make a graph with n on the x-axis and f on the y-axis. Print the graph.
n / f (Hz) / (m) / v (m/s)1
2
3
4
5
Table 2.1 Resonances
3. Resonance and length
3.1Set m = 200 g. For lengths from 20 cm to 1 m, find the resonant frequency f. Make a graph with L on the x-axis and f on the y-axis. Print the graph.
L (cm) / 20 / 40 / 60 / 80 / 100f (Hz)
Table 3.1 Resonant Frequency vs. Length
4. Resonance and tension
4.1Set L = 1 m. For masses below find the resonant frequency f.
m (g) / 50 / 200 / 800f (Hz)
Table 4.1 Resonant Frequency vs. Mass
Lab 14: Speed of SoundName: ______
1. Finding resonances
Find the resonances for a variety of frequencies. The practical range for f is 800 Hz to 3 kHz.
Table 10.1 Resonance Frequencies
fNominal / f
Actual / Position of nth Resonance / / v
1 / 2 / 3 / 4 / 5 / 6 / 7 / 8
800
1000
1200
1400
1700
2000
2500
3000
1.2The speed of sound depends on temperature. Find the average of your measured speeds, the book value for v, and the book value corrected to room temperature. Use the formula
.
T (ºC) / T (K) / v (m/s)Experimental average
Book value
Book value at room T
Error Analysis: Propagating Errors by Formula
Write the formula for V: ______
Find the errors on each quantity used in your formula. If you have a relative error, convert it to an absolute error.
Quantity / D
L
Find the error on v. To find this you will need to use derivatives:
Add the errors to get the total error on V:
Lab 13: StatisticsName ______
1. Trials and Randomness
1.1Put 8 pennies in a cup. Shake the cup, dump the pennies out,
and count the number of heads. This is a “trial.”
Make a mark in the appropriate column on table 1. For example, if you get 5 heads, put an “X” in column labeled “5.”
Do 20 trials per person, making an “X” for each one. Every person should keep his or her own record.
After this, combine all the data from the entire group.
This is called a histogram or a bar graph.
Column
/ 0 / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8# Heads / 0 / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8
Table 1.1: Tossing 8 Pennies Per Trial
2. Larger Numbers
2.1Repeat exercise 1, but use 32 pennies for each toss instead of 8.
Column
/ 0 / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8#Heads / 0-2 / 3-6 / 7-10 / 11-14 / 15-18 / 19-22 / 23-26 / 27-30 / 31-32
Table 2.1: Tossing 32 Pennies Per Trial
3. Averages
3.1Your instructor will tell you how to find the various different kinds of averages.
“Heads”
/ 8 pennies / 32 PenniesExpected
ModeMean
Median
3.2The mode is the column with the most X’s. There may be more than one.
3.3The mean is the total number of heads for all trials ÷ by the number of trials.
8 Pennies / 32 PenniesColumn / # of X’s / # of Heads / Column / # of X’s / # of Heads
0 / 1
1 / 4.5
2 / 8.5
3 / 12.5
4 / 16.5
5 / 20.5
6 / 24.5
7 / 28.5
8 / 31.5
Total / Total
3.4Use the following worksheet to find the median:
Start by adding all the X’s in each column. 8 ¢ 32 ¢