Edexcel A-Level Physics: Synoptic & Practical Skills

A satellite moves in a circular orbit around the Earth. The behaviour of such a satellite links two areas of the specification: Gravitational Fields and Space (the inverse-square gravitational field) and Further Mechanics (circular motion).

Explain why a geostationary satellite must orbit at one particular radius. By equating the gravitational force on the satellite to the centripetal force required to keep it in a circular orbit, derive Kepler's third law in the form $T^2 = \frac{4\pi^2}{GM}r^3.$T2=GM4π2​r3. Then calculate the radius of a geostationary orbit and the height of such an orbit above the Earth's surface.

Use the data: $G = 6.67\times10^{-11}\ \text{N m}^2\,\text{kg}^{-2}$G=6.67×10−11 N m2kg−2; mass of the Earth $M_E = 5.97\times10^{24}\ \text{kg}$ME​=5.97×1024 kg; orbital period $T = 24\ \text{h} = 86400\ \text{s}$T=24 h=86400 s; radius of the Earth $R_E = 6.37\times10^{6}\ \text{m}$RE​=6.37×106 m.

(9 marks)

A photocell is used to investigate the photoelectric effect. Monochromatic light of two different frequencies is shone in turn on a clean metal photocathode. For each frequency the stopping potential $V_s$Vs​ is found by making the collector electrode negative until the photocurrent just falls to zero. This experiment links Waves and the Particle Nature of Light (the photon model) with Electric Circuits (the role of the potential difference in stopping the electrons). The results are:

Frequency, $f$f	Stopping potential, $V_s$Vs​
$5.00\times10^{14}\ \text{Hz}$5.00×1014 Hz	$0.20\ \text{V}$0.20 V
$9.00\times10^{14}\ \text{Hz}$9.00×1014 Hz	$1.85\ \text{V}$1.85 V

Explain the photoelectric effect using the photon model - in particular why a threshold frequency exists, what is meant by the work function $\phi$ϕ, why a stopping potential is needed, and why $eV_s$eVs​ equals the maximum kinetic energy of the emitted electrons. Then use Einstein's photoelectric equation $eV_s = hf - \phi$eVs​=hf−ϕ at the two frequencies to determine Planck's constant $h$h and the work function $\phi$ϕ.

Use $e = 1.60\times10^{-19}\ \text{C}$e=1.60×10−19 C.

(9 marks)

In a Core Practical, a student determines the specific heat capacity $c$c of a metal block by the electrical method. An immersion heater is run for a measured time and the temperature rise is recorded, using $c = \frac{VIt}{m\,\Delta\theta},$c=mΔθVIt​, where $V$V and $I$I are the heater pd and current, $t$t is the heating time, $m$m is the mass of the block, and $\Delta\theta = \theta_2 - \theta_1$Δθ=θ2​−θ1​ is the temperature rise. The measurements, each with its uncertainty, are:

Quantity	Value	Uncertainty
Heater pd, $V$V	11.5 V	$\pm 0.1$±0.1 V
Heater current, $I$I	4.0 A	$\pm 0.1$±0.1 A
Heating time, $t$t	300 s	$\pm 1$±1 s
Mass of block, $m$m	0.70 kg	$\pm 0.001$±0.001 kg
Initial temperature, $\theta_1$θ1​	$19.0\ ^\circ\text{C}$19.0 ∘C	$\pm 0.5\ ^\circ\text{C}$±0.5 ∘C
Final temperature, $\theta_2$θ2​	$41.0\ ^\circ\text{C}$41.0 ∘C	$\pm 0.5\ ^\circ\text{C}$±0.5 ∘C

Calculate the specific heat capacity $c$c. Then determine the percentage uncertainty in each quantity - taking care with the temperature rise $\Delta\theta$Δθ - combine them correctly, and hence quote $c$c with its absolute uncertainty.

(6 marks)

In a Core Practical, a student determines the Young modulus $E$E of the metal of a long, thin wire by hanging masses from it and measuring the extension. The Young modulus is given by $E = \frac{FL}{Ax}, \qquad \text{where the cross-sectional area} \quad A = \frac{\pi d^2}{4}.$E=AxFL​,where the cross-sectional areaA=4πd2​. Here $F$F is the stretching force, $L$L is the original (unstretched) length, $x$x is the extension produced, and $d$d is the wire diameter, measured at several points with a micrometer and averaged. The measurements, each with its uncertainty, are:

Quantity	Value	Uncertainty
Stretching force, $F$F	19.6 N	$\pm 0.1$±0.1 N
Original length, $L$L	1.500 m	$\pm 0.002$±0.002 m
Diameter, $d$d	0.40 mm	$\pm 0.01$±0.01 mm
Extension, $x$x	1.8 mm	$\pm 0.1$±0.1 mm

Calculate the cross-sectional area $A$A and the Young modulus $E$E. Then determine the percentage uncertainty in $F$F, $L$L, $x$x and $d$d, combine them correctly (noting that $d$d is squared in the area), and hence quote $E$E with its absolute uncertainty.

(6 marks)

In a Core Practical from Electric Circuits, a student determines the electromotive force $\varepsilon$ε and internal resistance $r$r of a cell. A variable load resistor is connected across the cell; for each setting the terminal pd $V$V (voltmeter across the cell) and the current $I$I (ammeter in series) are recorded. Because $V = \varepsilon - Ir,$V=ε−Ir, a graph of $V$V against $I$I is a straight line whose intercept on the $V$V-axis is $\varepsilon$ε and whose gradient is $-r$−r.

The student takes a single pair of readings at each load setting and works fairly quickly through a wide range of currents.

Evaluate this experimental method. In your answer identify the independent, dependent and control variables; distinguish random from systematic error; explain why obtaining $\varepsilon$ε from the intercept and $r$r from the gradient of a best-fit line is more robust than using a single pair of readings; comment on reliability; and suggest improvements that would genuinely reduce the uncertainty (giving a reason for each).

(6 marks)

The same inverse-square ($1/r^2$1/r2) dependence appears in three different parts of the A-Level course:

• the gravitational field strength a distance $r$r from a point mass $M$M, $g = \dfrac{GM}{r^2}$g=r2GM​ (Gravitational Fields and Space);
• the electric field a distance $r$r from a point charge $Q$Q, $E = \dfrac{1}{4\pi\varepsilon_0}\dfrac{Q}{r^2}$E=4πε0​1​r2Q​, and the closely related Coulomb force (Electric and Magnetic Fields);
• the intensity of gamma radiation a distance $r$r from a small point source, $I \propto \dfrac{1}{r^2}$I∝r21​ (Nuclear Radiation).

Explain why each of these is an inverse-square law, and state what the constant of proportionality is in each case.

(5 marks)