[Maximum number: 7]

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)

Draw the line of best-fit for the data.

[ 1 ]

(b)

State why the line of best-fit suggests that $h_{\text {mean }}$ is not proportional to T.

[ 1 ]

(c)

(i)

State the uncertainty in each value of T.

[ 1 ]

(d)

Another hypothesis is that $h_{\text {mean }}=K T^{3}$ where K is a constant. Using the graph on page 2 , calculate the absolute uncertainty in K corresponding to $T=50^{\circ} \mathrm{C}$ .

[ 4 ]

[Maximum number: 1]

A student wants to determine the angular speed $\omega$ of a rotating object. The period T is $0.50 \mathrm{~s} \pm 5 \%$ . The angular speed $\omega$ is

\omega=\frac{2 \pi}{T}

What is the percentage uncertainty of $\omega$ ?

A

0.2 %

B

2.5 %

C

5 %

D

10 %

[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: 5]

In an experiment to measure the acceleration of free fall a student ties two different blocks of masses $m_{1}$ and $m_{2}$ to the ends of a string that passes over a frictionless pulley.

The student calculates the acceleration a of the blocks by measuring the time taken by the heavier mass to fall through a given distance. Their theory predicts that $a=g \frac{m_{1}-m_{2}}{m_{1}+m_{2}}$ and this can be re-arranged to give $g=a \frac{m_{1}+m_{2}}{m_{1}-m_{2}}$ .

(a)

In a particular experiment the student calculates that $a=(0.204 \pm 0.002) \mathrm{ms}^{-2}$ using $m_{1}=(0.125 \pm 0.001) \mathrm{kg}$ and $m_{2}=(0.120 \pm 0.001) \mathrm{kg}$ .

[ 5 ]

(i)

Calculate the percentage error in the measured value of g.

[ 3 ]

(ii)

Deduce the value of g and its absolute uncertainty for this experiment.

[ 2 ]

[Maximum number: 1]

Which of the following expresses the watt in terms of fundamental units?

A

$\mathrm{kgm}^{2} \mathrm{~s}$

B

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

C

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

D

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

[Maximum number: 9]

Data analysis question.

Connie and Sophie investigate the effect of colour on heat absorption. They make grey paint by mixing black and white paint in different ratios. Five identical tin cans are painted in five different shades of grey.

Connie and Sophie put an equal amount of water at the same initial temperature into each can. They leave the cans under a heat lamp at equal distances from the lamp. They measure the temperature increase of the water, T, in each can after one hour.

(a)

Connie suggests that T is proportional to B, where B is the percentage of black in the paint. To test this hypothesis, she plots a graph of T against B, as shown on the axes below. The uncertainty in T is shown and the uncertainty in B is negligible.

[ 4 ]

(i)

State the value of the absolute uncertainty in T.

[ 1 ]

(ii)

Comment on the fractional uncertainty for the measurement of T for B=10 and the measurement of T for B=90.

[ 2 ]

(iii)

On the graph opposite, draw a best-fit line for the data.

[ 1 ]

(b)

Sophie suggests that the relationship between T and B is of the form

T=k B^{\frac{1}{2}}+c

where k and c are constants.
To test whether or not the data support this relationship, a graph of T against $B^{\frac{1}{2}}$ is plotted as shown below. The uncertainty in T is shown and the uncertainty in $B^{\frac{1}{2}}$ is negligible.

[ 5 ]

(i)

Use the graph to determine the value of c with its uncertainty.

[ 4 ]

(ii)

State the unit of k.

[ 1 ]

[Maximum number: 4]

A student investigates the oscillation of a horizontal rod hanging at the end of a vertical string. The diagram shows the view from above.

The student starts the rod oscillating and measures the largest displacement for each cycle of the oscillation on the scale and the time at which it occurs. The student begins to take measurements a few seconds after releasing the rod.

The graph shows the variation of displacement x with time t since the release of the rod. The uncertainty for t is negligible.

(a)

On the graph above, draw the line of best fit for the data.

[ 1 ]

(b)

Calculate the percentage uncertainty for the displacement when $t=40 \mathrm{~s}$ .

[ 2 ]

(c)

The student hypothesizes that the relationship between x and t is $x=\frac{a}{t}$ where a is a constant.

To test the hypothesis x is plotted against $\frac{1}{t}$ as shown in the graph.

[ 1 ]

(i)

The data point corresponding to $t=15 \mathrm{~s}$ has not been plotted. Plot this point on the graph above.

[ 1 ]

[Maximum number: 6]

To determine the acceleration due to gravity, a small metal sphere is dropped from rest and the time it takes to fall through a known distance and open a trapdoor is measured.

The following data are available.

(a)

Determine the distance fallen, in m , by the centre of mass of the sphere including an estimate of the absolute uncertainty in your answer.

[ 2 ]

(b)

Using the following equation

\text { acceleration due to gravity }=\frac{2 \times \text { distance fallen by centre of mass of sphere }}{(\text { measured time to fall })^{2}}

calculate, for these data, the acceleration due to gravity including an estimate of the absolute uncertainty in your answer.

[ 4 ]

[Maximum number: 1]

What is the order of magnitude of the mass, in kg , of an apple?

A

$10^{-3}$

B

$10^{-1}$

C

$10^{+1}$

D

$10^{+3}$

(a)

Theory suggests that the relation between v and W is

where k is a constant.
To test this hypothesis a graph of $v^{\frac{1}{3}}$ against W is plotted.

At $W=5.5 \mathrm{~N}$ the speed is $250 \pm 20 \mu \mathrm{~m} \mathrm{~s}^{-1}$ .
Calculate the uncertainty in $v^{\frac{1}{3}}$ for a load of 5.5 N .

[ 3 ]

(b)

(i)

Using the graph in (c), determine k without its uncertainty.

[ 4 ]

(ii)

State an appropriate unit for your answer to (d)(i).

A2. This question is about magnetic fields.

A long straight vertical conductor carries an electric current. The conductor passes through a hole in a horizontal piece of paper.

[ 1 ]

Question 1

Question 1(a)

Question 1(b)

Question 1(c)

Question 1(c)(i)

Question 1(d)

Question 1

Question 1

Question 1(a)

Question 1(b)

Question 1(b)(i)

Question 1(b)(iv)

Question 1

Question 1(a)

Question 1(a)(i)

Question 1(a)(ii)

Question 1

Question 1

Question 1(a)

Question 1(a)(i)

Question 1(a)(ii)

Question 1(a)(iii)

Question 1(b)

Question 1(b)(i)

Question 1(b)(ii)

Question 1

Question 1(a)

Question 1(b)

Question 1(c)

Question 1(c)(i)

Question 1

Question 1(a)

Question 1(b)

Question 1

Question A1

Question A1(c)

Question A1(d)

Question A1(d)(i)

Question A1(d)(ii)