Physical quantities & units

Which of these physical constants requires the greatest number of different base SI units?

A Avogadro constant, N_A

B Boltzmann constant, k

C Gravitational constant, G

D Molar gas constant, R

A group of students investigate the circuit shown in the figure below.

There are N capacitors, each of capacitance C, connected in parallel.

There are N resistors, each of resistance R, connected in series.

Initially, the students close the switch X. They then note the reading on the ammeter.

The students then open the switch. They record the time T for the reading on the ammeter to fall to half of its initial value.

The table below shows the students’ results.

Show that T = (ln 2)N²RC. (a)

The results table is repeated below.

Complete the last column for N = 1 and N = 2 in the table below.

The students begin to plot a graph of T (y-axis) against N² (x-axis). (d)

Draw a straight line of best fit on the graph.

Calculate the gradient of the straight line of best fit.

The value of C is known to be 1000 F ± 5%.

Use your gradient value from (iii) to find a value for R, in units of k , including an absolute uncertainty.

R =........ ±........ k

Following the investigation, the students discovered that the sixth 1000 F capacitor connected to the circuit was actually two 470 F capacitors connected in parallel.

State the type of error caused by this mistake.

Explain the effect that this error would have had on the calculated value of R.

The diagram shows a road where vehicles travel at high speeds.

Markings painted on the road surface are spaced 40 m apart.

Drivers are advised to keep at least two markings visible on the road between them and the vehicle in front.

The maximum speed vehicles travel at on the road is 110 km/hr. The table shows data from a driving manual for a vehicle travelling on a straight, horizontal road.

Calculate the maximum speed v of vehicles on the road in S.I. units.

A vehicle passes over one of the markings.

Calculate time taken to travel the 40 m distance between the two markings.

Using the table, explain why having markings 40 m apart helps prevent collisions.

A vehicle with mass 1600 kg is travelling at 110 km / hr. The driver sees an obstruction and applies the brakes to bring the vehicle to rest in 5.6 s.

Estimate the magnitude of the average resultant force F required to bring the vehicle to rest.

Explain the effect on the distance required to bring the vehicle to rest if the road has an upwards slope.

Show that the equation above is homogeneous by reducing the equation to SI base units.

Explain why the magnitude of the resultant force F on the glider is given by F = 2 kx where x is the displacement at any time.

State and explain the effect, if any, of increasing the initial displacement on the period of the subsequent motion.

Masses are added to the glider, and the measurement of 20 T repeated.

The results table is below.

Describe two different errors in the table.

Plot the first data point from the table on the graph below.

The other points have all been plotted. The table of results is repeated on the opposite page.

Include on your graph a line of best fit.

Use the graph to determine the value of k.

=........ N m^–1 k

When the initial displacement is increased, one spring increases its extension while the extension of the other spring decreases.

Explain why the maximum kinetic energy of the motion increases.

A light-emitting diode (LED) can be used to determine the Planck constant h. When the LED just starts to emit light, the equation below is valid

where V is the potential difference (p.d.) across the LED, is the wavelength of the light emitted, c is the speed of light in vacuum and e is the elementary charge.

In the equation above, is the energy of a photon emitted from the LED.

Determine the S.I. base units for h.

* Describe how an experiment can be carried out in the laboratory to determine h from a graph. Your description must include how V and are accurately determined. Assume that the

values of e and c are known.

Additional answer space if required

Which pair of quantities have the same S.I. base units?

A force, strain

B force, stress

C pressure, stress

D strain, upthrust

Your answer

The Planck constant h is an important fundamental constant in quantum physics.

Determine the S.I. base units for h.

A researcher is investigating the de Broglie wavelength of charged particles.

The charged particles are accelerated through a potential difference V. The de Broglie wavelength of these particles is then determined by the researcher.

Each particle has mass m and charge q.

Which set of prefixes A, B, C or D are in order of increasing magnitude?

A micro, milli, centi, kilo

B milli, centi, micro, kilo

C kilo, centi, milli, micro

D centi, micro, milli, kilo

Your answer

Which of the following shows the correct base units for pressure?

kg m^–2 A

kg m^–2 s^–2 B

kg m^–1 s^–2 C

kg m² s^–3 D

Your answer

This question is about waves.

The period of a progressive wave can be determined from Fig. 16.1. Add a correct label to

the horizontal axis so that the period can be found.

A progressive wave has wavelength , frequency f and period T.

Show that the speed v of the wave is given by the equation v = f.

Calculate the period T of the light wave.

The rays of light are in phase at the dashed line X.

Use your two answers above to state the phase difference in degrees between the light rays at Y.

Question 16 continues on page 12

State Kirchhoff’s second law and the physical quantity that is conserved according to this law.

On Fig. 18.2 draw the straight line of best fit. Determine the gradient of this line.

gradient =........ A^–1 m^–1

Show that the gradient of the line is , where is the resistivity of the material of the wire, A is the area of cross-section of the wire and E is the e.m.f. of the cell.

The e.m.f. E of the cell is 1.5 V. The diameter of the wire is 0.38 mm.

Use your answer to (i) and the equation given in (ii) to determine .

=........ m

Which electrical quantity has S.I. units ampere-second (A s)?

A charge

B current

C resistance

D potential difference

Your answer

Derive the S.I. base units for resistance.

Fig. 16.1 shows the I-V characteristics of two electrical components L and R.

The component L is a filament lamp and the component R is a resistor.

Show that the resistance of R is 40 .

Which is not a unit of energy?

A kW h

B eV

C J

D W

Your answer

State one S.I. base quantity other than length, mass and time.

Show that the total resistance R of the wires is given by the equation

A student uses the equation in (i) to determine R. The table below shows the data recorded by the student in her lab book.

Quantity	Value
	4.7 10−7 m
L	9.5 ± 0.1 cm
d	0.270 ± 0.003 mm

1. Name the likely instruments used by the student to measure L and d.

2. Use the data in the table and the equation in (i) to determine R and the absolute uncertainty. Write your answer to the correct number of significant figures.

3. The instrument used to measure d has a zero-error. The measured d is much larger than the actual value. Discuss how the actual value of R compares with the value calculated above.