RMPh 2017, Теория, 27 октомври · критерии за оценяване на задача 2, част A — Задача 2. Theoretical Problem No. 2 – Part A Sir Geoffrey I. Taylor

• a. $R \sim t^{\frac{2}{5}} \cdot \left(\dfrac{E}{\rho}\right)^{\frac{1}{5}}$

• b. $3 \times 10^{12}$ J

  Estimated energy released at the atomic bomb explosion, $E \approx 3 \cdot 10^{12}\ J$, from the fit $A = 0.42$, $B = 2.48$.

Marking scheme

Any other solution that leads to correct results will be duly marked

a. For: [0.5p]

$R \sim t^{\alpha} \cdot E^{\beta} \cdot \rho^{\gamma}$ [0.1p]

$L = T^{\alpha} \cdot \left(M \cdot L^{2} \cdot T^{-2}\right)^{\beta} \cdot \left(M \cdot L^{-3}\right)^{\gamma}$ [0.1p]

[0.1p]

$\alpha = \dfrac{2}{5} \qquad \beta = \dfrac{1}{5} \qquad \gamma = -\dfrac{1}{5}$ [0.1p]

$R \sim t^{\frac{2}{5}} \cdot \left(\dfrac{E}{\rho}\right)^{\frac{1}{5}}$ [0.1p]

b. For: [1.5p]

$C \cong 1 \qquad R = t^{\frac{2}{5}} \cdot \left(\dfrac{E}{\rho}\right)^{\frac{1}{5}}$ [0.1p]

$log\ R = \dfrac{2}{5} \cdot log\ t + \dfrac{1}{5} \cdot log\ \dfrac{E}{\rho}$ [0.3p]

$y = A \cdot x + B$, where $\begin{cases} y = log\ R \\ x = log\ t \\ A = \dfrac{2}{5} \\ B = \dfrac{1}{5} log\ \dfrac{E}{\rho} \end{cases}$ [0.2p]

Table 1

Note: Graf plot of $\log R = f\left(\log t\right)$ is optional [0.5p]

The line fitting for the datasets in Table 1 has the following values of the slope and interception.

[0.2p]

estimation of the amount of energy released at the atomic bomb explosion for which the images in Figure 1

$E \approx 3 \cdot 10^{12}\ J$ [0.2p]

TOTAL SCORE: Theoretical Problem No. 2 – Part A 2.0p

© Marking scheme proposed by:
Prof. Dr. Delia DAVIDESCU
Conf. Univ. Dr. Adrian DAFINEI