EXPERIMENT ONE – MEASUREMENT & GRAPHICAL ANALYSIS
1. Measure length and mass with a meter stick, micrometer caliper, and balance
2. Estimate the probably percentage error in a measurement
3. Calculate the mean value and standard deviation from set of repeated measurements
4. Graphical methods of data analysis
Meter stick, measures to nearest onetenth mm, although the last digit may not be as accurate as the other three (27.13, ~ 27.1 or
27.2), it is significant and must be recorded. Digits in excess of 4 have no significance. Attempt to estimate 1/10 of the
UNCERTAINTY: any measure, due to nature of thing measured, and device used. Repeated measures give range, and a mean.
The uncertainty may be + 0.03. Calculate by
0.03 / Mean x 100, to get percent uncertainty
Uncertainty in D is much larger than that of L or M: relative error, R, is almost entirely due to D
R = M exp / MTh Th
STANDARD DEVIATION: when there are enough measurements made, this is better than ^
PART 1 – DETERMINATION OF THE VOLUME DENSITY OF A METAL WIRE
p = density in kg/m M = mass in kg, L = length in m, V = volume in m , R = radius in m, D = diameter in m
1. Measure the wire and take its length (x2)
2. Measure the density with micrometer (x10) –
a. Uncertainty of +0.001 mm, wire not perfectly uniform, thus, the percentage uncertainty in avg. value, D is much
b. Find zero error, e 0 in micrometer, correct readings for this (x10)
Standard Deviation…(calculate deviation from mean, then square, then sum, then..)
3. Calculate mean density – also find uncertainty in density with:
4. Determine which material it was based on board descriptions
PART 2 – GRAPHICAL DETERMINATION OF THE FORCE CONSTANT OF A SPRING
Hooke’s Law, F = kx Gravity, F = mg Combined, M = k/g(x)
1. Add masses to spring, observe extension, plot M & x (estimate pointer positions to one tenth of the smallest scale division) –
should be linear. Pointer does not need to be at zero when load is zero, extension can be found by subtracting the initial
position from all values. Won’t be exact. Draw best fit. Take two points as far away as possible (not experimental values), and
find the slope of line, find the force constant
k = (g)*(slope)
PART 3 – GRAPHICAL DETERMINATION OF THE TIME CONSTANT OF A TRANSIENT VOLTAGE
V 0= voltage at t=0, Vt= voltage at time t, t =time, t = time constant (dimensions of time) – after a time interval ( ) the voltage drops by a
factor of 1/e = ½.72 = 0.368…
Equation can be y = mx + b if…
1. Find experimental values for V(t) and t, plot log[V(t)] (vertical) vs. t (horizontal), straight line, slope = time constant
2. Use SEMILOG to graph. Plot line of best fit through data points, find slope (negative): rise = log(y1) – log(y2)
3. Find % uncertainty in slope ( ) = upper limit of slope – lower limit of slope x 100%
2 x (best estimate of slope) EXPERIMENT TWO – ADDITION OF VECTORS
1. To learn to add forces vectorially
2. To use Newton’s first law to find an unknown force
3. To become familiar with pulleys, cords, and weights
Theory: The component of the sum is equal to the sum of the components (each vector has an x and y component)
P , P for P Q , Q for Q So when, R = P + Q, R = P + Q & R = P + Q
x y 2 2x y x x x y y y
Know: Resultant = sqrt(R +xR ) y Tan(theta) = R /y x
Basically, the xcomponent of the sum, R, is equal to the sum of the xcomponents of the added vectors, P & Q (same for y).
Displacement: if object moves along R, it’s the same displacement if it were to move along Q, and then P (drawn continuous)
Parallelogram: the sum (resultant) of P and Q is shown differently, in the middle Q & P (drawn from a common origin)
PART 1 – set up P & Q forces, determine E – needed to balance their combination and put into equilibrium. R, will be the vector equal
and opposite in direction to E – will be the resultant of Q & P.
Force Table: three pulleys hanging from ring (should be centered about the middle peg) – P at 0 (100g), Q at 70 (200g)
Hang scale pan with 100g on (E), g = 9.80 exactly. Record combined mass of scale pan and angled position.
Calculate R, and the angle (should be within reasonable limits of experimental error.
Enter percentage difference between E & R
Enter difference between (alpha – b/w E & horizontal) & (theta – b/w P & Q)
Inaccuracy: expected, instruments are limited, masses aren’t completely accurate, scale is +0.1g, friction in pulley, equilibrium
judged by the eye.
PART 2 set up P & Q forces, determine E – needed to balance their combination and put into equilibrium. R, will be the vector equal
and opposite in direction to E – will be the resultant of Q & P.
Force Table: three pulleys hanging from ring (should be centered about the middle peg) – P at 0 (100g), Q at 140 (200g)
Hang scale pan with 100g on (E), g = 9.80 exactly.
Record combined mass of scale pan and angled position, then the weight
Record the degree mark of the third pulley
Magnitude of E (equilibrant), and makes what angle (beta) with the negative yaxis?
Percentage difference between E and R, and the difference between (beta) and (theta – b/w R and the yaxis)
PART 3 set up P & Q & S forces, determine E – needed to balance their combination and put into equilibrium. R, will be the vector
equal and opposite in direction to E – will be the resultant of Q & P & S.
Force Table: three pulleys hanging from ring (should be centered about the middle peg) – P at 0 (100g), Q at 60 (50g), S at 100 o
(100g). Calculate magnitude and direction of P, Q, S, and other values.
PART 4 – POLYGON OF VECTORS – if number of external forces (P1, P2, P3, etc.) all acting on a point in translational
equilibrium, the vector sum is equal to 0.
Space Diagram – shows the forces acting at point “A”, basically all force vectors extend from a common point in their own
individual magnitude and direction
Force Diagram – shows the forces drawn continuously (P1 > P2 > P3, etc.) all starting and ending near a common point in their own
individual magnitude and direction. This determines RESULTANT of all.
Normally, the last vector will close the polygon, reflecting that it is in EQUILIBRIUM.
IF A NUMBER OF FORCES ACT AT A POINT AND ARE PARALLEL AND PROPORTIONAL TO THE SIDES OF A
POLYGON TAKEN IN ORDER, THE FORCES ARE IN EQUILLIBRIUM.
Complete experimentally with 4 standard weights and locate the direction and magnitude of equilibrium.
Reasons why the polygon won’t close properly: human error, experimental equilibrant was approximate (the precise length
needed to close the polygon, it was slightly smaller than what would theoretically be required to close it.
PART 5 – given an unspecified weight, using the force table and standard weights, determine the weight (grams) – use math
Use mass and gravity divided by 1000 to determine mag and direction of forces used, then same math as before to determine
the resultant and direction, then find percentage difference. Actual weight is found by dividing resultant by 9.8 then multiplying by
1000. EXPERIMENT THREE – DETERMINATION OF G ON AIR TRACK
1. To examine relationships b/w time, distance, and speed for an object moving with constant linear acceleration.
2. To measure the acceleration due to gravity (using regular paper, using loglog paper, then computer)
3. To learn to read vernier scales
4. To analyze data graphically
Air Track: 150 holes per meter, each hole is about 0.5 mm in diameter. Lifts glider approximately 0.3mm above surface. Number of
holes under the glider is constant. Frictional resistance – so small, neglected.
DEMONSTRATES MOTION UNDER CONSTANT ACCERLATION.
THEORY: Frictionless assumed. Proof: show that equation 1 gives acceleration of the mass:
Equation of motion (gli2er) from rest:
Linear graph of d vs. t – slope:
PROCEDURE: Level track (to height H) with spacer– ensure minimum drift over the length of the track. Check this along track (not
perfectly straight). Set to angle (alpha). Determine alpha by H /Lav= avn(alpha).
VERNIER CALIPER – measure thickness of spacer with this. 3 sig figs after decimal point if the readings are in cm. Take 4
readings of H (get average). Take 4 readings of L (get average) – with meter stick (to nearest mm).
PART 1 – From equation of glider motion (above), t = time for travel distance d, from rest. Set up photocell receptors that you
position distance, d, apart from each other (for varying distances – 2m first). Glider should break the light beam immediately after
release. 5 trials for 8 distances (0.250m > 2m, in 0.25m increments). Calculate averages times for each.
GRAPH – plot d (y) vs. t (xav draw line of best fit, find slope, rearrange, and calculate acceleration due to gravit