What is the escape velocity for a mass m at the surface of Earth in terms of g and r?
v = √(2GM/r) = √(2 * gr)
A planet box has a mass M and a radius R.
Loose material at the equator only just remains in contact with the surface of the planet.
This is because the speed at which the planet rotates is very large.
What is the period of rotation of the planet?
GMm / r^2 = m omega^2 r
GM = (2 pi / T)^2 r^3
T^2 = (2 pi)^2 r^3 / GM
so T = 2 pi √(r^3/GM)
A particle of mass m and charge Q is accelerated from rest through a potential
difference V. The final velocity of the particle is u.
A second particle of mass 2
m and charge 2Q is accelerated from rest through a potential
difference 2V.
What is the final velocity of the second particle?
E = VQ = 1/2 mv^2
v^2 = 2VQ/m
v^2 is multiplied by 8, so v is multiplied by root(8) = 2root(2)
therefore v = 2√(2)u
In what direction does the field direction act on a point in a curved gravitational field diagram?
Tangential to the line at the point specified.
Explain what is represented by the area under the graph between r = R and r = 2R (where R is the radius of the planet) on a graph of g against r. [2 marks]
Increase in gravitational potential moving an object from the planet’s surface (R) to 2R away per unit mass.
Here’s a graph of gravitational potential against distance for a particular planet. The gradient of this graph is called the ____. This is equal to the ____.
gravitational potential gradient, negative gravitational field strength
Gravitational field strength values are negative
electric field strength at a point
The force per unit charge acting on a positive test charge at that point.
A negative electric field means
A field pointing opposite to what a positive field would do; if the charge is negative, the field strength is negative and points toward the charge’s center
It is attractive like the gravitational field, which is always negative.
A force is ____ when it is negative, and ____ when it is positive.
attractive, repulsive
Small positive particle moving away from another positive particle:
-> work done is ____ (done by ____ against ____)
-> electric potential energy ____ (____ repulsion effect)
negative, by particle against electrostatic force
decreases, less
if we move a negative charge in the direction of the electric field, then we do ____ work (i.e. we ____ energy)
positive, lose
(work is being done by the electrostatic force on the negative charge)
Explain the function of the core in a transformer. [1 mark]
Provides greater magnetic flux linkage (from the primary coil to the
secondary coil compared to an air core); ‘guides’/focusses the magnetic field through the secondary coil to maximise the flux through it (i.e minimises power loss)
Explain the function of the secondary coil in a transformer. [2 marks]
- (a conductor) has an alternating/changing magnetic flux/field passing
- through it
- Producing an induced emf / induces an emf that is determined by the number of turns in (the primary and) the secondary coils
Don’t mention induced current here, talk about induced emf
Figure 8 shows a cross-section through the transformer core. Thin iron sheets are separated by material M.
Explain how the efficiency of the transformer is increased by constructing the core in
this way. [3 marks]
Example A:
The (sheets) of material M / laminations are made from
insulator/high resistivity material
-> reduces (eddy) currents or charge flowing in the core.
Example B:
Thin sheets/laminations of iron are used
-> smaller emfs are induced in the core
-> resistance is high causing lower (eddy) currents
Suggest why engineers may choose to transfer electrical power at 132kV for long-distance transmission, but not higher [1 mark]
Too high potential differences will cause major insulation difficulties for transformers or isolation difficulties for transmission cables (have to be further apart or there will be sparking).
Transferring at higher voltages are therefore very expensive.
Transformer equations for current.
I1V1 = I2V2
Is/Ip = Np/Ns
What do the transformer equations assume? (2)
The transformer coils have zero resistance.
ALL the magnetic flux flows through the core
What material is typically used for the wires of the coils in a transformer?
Copper
In a step down transformer, the rate of change of flux linkage through the primary coil is ____ than the secondary coil.
greater
As a coil rotates in a magnetic field through 2 pi radians, the flux linkage changes from +BAN to ____. So the change in flux linkage is ____.
-BAN, 2BAN
Why can electron diffraction be used to accurately measure the nuclear radius?
Electrons are a type of lepton so don’t experience the strong nuclear force.
First minimum for electron diffraction appears where…
sinθ = 1.22 λ / 2R
or sinθ = 0.61 λ/R
[R sinθ = 0.61 λ]
N-Z plots - large heavy nuclei aren’t just neutron rich, they have a
high N/Z ratio
The density of a nucleus is calculated to be constant (equal to lots of constants, not on the nucleon number)
But not necessarily equal density in reality because…
- The volume equation assumes that the nucleus is a perfect sphere.
- The density equation that uses the nuclear radius formula implies that the density is uniform within a nucleus, which is not true.
- The mass of the nucleus is not exactly A * m, as it ignored the binding energy.
