Read the following passage and answer the accompanying questions - Leaving Cert Physics - Question 11 - 2019

(i) A transformer is used to reduce a.c. voltage.

(ii) A rectifier (or diode) is used to convert a.c. to d.c.

Hooke’s law states that the restoring force ($F$) is proportional to the displacement ($x$) from the equilibrium position, which can be expressed mathematically as:

$F = -kx$

Where:

• $F$ is the restoring force,
• $k$ is the spring constant, and
• $x$ is the displacement.

To find the force exerted by the wall on the ball, we first calculate the change in momentum ($ext{Δp}$):

Mass of the ball $m = 110 ext{ g} = 0.110 ext{ kg}$.

Initial velocity $u = 4 ext{ m s}^{-1}$ (towards the wall).

Final velocity $v = -4 ext{ m s}^{-1}$ (away from the wall).

Change in momentum,

$ext{Δp} = m(v - u) = 0.110 kg imes (-4 - 4) = 0.110 imes (-8) = -0.88$ kg m/s.

The time of contact $t = 0.2 ext{ s}$. The average force exerted by the wall is given by:

F = rac{ ext{Δp}}{t} = rac{-0.88}{0.2} = -4.4 ext{ N}.

Thus, the force exerted by the wall on the ball is approximately $4.4 ext{ N}$ in the opposite direction.

In the diagram, an object is placed within the focal length of a convex lens. The rays from the object converge to form an upright image on the same side as the object. The diagram should show the object, the lens, the principal axis, the focal points, and the formed image.

The nuclear equation for the fission of plutonium–239 can be written as:

$\text{Pu}^{239}_{94} + n \rightarrow \text{Xe}^{134}_{54} + \text{Zr}^{103}_{40} + 3n$

where $n$ represents the neutron produced during the reaction.

To calculate the energy released, we need the mass defect, which is the difference between the mass of the reactants and products. The mass of the reactants:

$m_{reactants} = m_{Pu} + m_{n} = 239.052163 u + 1.008665 u = 240.060828 u$

The mass of the products:

$m_{products} = m_{Xe} + m_{Zr} + 3m_{n} = 133.905395 u + 102.926599 u + 3(1.008665 u) = 239.859324 u$

The mass defect is:

$\Delta m = m_{reactants} - m_{products} = 240.060828 u - 239.859324 u = 0.201504 u$

The energy released in the reaction can be calculated using Einstein's equation:

$E = \Delta m c^2$

Where $c = 3 imes 10^8 ext{ m s}^{-1}$ and converting atomic mass units to energy (1 u = 931.5 MeV):

$E \approx 0.201504 u \times 931.5 ext{ MeV/u} \approx 187.783 MeV$.

The energy released in nuclear fission is primarily in the form of kinetic energy of the fission fragments and emitted neutrons. It is also released as heat energy, which can be harnessed for nuclear power generation.