NSAA 2018 Section 1 Part B (ESAT Physics)

An unstable nucleus X becomes a stable nucleus Y after a succession of decays, during which a total of 5 alpha particles and 2 beta (${\beta }^{-}$) particles are emitted.

How many fewer protons does nucleus Y contain than nucleus X?

The diagram shows three resistors $R_1$, $R_2$ and $R_3$ connected in series with a battery of constant voltage. The resistance of each resistor and the corresponding current are also shown: $R_1=12\Omega$, $R_2=15\Omega$, $R_3=3.0\Omega$, with a circuit current of $0.20\text{ A}$.

Resistor $R_3$ is now removed and the circuit is reconnected.

What is the new current in the circuit?

When travelling in a vacuum, visible light has a wavelength between $400\text{ nm}$ and $700\text{ nm}$.

The speed of light in a vacuum is $3.0\times 10^8{\text{ m s}}^{-1}$.

What can be concluded about ultraviolet radiation from this information?

The graph is the speed-time graph for a bus travelling in a straight line between two stops.

What is the average speed of the bus during this time?

A filament lamp working at its operating voltage converts electrical energy at a rate of $100\text{ W}$.

The lamp has an efficiency of $5.0\%$.

How much energy is wasted by the lamp in $10$ minutes?

A student is investigating heat flow along a solid uniform metal bar.

The bar has length $l$, cross-sectional area $A$, and has its ends maintained at temperatures $T_1$ and $T_2$ (where $T_1>T_2$).

Which relationship represents the rate of heat flow $P$ along the bar?

(Assume that there is no heat transfer through the sides of the bar.)

The potential difference across the motor in an electric car is $400\text{ V}$ and the current in the motor is $1250\text{ A}$.

The car accelerates along a horizontal road from rest for $4.0\text{ s}$.

The efficiency of the overall system is $45\%$.

What is the kinetic energy of the car at the end of the $4.0\text{ s}$?

(Ignore energy losses due to air resistance and due to friction between the tyres and the road.)

The momentum of a small object moving in a straight line is $24{\text{ kg m s}}^{-1}$ and its kinetic energy is $96\text{ J}$.

What is the mass of the object?

A radioactive isotope decays in a single step to a stable isotope.

A radiation detector is placed very near to a sample of the radioactive isotope in a laboratory. The count rate on the detector changes as time elapses. The graph shows how the measured count rate changes with time.

What is the background count rate and what is the half-life of the isotope?

A rock falling vertically experiences an air resistance force of $12\text{ N}$ at an instant when its acceleration is $2.0{\text{ m s}}^{-2}$ downwards.

What is the mass of the rock?

(gravitational field strength $=10{\text{ N kg}}^{-1}$)

A transverse wave with an amplitude of $4.0\text{ cm}$ and a frequency of $10\text{ Hz}$ travels along a rope at a speed of $2.4{\text{ m s}}^{-1}$.

What is the total distance travelled by a particle in the rope in a time of $20\text{ s}$?

A student places a measuring cylinder on a balance. She pours a volume $V$ of water into the measuring cylinder, and finds that the mass of the measuring cylinder and water together is $290\text{ g}$.

She then empties the measuring cylinder and dries it before putting it back on the balance.

She now pours the same volume $V$ of olive oil into the measuring cylinder, and finds that the mass of the measuring cylinder and olive oil together is $270\text{ g}$.

What is the mass of the measuring cylinder?

(densities: olive oil $=0.90{\text{ g cm}}^{-3}$; water $=1.0{\text{ g cm}}^{-3}$)

A skydiver of weight $1000\text{ N}$ falls vertically.

The distance-time graph for the skydiver is shown below.

The air resistance $F$ (in N) acting on the skydiver travelling at velocity $v$ (in ${\text{m s}}^{-1}$) is given by the equation $$F=k{v}^2$$ where $k$ (in ${\text{N m}}^{-2}{\text{s}}^2$) is a constant.

What is the numerical value of $k$ for the skydiver?

A source generates water waves of fixed frequency that have a wavelength of $1.5\text{ cm}$.

As they cross a boundary into shallower water their frequency does not change, but their speed is reduced by $18{\text{ cm s}}^{-1}$.

The new wavelength is $1.2\text{ cm}$.

What is the speed of the waves in the shallower water?

A neutron is absorbed by a uranium-235 (${}_{92}^{235}\text{U}$) nuclide.

The resulting nuclide undergoes fission to produce a bromine-88 (${}_{35}^{88}\text{Br}$) nuclide, a lanthanum-145 nuclide and some neutrons.

The lanthanum-145 nuclide is radioactive and emits a beta (${\beta }^{-}$) particle.

How many neutrons are emitted in the fission reaction and how many protons are there in the nuclide formed by the decay of lanthanum-145?

The diagram shows a circuit containing a battery and three identical resistors X, Y and Z. Resistors X and Y are connected in parallel with each other, and this combination is connected in series with resistor Z, across the battery.

The total power supplied by the battery is $18\text{ W}$.

What is the power dissipated as heat in resistor X?

A filament lamp and a $0$-$10\Omega$ variable resistor are connected in series with a power supply of constant voltage.

The graph shows the voltage-current ($V$-$I$) characteristic of the filament lamp.

When the resistance of the variable resistor is $4.0\Omega$, the current in the lamp is $2.0\text{ A}$.

What is the power dissipated in the lamp when the resistance of the variable resistor is zero?

Three detectors X, Y and Z are separated by large distances.

Each of the detectors records a seismic wave from the same earthquake whose epicentre (source) is very close to the surface of the Earth.

The wave travels out from the epicentre at $4.0{\text{ km s}}^{-1}$.

Detectors X and Y start to detect the wave at the same time, but detector Z starts to detect it one minute later.

Which of the following statements must be correct?

1. The epicentre is at the midpoint of the line XY.
2. Z is equidistant from X and Y.
3. Z is no more than $240\text{ km}$ away from X and from Y.