accuracy
how close a measurement is to its true value
estimation
making a reasonable approximation of a value in order to check a calculation or make a comparison to another value
precision
how close a set of repeated measurements are to one another but not the true value
random error
the unpredictable variation in a measurement
repeatability
an experiment is repeatable if the same person uses the same equipment to obtain the same result when doing the same experiment a number of different times
reproducability
an experiment is reproducible if different people with different equipment get similar results
resolution
the smallest interval that a given measuring device can measure
systematic error
a consistent shift in readings causing a deviation from the true value
uncertainty
the range of values that could reasonably contain the true value of a measurement, based on the confidence an experimenter has about their result
how to reduce to random error
by taking many repeated measurements and calculating their mean
validity
cpac 1 - determine the acceleration of a free falling object
equipment : light gate, data logger, ball bearing
method:
- drop the ball bearing from rest and record the time taken for the object to pass through the light gate
- repeat the measurement 2 more times and work out mean value of t
- measure height fallen by the ball bearing (from end of electromagnet to start of trapdoor)
- repeat the timing of the drop as you vary height - record at least 6 readings
- calculate % uncertainty in t
results:
- use data to plot a graph of h against t^2
- calculate gradient = m
- work out g when g = 2 x s/t^2 (gradient)
- calculate % difference in your value compared to 9.81 and comment on accuracy
why is it better to use a light gate
less uncertainty in time measurement as its electrical and no human error
cpac 2 - determine the electrical resistivity of a metal
method:
- at various points along the wire, measure diameter, d, using a micrometer and calculate an avg d
- find cross-sectional area of the wire by A = πd^2/4
- clamp wire to a ruler and connect to rest of the circuit where ruler reads 0
- ammeter in series with variable resistor and voltmeter in parallel
- at 0.10m intervals from crocodile clips, record voltage and current on
- calculate R by R = V/I
- measure length, L, of wire using a ruler
- vary L by changing position of clips along the wire and record new V and I and work out R
- plot a graph of R against L
- determine gradient and work out the resistivity
- ρ = gradient x A
sources of uncertainty in
- contact resistance between wire and plug,
- resistance between crocodile clip and wire at ‘zero’ end of wire,
- Crocodile clip at ‘zero’ mark.
what does resistivity depend on?
depends on temperature so resistivity can only be determined at a certain temp. Current flowing in wire can cause temp to increase so its important to keep temp constant so results are not invalidated.
Keep only a small current flowing through the wire
cpac 3 - determine the e.m.f and internal resistance of an electrical cell
method:
- vary the current in circuit by changing the value of the resistance R, using a variable resistor. Measure p.d. for several different values of current, I
- record the data for V and I in a table and plot a graph of V against I
- 𝜀 = V + Ir . Re-arrange to give V = -rI + 𝜀
- 𝜀 and r are constants; compare to y = mx + c
- y-intercept is 𝜀
- gradient is -r
CPAC 4 - use a falling-ball method to determine the viscosity of a liquid
methods:
- fill a wide clear tube with the liquid and make sure you know the density of the liquid
- put one rubber band about halfway down the tube at a position where the ball bearings will have achieved terminal velocity
- place two more elastic bands below the first so that the distance between each band is equal and the lowest band is near the bottom of the tube. Record the distance between them. These are the points where you will record t1 & t2
- measure diameter of your ball bearing and halve it to get the radius
- drop ball bearing into the tube. Start a stopwatch when the ball reaches the first band and record the time at which it reaches the other bands. Record the results in a table
- repeat this at least 3 times for each ball bearing to reduce the effect of random errors on your results, then repeat the whole thing for diff sizes of ball bearing
- calculate average time taken for each size of ball bearing to fall between elastic bands. Use average time and distance between bands to calculate the average velocity of the ball bearing between elastic bands
- calculate viscosity = (2 x (ball density – liquid density) x g x a^2) / (9 x v)
CPAC 5 - determine the young modulus of a material
- use a wire that is thin and long
- find the cross-sectional area of the wire. Measure diameter in several places and take an average
- clamp the wire to bench so you can hang weights off one end of it. start with smallest weight to straighten the wire
- measure the distance between the fixed end of the wire and the marker
- increasing weight causes wire to stretch and marker moves
- increase the weight in equal steps recording the marker each time - the extension is the difference between this reading and the un-stretched length
- plot a graph of stress against strain
- gradient of graph is young modulus E
- area under graph gives strain energy
why should the wire being used be long and thin?
the wire will extend more for the same force
it reduces the uncertainty in your measurements
CPAC 6 - determine the speed of sound in air using a 2-beam oscilloscope, signal generator, speaker and microphone
- connect signal generator and microphone to 2-beam oscilloscope
- adjust the dials on the oscilloscope so you can see at least one complete cycle of each wave
- change the distance between the microphone and speaker so that the peaks of one wave line up with the troughs of the other wave. then measure the distance between the microphone and speaker
- calculate the frequency of the wave by measuring the period of the wave from the oscilloscope. f = 1/T
- move the microphone away from or towards the speaker so that the microphone’s corresponding wave on the oscilloscope moves one full wavelength along the signal generators wave
- measure new distance between the microphone and loudspeaker
- the difference in your two recorded distances is equal to the wavelength of the sound wave
- repeat previous 2 steps and use the results to find a mean value for the distance moved by the microphone each time
- then use equation v = fλ to find the value for speed of sound
CPAC 7 - Investigate the effects of length, tension and mass per unit length on the frequency of a vibrating string or wire
- Set up the apparatus by attaching one end of the string to the vibration generator and pass the other end over the bench pulley and secure to the mass hanger
- Adjust the position of the bridge so that the length L is measured from the vibration generator to the bridge using a metre ruler
- Turn on the signal generator to set the string oscillating
- Increase the frequency of the vibration generator until the first harmonic (nodes at both ends and an antinode in the middle) is observed and read the frequency that this occurs at
- Repeat the procedure with different lengths of L
- Repeat the frequency readings at least two more times and take the average of these measurements
- Measure the tension in the string using T = mg
- Where m is the mass attached to the string and g is the gravitational field strength on Earth (9.81 N kg–1)
- Measure the mass per unit length of the string, μ = mass of string ÷ length of string
- Simply take a known length of the string (1 m is ideal) and measure its mass on a balance
CPAC 8 - investigating diffraction gratings
- Place the laser on a retort stand and the diffraction grating in front of it
- Use a set square to ensure the beam passes through the grating at normal incidence and meets the screen perpendicularly
- Set the distance D between the grating and the screen to be 1.0 m using a metre ruler
- Darken the room and turn on the laser
- Identify the zero-order maximum (the central beam)
- Measure the distance h to the nearest two first-order maxima (i.e. n = 1, n = 2) using a vernier caliper
- Calculate the mean of these two values
- Measure distance h for increasing orders
- Repeat with a diffraction grating with a different number of slits per mm
CPAC 9 -
