Mock Exam Set 1 - Paper 2

[Maximum mark: 7]

While practising, a table tennis player hits a ball of mass 2.8 $g$ that collides with the floor and then bounces back from the wall. The speed of the ball just before reaching the floor is 8.0 $m \, s^{-1}$. The ball leaves the floor with an angle of 65$\degree$ to the floor as shown.

1. Due to the collision with the floor, the ball losses 30$\%$ of its initial kinetic energy. Show that the leaving speed of the ball from the floor is around 7 $m \, s^{-1}$. [2]
   

2. The ball strikes the wall just as it reaches the highest point of its motion. Determine the horizontal distance between the bounce point and the wall. [3]
   

3. The ball collides elastically with the wall, with the time of contact during the collision is $0.040\, s$. Calculate the average horizontal force exerted by the wall on the ball during the collision. [2]
   

[Maximum mark: 4]

1. An electric heater with a power rating of 2.8 $kW$ heats liquid that flows through it. The temperature of the liquid increases from $18°C$ to $38°C$ while passing through the heater. The flow rate of the liquid $\sigma$ is $0.035\,kg\,s^{-1}$. Calculate the specific heat capacity of the liquid. [2]
   

2. Suggest whether your answer for (a) is above or below the actual value of the specific heat capacity. Justify your answer. [2]
   

[Maximum mark: 5]

A longitudinal wave is travelling in a medium from left to right. The diagram below is a snapshot of plane wave fronts of showing position of particles $X$ (center of compression) and $Y$ (center of rarefaction) in the medium at $t =0 \ s$.

1. Distinguish between a transverse wave and a longitudinal wave. [2]
   

2. In the graph below, the solid line shows the variation of displacement $s$ of particle $X$ with time, and the dotted line shows the variation of displacement of particle $Y$ with time.

   

   1. State the phase difference between particles $X$ and $Y$. [1]
      

   2. Calculate the speed of the wave in the medium. [2]
      

[Maximum mark: 8]

1. The diagram below shows a small section of wire which is a part of a closed electric circuit.

   

   Due to a potential difference across the circuit, an electric field exists in the wire, as shown. Explain, in terms of the charge carriers, why current exists in the wire. [2]
   

2. The electric field is due to a potential difference of $120 \,V$ across the circuit. If the field performs $600 \,J$ of work moving negative charges over a time period of 2 seconds, show that approximately $3 \times 10^{19}$ electrons move through a cross-section of wire in this time. [2]
   

3. Calculate the current in the wire. [1]
   

4. If the density of mobile electrons in this wire segment is $8 \times 10^{28}$ electrons $m^{-3}$, and the wire has a diameter of $2.6\, mm$, calculate the drift speed of the electrons in the wire. [3]
   

[Maximum mark: 7]

A roller coaster car with a mass of 80 $kg$ moves on the track shown in the diagram starting from point A.

At points B and C, the track approximates a circular path so that the radii at at B and C are 12 $m$ and 18 $m$ respectively.

1. Compare the normal force exerted by the track on the car at points B and C. [2]
   

2. Draw and label the free body diagram of the car at point C. [2]
   

3. Calculate the maximum speed of the car at point C so that it could remain on the track. [3]
   

[Maximum mark: 5]

1. State Newton's law of Gravitation. [2]
   

2. A geostationary orbit is a special orbit in which satellites follow a circular path and remain above a fixed point above the Earth's surface. A satellite orbits in geostationary orbit at a constant speed of $v$ and orbital radius of $R$. The mass of the Earth is $M$.

   The radius of the satellite's orbit is 4.23 $\times 10^7\, m$. Use this information to estimate mass of the Earth. [3]
   

[Maximum mark: 7]

1. A kaon that has a quark structure of $u \bar{s}$ decays into an antimuon and muon neutrino.

   $K^{+} \rightarrow μ^+ + \nu_\mu$

   1. Explain how it can be deduced that this decay happens through weak interaction. [2]
      

   2. Using the quark structure for the kaon, draw a Feynman diagram for this decay. [2]
      

   

2. Explain, by reference to properties of nuclear and electrostatic forces, why small stable nuclei have equal numbers of protons and neutrons but in large nuclei there is an imbalance in the number of protons and neutrons. [3]
   

[Maximum mark: 7]

The government of a medium sized city plans to replace coal power plants with photovoltaic cells to power the city.

The following data are available:

• $\bullet \hspace{1em}$ Total area available for photovoltaic cells = 62.6 $km^2$
• $\bullet \hspace{1em}$ Maximum intensity of light incident on photovoltaic cells = $1.36 \times 10^3\ W \, m^{-2}$
• $\bullet \hspace{1em}$ Average efficiency of energy conversion in photovoltaic cells = 20 $\%$
• $\bullet \hspace{1em}$ Hours of sunshine in one month = 150 hours

1. Explain why the government's choice to reduce its reliance on coal would be beneficial to the Earth's climate. [2]
   

2. Outline, in terms of energy changes, how electrical energy is generated from coal. [3]
   

3. Using the data given, calculate in $GJ$ the maximum expected energy generation for one month. [2]