[Maximum number: 3]

Data analysis question.

An experiment is undertaken to investigate the relationship between the temperature of a ball and the height of its first bounce.

A ball is placed in a beaker of water until the ball and the water are at the same temperature. The ball is released from a height of 1.00 m above a bench. The maximum vertical height h from the bottom of the ball above the bench is measured for the first bounce. This procedure is repeated twice and an average $h_{\text {mean }}$ is calculated from the three measurements.

The procedure is repeated for a range of temperatures. The graph shows the variation of $h_{\text {mean }}$ with temperature T.

(a)

(i)

State the uncertainty in each value of T.

[ 1 ]

(ii)

The temperature is measured using a liquid in glass thermometer. Explain why it is likely that the uncertainty in T is constant.

[ 2 ]

[Maximum number: 1]

A thermometer and an electrical heater are inserted into small holes in a solid aluminium block.

The heater is turned on at time t=0. The graph shows the variation of the temperature $\theta$ of the block with time t.

(a)

(i)

Estimate the initial temperature of the block.

[ 1 ]

[Maximum number: 1]

A thermometer and an electrical heater are inserted into small holes in a solid aluminium block.

The heater is turned on at time t=0. The graph shows the variation of the temperature $\theta$ of the block with time t.

(a)

(i)

Estimate the initial temperature of the block.

[ 1 ]

[Maximum number: 2]

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)

Calculate D.

[ 1 ]

(b)

State one way in which the procedure for the measurement of D can be improved using the same digital caliper.

[ 1 ]

[Maximum number: 2]

A group of students uses pressurized air to move a piston that forces a nail into a block of wood. A gauge is used to measure the pressure P of compressed air above atmospheric pressure. The nail enters the wood perpendicular to its surface.

The students use a ruler to measure the length of the nail which remains above the surface of the wood as shown. The depth of the nail inside the wood is d. All necessary length measurements are recorded using a ruler with uncertainty $\pm 1 \mathrm{~mm}$ .

(a)

Describe one consideration that must be made when placing the ruler to ensure that the length of the nail remaining above the surface of the wood is measured accurately.

[ 1 ]

(b)

The students systematically increase the pressure and calculate d.

[ 1 ]

(i)

Outline how the students determined the value of d.

[ 1 ]

[Maximum number: 2]

A student determines the resistivity $\rho$ of a metal that is in the form of a cylindrical wire. The student makes the following measurements:

\text { Length } L \text { of the wire }=(462 \pm 2) \mathrm{mm}

Readings for the diameter d of the wire:

\text { Resistance } R \text { of the wire }=13.7 \Omega \pm 1.5 \%

(a)

Suggest suitable instruments for the measurement of

[ 2 ]

(i)

$\quad L$

[ 1 ]

(ii)

d

[ 1 ]

[Maximum number: 1]

A student is analysing a sample of water. To determine its density, the student measures the volume with a measuring cylinder and the mass with an electronic balance.

(a)

Identify one way to ensure that the volume is read accurately.

The following data are collected:

\begin{array}{ll} \text { Volume } & =(10.6 \pm 0.2) \mathrm{cm}^{3} \\ \text { Mass } & =(10.82 \pm 0.01) \mathrm{g} \end{array}

[ 1 ]

[Maximum number: 2]

A student determines the resistivity $\rho$ of a metal that is in the form of a cylindrical wire. The student makes the following measurements:

\text { Length } L \text { of the wire }=(462 \pm 2) \mathrm{mm}

Readings for the diameter d of the wire:

\text { Resistance } R \text { of the wire }=13.7 \Omega \pm 1.5 \%

(a)

Suggest suitable instruments for the measurement of

[ 2 ]

(i)

$\quad L$

[ 1 ]

(ii)

d

[ 1 ]

[Maximum number: 1]

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)

Calculate D.

[ 1 ]

[Maximum number: 1]

The diagram shows an analogue meter with a mirror behind the pointer.

What is the main purpose of the mirror?

A

To provide extra light when reading the scale

B

To reduce the risk of parallax error when reading the scale

C

To enable the pointer to be seen from different angles

D

To magnify the image of the pointer