A. Space, time and motion

A.1 Kinematics

A.2 Forces and momentum

A.3 Work, energy and power

A.4 Rigid body mechanics

A.5 Galilean and special relativity

B. The particulate nature of matter

B.1 Thermal energy transfers

B.2 Greenhouse effect

B.3 Gas laws

B.4 Thermodynamics

B.5 Current and circuits

C. Wave behaviour

C.1 Simple harmonic motion

C.2 Wave model

C.3 Wave phenomena

C.4 Standing waves and resonance

C.5 Doppler effect

D. Fields

D.1 Gravitational fields

D.2 Electric and magnetic fields

D.3 Motion in electromagnetic fields

D.4 Induction

E. Nuclear and quantum physics

E.1 Structure of the atom

E.2 Quantum physics

E.3 Radioactive decay

E.4 Fission

E.5 Fusion and stars

S Skills in Physics

S1.1 Experimental techniques

S1.2 Technology

S1.3 Mathematics

S2.1 Exploring and designing

S2.2 Collecting and processing data

S2.3 Concluding and evaluating

IB Physics HL S1.3 Mathematics Question Bank

[Maximum number: 4]

A student attaches one end of a copper wire to an oscillator operating at a fixed frequency. The other end of the wire passes over a pulley to weights that hang vertically. The first harmonic standing wave is established by using the slider to change the length of the wire. The procedure is repeated for different weights.

The mass m of the weights and the wavelength $\lambda$ of the wave are related by

m=\frac{\mu f^{2}}{g} \lambda^{2}

where $\mu$ is a constant, f is the frequency of the wave and $g=9.8 \mathrm{~ms}^{-2}$ .

(a)

Deduce the unit of $\mu$ in terms of fundamental SI units.

[ 1 ]

(b)

The graph shows the data obtained by the student, plotted to show the variation of m with $\lambda^{2}$ .

[ 3 ]

(i)

Draw the line of best fit for these data.

[ 1 ]

(ii)

Calculate the gradient of the graph.

[ 2 ]

[Maximum number: 4]

The density of a metal sphere is determined using a digital caliper and a mass balance.

The digital caliper is used to measure the diameter D of the sphere by placing the sphere in the jaws of the digital caliper. This reading is shown.

The sphere is then removed and another reading is taken immediately afterwards with the jaws closed.

(a)

(i)

The manufacturer of the digital caliper states that the uncertainty in the device reading is $\pm 0.1 \mathrm{~mm}$ .

Calculate the percentage uncertainty in D.

[ 1 ]

(b)

The mass M of the sphere is $(54.0 \pm 0.2) \mathrm{g}$ .

The density of the sphere $\rho$ is calculated to be $11.3 \times 10^{3} \mathrm{~kg} \mathrm{~m}^{-3}$ , using $\rho=\frac{6 M}{\pi D^{3}}$ .

[ 3 ]

(i)

Calculate the percentage uncertainty in $\rho$ .

[ 2 ]

(ii)

State the value of $\rho$ , including the absolute uncertainty of $\rho$ .

[ 1 ]

[Maximum number: 11]

This question is about the flow of liquids.

A student carries out an experiment to investigate how the rate of flow R of water through a narrow tube varies with the pressure difference across the tube. The pressure difference is proportional to the height h shown in the diagram. The student measures h in cm with a metre ruler. R is obtained by measuring the volume of water collected in a measuring cylinder in a time of 100 s .

(a)

State a suitable unit for R.

[ 1 ]

(b)

The student enters the data on a spreadsheet and produces the graph and trend line shown below.

The data point for $h=57 \mathrm{~cm}, R=1.70$ units has not been shown on the graph. The student estimates the uncertainties in all values of h to be $\pm 1 \mathrm{~cm}$ and the uncertainties in the values of R to be $\pm 5 \%$ .

[ 5 ]

(i)

On the graph, draw the missing data point.

[ 1 ]

(ii)

On the graph, draw the error bars for this data point.

[ 2 ]

(iii)

Explain why the student's estimate of a 5 % uncertainty in all values for R is unlikely to be correct.

[ 2 ]

(c)

The equation of the trend line shown in (b) is given by

R=-0.0005 h^{2}+0.0843 h-1.5632 .

[ 1 ]

(i)

Calculate the value of R for h=0.

[ 1 ]

(d)

The student estimates that the uncertainty in timing 100 s is $\pm 1 \mathrm{~s}$ . Using the data on the graph, deduce the absolute uncertainty in the volume of water collected when R=2.1 units.

[ 4 ]

[Maximum number: 6]

A student investigates the relationship between the pressure in a ball and the maximum force that the ball produces when it rebounds.

A pressure gauge measures a difference $\Delta p$ between the atmospheric pressure and the pressure in the ball. A force sensor measures the maximum force $F_{\text {max }}$ exerted on it by the ball during the rebound.

measuring gauge pressure

The student collects the following data.

The student initially hypothesizes that $F_{\text {max }}$ is proportional to $\Delta p$ .

(a)

The student now proposes that $F_{\text {max }}^{3}=k \Delta p$ .
The student plots a graph of the variation of $F_{\text {max }}^{3}$ with $\Delta p$ .

[ 2 ]

(i)

State the unit for k.

[ 1 ]

(ii)

Plot on the graph the position of the missing point for the $\Delta p$ value of 40 kPa .

The percentage uncertainty in $F_{\text {max }}$ is $\pm 5 \%$ . The error bars for $F_{\text {max }}^{3}$ at $\Delta p=10 \mathrm{kPa}$ and $\Delta p=80 \mathrm{kPa}$ are shown.

[ 1 ]

(b)

(i)

Calculate the absolute uncertainty in $F_{\text {max }}^{3}$ for $\Delta p=30 \mathrm{kPa}$ . State an appropriate number of significant figures for your answer.

[ 3 ]

(ii)

Explain why the new hypothesis is supported.

[ 1 ]

[Maximum number: 1]

What is a correct value for the charge on an electron?

$1.60 \times 10^{-12} \mu \mathrm{C}$

$1.60 \times 10^{-15} \mathrm{mC}$

$1.60 \times 10^{-22} \mathrm{kC}$

$1.60 \times 10^{-24} \mathrm{MC}$

[Maximum number: 5]

In an experiment, data were collected on the variation of specific heat capacity of water with temperature. The graph of the plotted data is shown.

(a)

Draw the line of best-fit for the data.

[ 1 ]

(b)

(i)

Determine the gradient of the line at a temperature of $80^{\circ} \mathrm{C}$ .

[ 3 ]

(ii)

State the unit for the quantity represented by the gradient in your answer to (b)(i).

[ 1 ]

[Maximum number: 1]

A rocket travels a distance of 3 km in 10 s .

What is the order of magnitude of $\frac{\text { the speed of the rocket }}{\text { the speed of light in a vacuum }}$ ?

-5

-6

-7

-8

[Maximum number: 1]

The intensity of a wave can be defined as the energy per unit area per unit time. What is the unit of intensity expressed in fundamental SI units?

$\mathrm{kg} \mathrm{m}^{-2} \mathrm{~s}^{-1}$

$\mathrm{kg} \mathrm{m}^{2} \mathrm{~s}^{-3}$

$\mathrm{kgs}^{-2}$

$\mathrm{kgs}^{-3}$

[Maximum number: 8]

In an investigation to measure the acceleration of free fall a rod is suspended horizontally by two vertical strings of equal length. The strings are a distance d apart.

When the rod is displaced by a small angle and then released, simple harmonic oscillations take place in a horizontal plane.

The theoretical prediction for the period of oscillation T is given by the following equation

T=\frac{C}{d \sqrt{g}}

where c is a known numerical constant.

(a)

State the unit of C.

[ 1 ]

(b)

A student records the time for 20 oscillations of the rod. Explain how this procedure leads to a more accurate measurement of the time for one oscillation T.

[ 2 ]

(c)

In one experiment d was varied. The graph shows the plotted values of T against $\frac{1}{d}$ . Error bars are negligibly small.

[ 1 ]

(i)

Draw the line of best fit for these data.

[ 1 ]

(d)

The numerical value of the constant c in SI units is 1.67. Determine g, using the graph.

[ 4 ]

(a)

Outline why the student has recorded the $\varepsilon$ values to different numbers of significant digits but the same number of decimal places.

[ 2 ]

(b)

The graph shows some of the data points with the uncertainty in the d values.

On the graph

[ 3 ]

(i)

draw the data point corresponding to the value of $d=19.1 \mathrm{~cm}$ .

[ 1 ]

(ii)

assuming that there is a constant absolute uncertainty in measuring all values of d, draw the error bar for the data point in (b)(i).

[ 1 ]

(iii)

sketch the line of best-fit for all the plotted points.

[ 1 ]

(c)

All values of $\varepsilon$ have a percentage uncertainty of $\pm 3 \%$ . Calculate the percentage uncertainty in the product $d \varepsilon$ for the value of $d=18.0 \mathrm{~cm}$ .

[ 2 ]

(d)

The student hypothesises that there may be an exponential relationship between $\varepsilon$ and d of the form shown below, where a and k are constants.

\varepsilon=a \mathrm{e}^{-k d}

[ 3 ]

(i)

Deduce a suitable unit for k.

[ 1 ]

(ii)

Suggest the graph that the student should plot in order to get a straight-line graph if the hypothesis is valid.

[ 2 ]

0 selected

Question 1

Question 1(a)

Question 1(b)

Question 1(b)(i)

Question 1(b)(iv)

Question 1

Question 1(a)

Question 1(a)(ii)

Question 1(c)

Question 1(c)(i)

Question 1(c)(ii)

Question 1

Question 1(a)

Question 1(b)

Question 1(b)(i)

Question 1(b)(ii)

Question 1(b)(iv)

Question 1(c)

Question 1(c)(i)

Question 1(d)

Question 1

Question 1(c)

Question 1(c)(i)

Question 1(c)(ii)

Question 1(d)

Question 1(d)(i)

Question 1(d)(iii)

Question 1

Question 1

Question 1(a)

Question 1(b)

Question 1(b)(i)

Question 1(b)(ii)

Question 1

Question 1

Question 1

Question 1(a)

Question 1(b)

Question 1(c)

Question 1(c)(i)

Question 1(d)

Question A1

Question A1(a)

Question A1(b)

Question A1(b)(i)

Question A1(b)(ii)

Question A1(b)(iii)

Question A1(c)

Question A1(d)

Question A1(d)(i)

Question A1(d)(ii)