Methods/practicles that will come up in Unit 1

Question 1

Describe the measurement of the density of solids practical?

Answer 1

Density of regular shaped solids can be determined by measuring their mass, m, and calculating their
volume, V. The density, ρ, can then be found using: 𝜌 = 𝑚/v.

You will need:
Various regularly shaped solids both rectangular and circular
30 cm ruler (resolution ± 0.1 cm)
Vernier calipers/micrometer (resolution ± 0.01 mm)
Balance (resolution ± 0.1 g/1 g)

Experimental method:
Determine the mass of the object using the balance. The volume of a rectangle can be found by measuring the
length, l, width, w, and height, h. Calculate the volume, V using:
V = l × w × h. The volume of a sphere is found by measuring the diameter to find the radius, r, and then calculate
the volume using: 𝑽 =
𝟒/3 𝝅𝒓𝟑 .
In both cases calculate the density using p=m/v.

Question 2

Describe the determination of unknown masses by using the principle of moments?

Answer 2

Apply the principle of moments to a metre rule to first determine its mass and then determine the mass of an
unknown object.

Apparatus:
Metre rule
Clamp and stand
Nail
200 g mass and hanger
150 g mass (covered in tape and labelled as W) and hanger
Loops of thread

Experimental method:
Loop a 200 g (1.96 N) mass over the metre rule and adjust it until the ruler
is horizontal.
Note down the distance, Ɩ, of the mass from the pivot. The mass (or weight)
of the metre rule can now be calculated using the principle of moments:
0.20 × metre rule weight = Ɩ × 1.96
Now remove the 200 g mass and replace it with the unknown weight, W,
and again adjust the position of the weight until the ruler balances. Measure
the distance, d, of the unknown weight from the pivot. The unknown weight
can again be calculated by applying the principle of moments:
0.20 × metre rule weight = d × unknown weight
The unknown weight can be converted into a mass (in kilograms) by
dividing by 9.81. This can then be checked using a top pan balance.

Question 3

Describe the measurement of g by free fall?

Answer 3

An equation of motion(suvat) can be used to calculate the acceleration due to gravity g.
s = ut + 1/2at^2
Where:
u = initial velocity = 0,
s = height, h and
a = acceleration due to gravity, g.
This gives h=1/2gt^2
If a graph of height, h (y-axis), is plotted against time squared, t
2
(x-axis), the gradient will equal g/2, or g = 2 ×
gradient.

Apparatus:
Electromagnet
Metal plate
Metal sphere
Timer
Switch
Break contact

Experimental method:
When the switch is pressed it disconnects the electromagnet releasing the
metal sphere. At the same instant the timer starts. When the sphere hits the
magnetic switch it breaks the circuit stopping the timer, thus recording the
time it takes for the sphere to fall through a height, h. The time taken for the
ball bearing to fall through a range of different heights needs to be
measured. Plot a graph of height, h (y-axis), against time squared, t
2
(xaxis), and calculate the value of g using: g = 2 × gradient.

Students could progress to use their value for g to estimate the mass of the Earth,
M_e.

From F = GM_em all over/ r^2 and f =mg we get:M_e = gR^2 all over/G
Where:
ME = mass of the Earth
R = radius of the Earth (6.38 × 106 m)
G = gravitational constant (6.67 × 10-11 N m2
kg-2

Question 4

Describe an investigation of newtons 2nd law?

Answer 4

The gravitational force of the slotted masses attached via the pulley causes the entire mass of the system to
accelerate. That is the mass of the rider, M, and the total mass of the slotted masses, m. Newton’s second law,
therefore, can be written as:
𝑚𝑚 = (𝑀 + 𝑚)𝑎
and so the acceleration of the system is:
𝑎 = mg all over/(M+m)

We can use this to test Newton’s second law. If the total mass of the system (M + m) remains constant, then
the acceleration, a, should be proportional to the gravitational force, mg.

Apparatus:
Linear air track
Rider of known mass, M
Pulley
Light gates to measure acceleration
Slotted masses, mass m

Experimental method:
Fix the thread to the rider and attach five slotted 5 gram masses to the other
end as shown in the diagram. Set the light gates to record the acceleration
and allow the slotted masses to fall to the ground. Record the gravitational
force, mg and the acceleration, a. Remove one of the slotted masses and
place it on the rider (so keeping the total mass of the system constant).
Repeat the experiment until all the different accelerating masses have been
removed. Plot a graph of acceleration (y-axis) against gravitational force, mg
(x-axis). This should be a straight line through the origin.

By finding the gradient of the graph it is possible to get a value for the mass of the rider, M.
gradient = 1 all over/(M=m)
Where m = 25 grams – the total mass of the slotted masses.
This set up can also be used to investigate many collision and momentum problems.

Question 5

Describe the determination of Young Modulus of a metal in the Form of a wire?

Answer 5

Young modulus E = stress/strain = F/A / x/l
rearranging = Fl/xA
F = applied load
A = area of cross-section of the wire
x = extension
l = original length
If a graph of applied load, F (y-axis), is drawn against extension, x (x-axis), the gradient is 𝐹/x and so:
𝐸 = gradient × l/A
The original length l can be measured and the area of the wire found using 𝐴 = 𝜋𝑟^2 hence E can be
determined.

Apparatus:

Support beam
Small fixed weight to keep wire straight
Comparison wire Vernier arrangement to measure the extension of test wire
Test wire
Variable load.

Experimental method:
Hang two identical wires from a beam and attach a scale to the first wire
and a small weight to keep it straight. Also put a small weight on the second
wire to straighten it and a vernier scale linking with the scale on the
comparison wire. Measure the original length, l, of the test wire and its
diameter at various points along its length. Use this to calculate the mean
cross-sectional area A.
Then place a load of 5 N on the test wire and find the extension, x. Repeat
this in 5 N steps up to at least 50 N. Plot a graph of load (y-axis) against
extension (x-axis) and calculate the gradient. Use this to find a value for the
Young modulus.

By comparing the Young modulus to known constants it would be possible to determine the type of metal the
wire was made from.

Question 6

Describe an investigation of the Force-Extension Relationship for Rubber?

Answer 6

Rubber – an example of a polymer with weak cross bonds. Natural rubber is a polymer of the molecule
isoprene. It has weak van der Waals cross bonds and only a few covalent (strong) cross bonds.

Apparatus:
Clamp and stand G-clamp to secure (if required)
Metre rule (resolution ± 0.001 m) Micrometer (resolution ± 0.01 mm)
Optical pin (for use as a pointer if required) 50 g mass holder plus a number of 50 g masses
Rubber band of cross-section approximately 1 mm by 2 mm.

Experimental method:
Hang a (cut) rubber band of (approximate) cross-section 1 mm by 2 mm vertically from a stand, boss and clamp.
The base of the stand should be secured using a G-clamp. Hang a 50 gram mass holder from the band. Place a
metre rule as close as possible to the mass holder. The length can be read using an optical pin attached to the
base of the mass holder.
Measure the length, width and thickness of the rubber when it is supporting the 50 gram holder. Try to avoid
squashing the rubber with the micrometer screw gauge.
Increase the mass in 50 gram steps, measuring the extension each time. Continue until the band breaks.
Plot the force–extension curve and determine the Young modulus from the linear section.