Probeware WorkshopSEPS/AAPT

April 2, 2011

University of the Sciences

Bill Berner, Univ. PennsylvaniaBarry Feierman, Westtown School

We will review in this session how touse the following Vernier probes:

Motion sensor - one dimension Force probe - dual range Acceleration probe – one dimension Microphone Voltage and Current probes

SETUP sensorsSETUP sensors

DATA COLLECTIONDATA COLLECTIONchoiceschoices

SET UP your WindowsSET UP your Windowswith tables, meters, graphswith tables, meters, graphs

What can you do with a “motion sensor”?

Record position (+ / - 1 mm)

Calculate velocity

Calculate acceleration

Plot graphs instantly

Start with the easy stuff …..

Ask students to first predict the shapeof the position-time graph for an object which is AT REST

Will they know that the graph of position-time is a horizontal linefor an object at rest?

Next, ask students to predict the position-time graph for an object moving at constant velocity.

Most of the “learning” takes placehere where students get to test out their initial ideas and assumptions

Here is the graph of a Vernier cartmoving along a horizontal track afterbeing given an initial push.

The data are sampled at 10 Hz.

cart moving at constant speed

Ask students to figure out the speedof the cart from the graph itself

Some will estimate the number of meters covered during each second

Some will estimate the time neededto cover each meter.

some might think of “slope”

slope of graph indicates the average speed of the cart about 0.5 m/s

Logger Pro can display graphs of position - time velocity – time acceleration – time

Logger Pro will also “fit” a varietyof mathematical functions to the data

average speed about 0.52 m/s

Acceleration is one of the toughestconcepts to understand since it is a “rate of a rate”

Acceleration occurs whenever the speed or direction changes

Always begin with the motion of anobject with constant acceleration

Investigate the motion of a cart moving up and down an inclined plane.

The cart begins at the bottom, is given apush up the plane, and then let go.

Ask students to first predict the shape of the position-time graph for both theuphill and downhill motion of the cart.

Will the graph be a line or a curve?

This is a challenge for students, sincethey can see the speed of the cart changing throughout the experiment.

They know the cart slows down on theway uphill, stops for a moment, and then speeds up on the way downhill.

The motion sensor is located at the TOP of the inclined plane, facingdownwards.

cart moving up plane

cart at the top of the plane: speed is zero

cart moving down plane

cart at rest cart at rest

PUSH CART

speeding upslowing down

Now predict the velocity-time graphfor this same event.

note on +/- sign convention

Any object moving towards the motion sensor has a “negative velocity”.

Any object moving away from the motion sensor has a “positive” velocity.

cart pushed by hand

cart moving uphill slowing down

cart at rest at top of inclined plane

cart moving downhill speeding up

What is the acceleration of the cartwhen moving uphill?

What is the acceleration of the cart when it comes to rest at the top?

What is the acceleration of the cartwhen moving downhill?

Is the acceleration reasonably constant?

slope = average acceleration acc = 1.0 m/s/s

Physics classses often measurethe acceleration of gravity by various methods

In this next demo, we drop a ball froma height of about 2 meters and recordthe ball’s position and calculate the ball’s instantaneous velocity.

The motion sensor is in the ceilingfacing downwards

First, ask students to PREDICT the shapes of the position-time graph andthe velocity-time graph for a ball bouncingon the floor a few times.

Question: is the deceleration of the ballwhen rising the same value as the acceleration of the ball when falling?

ball hits floor

max height above floor

ball falling

falling

ball rising

ball falling

ball hits floor

max height

hit floor

average acceleration about 9.5 m/s2

ball rising

ball at rest

ball falling

You could use a motion sensor to investigate the potential and kineticenergy of a falling object.

Here is a tray falling from a heightof about 1.5 meters. The motion sensoris near the ceiling, facing down.

First ask students to PREDICT theshapes of the potential energy graph, the kinetic energy graph, and the total energy graph for a falling object.

Hint: think conservation of energy

Here is an interesting question.

If a tray is dropped, what would the graphof the PE vs. KE look like?

As the tray falls, it loses PE and it gainsKE producing a graph with the shapeof a ________________ ?

What about the PE, KE and total mechanical energy of a bouncing ball?

Let’s look at the gravitational PE first,found by plotting the height of the ballabove the floor

The ball has zero PE when on the floor

Now let’s examine the KE of the same bouncing ball.

When the ball is AT RESTits kinetic energy is zero.

Predict the shape of this graph first.

Now predict the total mechanicalenergy of the bouncing ball

The SUM of the PE + KEplotted against time.

One could ask whether the samePERCENT of energy is “lost”(to heat and sound) on each bounce.

Looks like an exponential decay!

At times the total energy is near zero.So if not PE nor KE, what kind of energy does the ball possess?

What could you do with TWO motion detectors?

How about test for the conservation of momentum in an elastic collision of twotoy carts of equal mass.

Each cart’s velocity is determined by amotion sensor both before and after ahead-on collision.

Here is a snapshot of the velocity ofeach cart a moment before they makea head-on collision

Both velocities are “positive” sinceeach cart is moving away from itsown motion sensor

Now let’s look at the velocity of eachcart just after the head-on collision.

Each cart has a “negative” velocity since each cart rebounded and is movingback towards the motion sensor.

change in velocity of cart 1 = 0.73 m/s

change in velocity of cart 2 = 0.72 m/s

carts had equal mass: 1.0 kilogram

The change in momentum of cart 1 closely matches the change in momentum of cart 2

FORCE PROBES

Force probes can measure forces from 0 – 10 N at high resolution +/- 0.001 N

and from 0 – 50 N at a lower resolution +/- 0.01 N

Forces can be measured at high sampling rates.

Predict the FORCE – TIME graphfor lifting a 1000 gram mass (10N)very slowly ……….

and then lowering it very slowly.

the force is constant if there isno acceleration

Now predict the force-time graph forQUICKLY raising a 500 gram mass, holding it steady for a moment, and thenthen lowering it QUICKLY

Hint: the weight must accelerate and then decelerate, then stop.

hold steady

raise quickly

hold steady

lower quickly

hold steady

Holding it steady is a constant 5 N

Accelerating upwards the force moves up to 10N maximum, then drops to about 2N when the weight decelerates

Then steady again at 5 N

Lowering it quickly reduces the force to2 N, and then catching it increases the force back up to 10 N maximum

One can demonstrate that the forcerecorded by the force meter isthe sum of the static weight (mg) plus the force needed to accelerate the weight (ma)

F = mg + ma

where mg = 5NThe maximum acceleration was about +/- 10 m/s2

With a force sensor you can demonstrate that starting friction is higher than kinetic friction

Attach a force sensor to a 4x4 blockof wood and drag it across the tableat constant speed

starting friction force

kinetic friction force

block at rest

A force probe can be used to determine the WORK required to stretch an elastic material a known distance (area under curve).

Here we see the force-displacement graph acting on an elastic band.

The elastic was then used to acceleratea toy cart of known mass, predicting its velocity by the Work-Energy Theorem.

What kind of probes would you needto test the validity of

Newton’s Second Law?

How about one force probe and oneacceleration probe.

What if you wanted to investigate theforce and the acceleration of a weighted can bouncing at the end of a long spring?

You could use a force sensor at the top of the spring to measure the tension inthe spring, and an acceleration sensor attached to the can to measure theacceleration of the can.

Give the can an initial push or pull and then predict the shape of the

force – time graph

acceleration – time graph

force – acceleration graph

force

acceleration

Note that the force and the accelerationare “in step”.

When the force is maximum, the acceleration is maximum.

When the force is minimum, the acceleration is minimum.

The force is never zero…. why not?

Again, the force meter reads thetension in the spring which is the sumof two parts, the static weight (mg)of the can and spring, and the force needed to accelerate the can and spring.

T = mg + ma

Now what happens if we plot

force vs. acceleration

What shape graph do you predict?Why?

What does the SLOPE of thisgraph represent?

What does the Y-intercept of thisgraph represent?

Use Newton’s Second Law to guideyour thinking.

F (net) = M A

slope = mass about 0.7 kg

Another useful sensor is the

microphone

You can set up the software to looklike a traditional oscilloscopeplotting sound pressure vs. time or

You can set up the software to showthe frequency distribution (spectra) of the sound to measure the harmonics or timbre of a musical source.

Here are some examples of a varietyof sound sources.

The first trace is the sound made byblowing over an empty soda bottle. This usually produces a clean “sine wave”.

Note the fundamental note (200 Hz)and its second harmonic (400 Hz)

Here is my voice saying

“ahhhhhh”

Note the simple harmonic seriesstarting at about 125 Hz with theLoudest harmonic at 630 Hz

Here is the much more complex sound(and waves) from an alto saxophone

Saxophones play both “even” and “odd” harmonics of the fundamental note(which is why they sound so cool)

Voltage and Current probes can be used to test Ohm’s Law

Charge a capacitor to 6 v dcDischarge it into a 10 ohm wire resistor

Measure the voltage across the resistorMeasure the current through the resistor.Calculate the ratio of voltage/current

Plot the voltage-current graph.

The voltage – current graph is linearfor this wire resistor

This indicates that the resistanceof this wire resistor is constant(the ratio of voltage/current is 10 ohms)

We call this kind of device an“ohmic device as it obeys Ohm’s Law

What if we did the same experimentbut discharged the capacitor into a6 volt incandescent lamp

Would the voltage-current graph still be linear?

Would the resistance of the bulbremain constant?

The voltage – current graph is clearlynon-linear for the incandescent lampyet linear for the 10 ohm wire resistor.

Does this imply the resistance of the lamp filament is changing during this experiment?

Could the temperature of the filament affect its resistance?

The resistance of the incandescent lamp began at about 22 ohms when it was hot(at high current) and decreased steadilyto a low value of 5 ohms when it wascooler (at low current)

Clearly the temperature of the filamentaffects its electrical resistance. hot wire = more resistance cool wire = lower resistance

Let’s now investigate the charging of a large capacitor with a 6 volt battery.We will put a 10 ohm resistor in seriesto limit the initial current surge.

The voltage is measured across the capacitor, and the current is measuredentering (or leaving) the capacitor.

Charging a capacitor with a battery

Predict the shapes of the graphs of

voltage vs. time

current vs. time

power vs. time

energy vs. time

The capacitor was just about fully“charged” after 30 seconds.

The total energy stored in the capacitorwas about 2.5 joules.

You can also look at the current-timegraph and ask the question

How much charge entered (or left) the capacitor?

By integrating the current-time graphyou can determine the number ofcoulombs of charge stored on eitherplate of the capacitor.

It looks like 0.92 coulombs of charge was placed on the plates ofthis capacitor when charged to 6 volts

The “capacitance” of the capacitor is

C = Q / V = 0.9 coulomb / 6 volts

C = 0.15 farad = 150,000 microfarads

You can also examine the graphs of thedischarge of the capacitor into awire resistor.

What will the graphs like for

voltage vs. time

current vs. time

Then use the “curve fit” function ofLogger Pro to fit an exponential decaytype of curve.

The current that flows out of the capacitor into a fixed resistance isdirectly proportional to the voltageleft on the capacitor.

But as charge leaves the capacitor, itsvoltage decreases (unlike a battery).

Here is the voltage vs. current graphfor the discharging capacitor