NSAA 2020 Section 1 Part B (ESAT Physics)

A soldering iron has a copper tip of mass $2.0\text{ g}$.

The tip is heated with $30\text{ W}$ of thermal power. In $50\text{ s}$, the temperature of the tip increases by $200{}^{\circ }\text{C}$.

How much energy is transferred from the tip to the surroundings in this time?

(specific heat capacity of copper $=400{\text{ J kg}}^{-1}{}^{\circ }{\text{C}}^{-1}$)

The diagram represents the structure of a charged atom (ion) of one isotope of an element: a nucleus of $4$ shaded particles and $3$ unshaded particles, with $2$ electrons on the inner shell and $2$ electrons on the outer shell.

Which diagram represents the structure of an oppositely charged ion of a different isotope of the same element?

A sample of an ideal gas is sealed in a cylindrical container by a piston, as shown in the diagram.

The particles of the gas are moving with an average speed $v$, and collide with the surface of the piston with a frequency $f$.

The piston is now slowly pushed into the cylinder until the gas occupies half of its original volume, but the gas remains at the same temperature.

What is the new average speed of the particles of the gas, and at what frequency do they now collide with the surface of the piston?

A water wave is travelling in a shallow tank of water. The wave passes from region X into region Y where the speed of the wave differs from that in region X. The diagram shows the directions of travel in the two regions and peaks of the wave that are separated by one wavelength.

In region X, the angle between the wave peaks and the boundary between the regions is $\theta$.

In region Y, the angle between the wave peaks and the boundary is $\varphi$ (measured in the diagram as a visibly smaller angle than $\theta$).

What are the angle of incidence and the angle of refraction, and in which region is the speed of the wave greater?

Uranium-238 $\left({}_{92}^{238}\text{U}\right)$ decays by a series of alpha and beta (${\beta }^{-}$) emissions to become the stable isotope lead-206 $\left({}_{82}^{206}\text{Pb}\right)$.

How many beta (${\beta }^{-}$) particles are emitted in the decay of one uranium-238 nucleus to lead-206?

In a laboratory, liquid nitrogen is stored at a very low temperature in a double-walled vessel with a vacuum in the gap between the two walls. The vessel is made from a poor thermal conductor. The inner surface of the inner wall is shiny, and the outer surface of the outer wall is shiny.

These features insulate the liquid nitrogen by reducing the rate at which thermal energy is transferred to the liquid nitrogen.

Which of the following statements explain(s) why these features help to insulate the liquid nitrogen?

1. The shiny inner surface of the inner wall is a good emitter of thermal radiation.
2. Thermal radiation cannot travel in a vacuum.
3. The shiny outer surface of the outer wall is a poor absorber of radiation.

The primary coil of an ideal, $100\%$ efficient transformer is connected to a $240\text{ V}$ mains supply.

A lamp L that is connected to the secondary coil has a voltage of $12\text{ V}$ across it. An identical lamp and a switch S are also connected to the transformer: lamp L is connected directly across the secondary coil, and a second, identical lamp in series with switch S forms a separate branch also connected across the secondary coil.

With the switch open, the current in the primary coil is $0.10\text{ A}$.

The switch is now closed.

What is the current in the primary coil now and what is the current in lamp L?

A dc electricity transmission system uses an undersea cable to send electricity from one country to another. On a particular day, the first country supplies electricity at a voltage of $400\text{ kV}$ and $2000\text{ A}$ to the transmission system. The second country receives electricity from the transmission system at $160\text{ kV}$ and $4000\text{ A}$.

What is the percentage efficiency of the system and how much energy is wasted every minute?

A circuit contains a $12\text{ V}$ battery, a thermistor and a fixed resistor connected in series. The graph shows how the resistance of the thermistor varies with temperature: it falls smoothly from about $400\Omega$ at $10{}^{\circ }\text{C}$ to about $40\Omega$ at $80{}^{\circ }\text{C}$.

When the temperature of the thermistor is $10{}^{\circ }\text{C}$ the current in the circuit is $25\text{ mA}$.

What is the current when the temperature of the thermistor is $80{}^{\circ }\text{C}$?

Two fixed horizontal metal rails are side by side and $12\text{ cm}$ apart. The rails are connected to a dc power supply by a switch that is initially open.

A freely moveable metal rod of length $20\text{ cm}$ is placed on the rails, perpendicular to them (angle $90^{\circ }$), as shown in the diagram (seen from above).

The whole arrangement is placed in a uniform magnetic field of magnitude $0.50\text{ T}$ that is directed perpendicularly into the page.

The moveable rod has a weight of $0.40\text{ N}$.

The switch is now closed. As a result, there is a current of $2.4\text{ A}$ in the circuit and the rod moves.

What is the initial magnitude of the acceleration of the rod and what is its direction?

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

Visible light waves are electromagnetic waves that travel through a vacuum at $300000{\text{ km s}}^{-1}$ with wavelengths that range from $400\text{ nm}$ to $750\text{ nm}$.

The electromagnetic waves emitted by a source are all at frequencies between $6.0\times 10^{12}\text{ Hz}$ and $6.0\times 10^{14}\text{ Hz}$.

Which statement about the waves emitted by the source is correct?

Two trolleys are moving towards each other along a straight horizontal track.

One trolley has mass $8.0\text{ kg}$ and is travelling to the right at $4.0{\text{ m s}}^{-1}$.

The other trolley has mass $2.0\text{ kg}$ and is travelling to the left at $1.0{\text{ m s}}^{-1}$.

When the trolleys collide they stick together.

How much kinetic energy is transferred to other forms of energy in the collision?

A car of mass $800\text{ kg}$ travels in a straight line along a horizontal road.

The car accelerates non-uniformly from rest for $5.0$ seconds and then moves at constant speed, as shown in a distance-time graph: the car covers $10\text{ m}$ in the first $5.0\text{ s}$ (a curved, accelerating section from rest), and then a further $30\text{ m}$ (from $10\text{ m}$ to $40\text{ m}$) in the next $5.0\text{ s}$ at constant speed.

What is the average resultant force acting on the car over the time for which it is accelerating?

Cubes of side $2.0\text{ cm}$ are tightly packed into a rectangular box with internal dimensions $12.0\text{ cm}\times 10.0\text{ cm}\times 6.0\text{ cm}$.

Each cube is either solid concrete or solid steel. There are twice as many steel cubes as concrete cubes.

What is the total mass of the cubes in the box?

(density of concrete $=2.0{\text{ g cm}}^{-3}$; density of steel $=8.0{\text{ g cm}}^{-3}$)

P and Q are two fixed points on the surface of the ocean which are $6.0\text{ m}$ apart.

An ocean wave travels in the direction P to Q.

The wave has a frequency of $0.50\text{ Hz}$ and travels at a constant speed.

A wave peak passes Q at time $t=0\text{ s}$.

The next wave peak travelling towards Q passes P at time $t=0.80\text{ s}$.

What is the speed of the wave?

A sample contains only one radioactive isotope. This isotope decays in a single step with a half-life of $120$ minutes to a stable isotope.

The sample is placed near to a radiation detector which measures the count rate. The count rate reading is $910$ counts per minute (cpm).

After $240$ minutes the measurement is repeated. The count rate reading is now $238\text{ cpm}$.

After a further $360$ minutes have elapsed, a third measurement of the count rate is made.

What is the count rate due to background radiation and what is the expected reading in the third measurement?

A solid uniform sphere is made of metal of density ${\rho }_S$ and has radius $r$ and volume $V$. It falls vertically through a viscous liquid of density ${\rho }_L$.

Three forces act on it: its weight, a drag force $D$ and an upthrust $U$. The magnitude of the upthrust force is equal to the weight of the liquid displaced by the sphere.

The magnitude of the drag force is given by:$$D=krv$$where $v$ is the speed of the metal sphere and $k$ is a constant.

What is the terminal speed of the metal sphere as it falls through this liquid?

(gravitational field strength $=g$)

A parachutist of mass $80.0\text{ kg}$ drops from a plane travelling at $40.0{\text{ m s}}^{-1}$, $2000\text{ m}$ above the Earth's surface.

The parachutist hits the ground at a speed of $5.00{\text{ m s}}^{-1}$.

How much work is done by the parachutist against drag forces during the fall?

(Take the Earth's gravitational field strength to be $10.0{\text{ N kg}}^{-1}$.)

A light spring of unstretched length $0.10\text{ m}$ has a spring constant of $20{\text{ N m}}^{-1}$. The spring is suspended so that it is vertical and a load of mass $0.050\text{ kg}$ is attached to the end of the spring.

The load is pulled vertically downwards until the length of the spring is $0.30\text{ m}$. The load is then released.

What is the speed of the load at the instant that the spring returns to its unstretched length?

(gravitational field strength $=10{\text{ N kg}}^{-1}$; assume that resistive forces are negligible)

A rocket travelling in space is burning its fuel at a constant rate. By expelling the burnt fuel through a nozzle, the engine is applying a constant force to the rocket.

What is happening to the magnitude of the acceleration of the rocket?