NSAA 2019 Section 1 Part B (ESAT Physics)

A transverse wave is travelling through a medium. The distance between successive wave peaks is $8.4\text{ cm}$ and the total distance travelled by a particle during one complete oscillation is $5.6\text{ cm}$.

What is the amplitude and wavelength of the wave?

A builder lifts bags of cement onto the back of a lorry, as shown in the diagram. Each bag has a mass of $25\text{ kg}$. It takes the builder $2.5$ minutes to load ten bags.

What are the total work done, $T$, on the ten bags and the average power required for $T$?

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

The current-voltage graph for a diode is shown.

The diode is connected in series with a resistor and a $6.0\text{ V}$ battery. The current in the circuit is $8.0\text{ mA}$.

What is the resistance of the resistor?

(Assume that the battery has negligible resistance.)

Two electromagnetic waves P and Q travel in a vacuum and the ratio of their wavelengths is:$$\frac{\text{wavelength of P}}{\text{wavelength of Q}}=1.0\times 10^8$$Which row in the table shows the ratio of their speeds, the ratio of their frequencies, and identifies the possible natures of P and Q?

A block of aluminium of mass $0.80\text{ kg}$, initially at a temperature of $-21{}^{\circ }\text{C}$, is supplied with $54000\text{ J}$ of thermal energy.

The specific heat capacity of aluminium is $900{\text{ J kg}}^{-1}{}^{\circ }{\text{C}}^{-1}$.

What is the final temperature of the block?

(Assume that there is no other transfer of energy between the block and the surroundings.)

A light spring is used to support a range of loads.

The spring obeys Hooke's law. The system is in equilibrium.

Which of the following statements is/are correct?

1. The tension in the spring is directly proportional to the length of the spring.
2. The tension in the spring and the weight of the load it supports are a Newton's third law pair of forces.
3. When the extension of the spring is doubled, the energy stored in the spring increases by a factor of four.

A water-tight cylinder with a thin, freely moving piston contains $2.0\times 10^{-3}{\text{ m}}^3$ of trapped air at atmospheric pressure of $1.0\times 10^5\text{ Pa}$.

When the cylinder is submerged in water of constant density $1000{\text{ kg m}}^{-3}$, the volume of air in the cylinder decreases to $4.0\times 10^{-4}{\text{ m}}^3$.

The piston is at a depth $h$ below the surface of the water and the water surface is open to the atmosphere.

What is the depth $h$?

(gravitational field strength $=10{\text{ N kg}}^{-1}$; assume that the temperature of the air remains constant and that air is an ideal gas)

The secondary coil of an ideal, $100\%$ efficient transformer is connected to a resistor by cables of total resistance $1500\Omega$. The current in the primary coil is $4.0\text{ A}$. There are $240$ turns in the primary coil and $4800$ turns in the secondary coil.

What is the power produced as heat in the cables?

Heat is supplied to an initially solid substance at a rate of $60\text{ W}$.

The graph shows the variation of the temperature of the substance with time.

What is the mass of the substance?

(specific latent heat of fusion of substance $=100{\text{ J g}}^{-1}$; assume that there is no heat transferred to the surroundings)

Two tanks of water are connected by a solid cylindrical copper bar of length $l$ and diameter $d$.

The bar is insulated.

One tank contains water at $90{}^{\circ }\text{C}$ and the other tank contains water at temperature $\theta$.

For which of the following conditions is thermal energy conducted along the bar at the lowest rate?

A U-shaped permanent magnet rests on a balance.

A straight, horizontal wire of length $5.0\text{ cm}$ is fixed in position between the poles of the magnet, perpendicular to the horizontal magnetic field.

There is a current of $2.0\text{ A}$ in the wire and the reading on the balance is $202\text{ g}$.

When the direction of the $2.0\text{ A}$ current is reversed, the reading changes to $198\text{ g}$.

What is the strength of the magnetic field?

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

The radioactive isotope X becomes the stable isotope Y after a succession of decays involving only the emission of alpha and beta (${\beta }^{-}$) particles.

During the decay of one nucleus from X to Y, a total of seven particles are emitted. It is known that more of these particles are alpha particles than beta particles.

The atomic number of X is $Z$ and the mass number of X is $A$.

Which row in the table could give the atomic number and the mass number of Y?

The kinetic energy of an object of mass $4.0\text{ kg}$, travelling in a straight line, increases from $32\text{ J}$ to $200\text{ J}$ in $3.0$ seconds due to a constant resultant force.

What is the value of this resultant force?

In the following circuit, all five resistors have the same resistance.

The reading on the voltmeter is $1.0\text{ V}$.

What is the voltage across the battery?

Two hovercraft travel horizontally in opposite directions along the same straight line, as shown in the diagram. Horizontal resistive forces acting on each hovercraft are negligible.

The hovercraft collide and stick together. The collision lasts for $0.10\text{ s}$.

Just before the collision, what is the total kinetic energy and the magnitude of the total momentum of the two hovercraft, and what is the magnitude of the average force acting horizontally on each hovercraft during the collision?

The graph shows how a car's velocity changes in $85$ seconds.

What proportion of the total distance is travelled at constant velocity?

A block is designed with a cylindrical channel to accommodate a hot-water pipe. The block is $100\text{ cm}$ long and it has a square cross-section of side $22.0\text{ cm}$ with a cylindrical hole in the middle, as shown in the diagram.

The diameter of the cylindrical hole is $14.0\text{ cm}$ and the density of the material from which the block is made is $0.100{\text{ g cm}}^{-3}$.

What is the mass of the block?

(take $\pi$ to be $\frac{22}{7}$)

A sample initially contains equal numbers of atoms of a radioactive isotope X and a stable isotope Y.

Isotope X has a half-life of $3$ years and decays in a single stage to the stable isotope Y.

What is the ratio$$\text{number of atoms of X}:\text{number of atoms of Y}$$in the sample $6$ years later?