1.2 – Uncertainties and errors

Outline how using a variable resistance could improve the accuracy of the value found for the internal resistance.

Outline how using a variable resistance could improve the accuracy of the value found for the internal resistance.

Outline how using a variable resistance could improve the accuracy of the value found for the internal resistance.

Using the following equation

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

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

Using the following equation

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

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

Using the following equation

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

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

This relationship can also be written as follows.

$$\frac{1}{\sqrt{I}}=Kx+KC$$

Show that $K=2\sqrt{\frac{\pi }{P}}$.

This relationship can also be written as follows.

$$\frac{1}{\sqrt{I}}=Kx+KC$$

Show that $K=2\sqrt{\frac{\pi }{P}}$.

This relationship can also be written as follows.

$$\frac{1}{\sqrt{I}}=Kx+KC$$

Show that $K=2\sqrt{\frac{\pi }{P}}$.

Estimate C.

Estimate C.

Estimate C.

Determine P, to the correct number of significant figures including its unit.

Determine P, to the correct number of significant figures including its unit.

Determine P, to the correct number of significant figures including its unit.

State the unit of c.

State the unit of c.

State the unit of c.

Suggest whether the data are consistent with the theoretical prediction.

Suggest whether the data are consistent with the theoretical prediction.

Suggest whether the data are consistent with the theoretical prediction.

When d = 0.200 mm, s = 0.9 mm and D = 280 mm, determine the percentage uncertainty in the wavelength.

When d = 0.200 mm, s = 0.9 mm and D = 280 mm, determine the percentage uncertainty in the wavelength.

When d = 0.200 mm, s = 0.9 mm and D = 280 mm, determine the percentage uncertainty in the wavelength.

Determine the fractional uncertainty in v when T = 2.115 s, correct to one significant figure.

Determine the fractional uncertainty in v when T = 2.115 s, correct to one significant figure.

Determine the fractional uncertainty in v when T = 2.115 s, correct to one significant figure.

The lines of the minimum and maximum gradient are shown.

Estimate the absolute uncertainty in a.

The lines of the minimum and maximum gradient are shown.

Estimate the absolute uncertainty in a.

The lines of the minimum and maximum gradient are shown.

Estimate the absolute uncertainty in a.

A rectangular sheet of paper has dimensions of (30.0 ± 0.5) cm and (20.0 ± 0.5) cm.

What is the percentage uncertainty of the perimeter of the paper?

A.  1 %

B.  2 %

C.  2.5 %

D.  4 %

A rectangular sheet of paper has dimensions of (30.0 ± 0.5) cm and (20.0 ± 0.5) cm.

What is the percentage uncertainty of the perimeter of the paper?

A.  1 %

B.  2 %

C.  2.5 %

D.  4 %

A student measures the radius r of a sphere with an absolute uncertainty Δr. What is the fractional uncertainty in the volume of the sphere?

A.     ${\left(\frac{\mathrm{\Delta }r}{r}\right)}^3$

B.     $3\frac{\mathrm{\Delta }r}{r}$

C.     $4\pi \frac{\mathrm{\Delta }r}{r}$

D.     $4\pi {\left(\frac{\mathrm{\Delta }r}{r}\right)}^3$

A student measures the radius r of a sphere with an absolute uncertainty Δr. What is the fractional uncertainty in the volume of the sphere?

A.     ${\left(\frac{\mathrm{\Delta }r}{r}\right)}^3$

B.     $3\frac{\mathrm{\Delta }r}{r}$

C.     $4\pi \frac{\mathrm{\Delta }r}{r}$

D.     $4\pi {\left(\frac{\mathrm{\Delta }r}{r}\right)}^3$

Draw on the graph the line of best fit for the data.

Draw on the graph the line of best fit for the data.

Draw on the graph the line of best fit for the data.

Write down the time taken for one oscillation when B = 0.005 T with its absolute uncertainty.

Write down the time taken for one oscillation when B = 0.005 T with its absolute uncertainty.

Write down the time taken for one oscillation when B = 0.005 T with its absolute uncertainty.

State the unit of K.

State the unit of K.

State the unit of K.

The student plots a graph to show how P² varies with $\frac{1}{B}$ for the data.

Sketch the shape of the expected line of best fit on the axes below assuming that the relationship $P=\frac{K}{\sqrt{B}}$ is verified. You do not have to put numbers on the axes.

The student plots a graph to show how P² varies with $\frac{1}{B}$ for the data.

Sketch the shape of the expected line of best fit on the axes below assuming that the relationship $P=\frac{K}{\sqrt{B}}$ is verified. You do not have to put numbers on the axes.

The student plots a graph to show how P² varies with $\frac{1}{B}$ for the data.

Sketch the shape of the expected line of best fit on the axes below assuming that the relationship $P=\frac{K}{\sqrt{B}}$ is verified. You do not have to put numbers on the axes.

State how the value of K can be obtained from the graph.

State how the value of K can be obtained from the graph.

State how the value of K can be obtained from the graph.

Draw a suitable circuit diagram that would enable the internal resistance to be determined.

Draw a suitable circuit diagram that would enable the internal resistance to be determined.

Draw a suitable circuit diagram that would enable the internal resistance to be determined.

It is noticed that the resistor gets warmer. Explain how this would affect the calculated value of the internal resistance.

It is noticed that the resistor gets warmer. Explain how this would affect the calculated value of the internal resistance.

It is noticed that the resistor gets warmer. Explain how this would affect the calculated value of the internal resistance.

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

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

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

A student wants to determine the angular speed ω of a rotating object. The period T is 0.50 s ±5 %. The angular speed ω is

$$\omega =\frac{2\pi }{T}$$ 

What is the percentage uncertainty of ω?

A. 0.2 %

B. 2.5 %

C. 5 %

D. 10 %

A student wants to determine the angular speed ω of a rotating object. The period T is 0.50 s ±5 %. The angular speed ω is

$$\omega =\frac{2\pi }{T}$$ 

What is the percentage uncertainty of ω?

A. 0.2 %

B. 2.5 %

C. 5 %

D. 10 %

A student measures the radius R of a circular plate to determine its area. The absolute uncertainty in R is ΔR.

What is the fractional uncertainty in the area of the plate?

A. $\frac{2\mathrm{\Delta }R}{R}$

B. ${\left(\frac{\mathrm{\Delta }R}{R}\right)}^2$

C. $\frac{2\pi \mathrm{\Delta }R}{R}$

D. $\pi {\left(\frac{\mathrm{\Delta }R}{R}\right)}^2$

A student measures the radius R of a circular plate to determine its area. The absolute uncertainty in R is ΔR.

What is the fractional uncertainty in the area of the plate?

A. $\frac{2\mathrm{\Delta }R}{R}$

B. ${\left(\frac{\mathrm{\Delta }R}{R}\right)}^2$

C. $\frac{2\pi \mathrm{\Delta }R}{R}$

D. $\pi {\left(\frac{\mathrm{\Delta }R}{R}\right)}^2$

Calculate the percentage error in the measured value of g.

Calculate the percentage error in the measured value of g.

Calculate the percentage error in the measured value of g.

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

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

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

There is an advantage and a disadvantage in using two masses that are almost equal.

State and explain the disadvantage with reference to your answer to (a)(ii).

There is an advantage and a disadvantage in using two masses that are almost equal.

State and explain the disadvantage with reference to your answer to (a)(ii).

There is an advantage and a disadvantage in using two masses that are almost equal.

State and explain the disadvantage with reference to your answer to (a)(ii).

A student is verifying the equation

$$x=\frac{2\lambda Y}{z}$$

The percentage uncertainties are:

What is the percentage uncertainty in x?

A. 5 %

B. 15 %

C. 25 %

D. 30 %

A student is verifying the equation

$$x=\frac{2\lambda Y}{z}$$

The percentage uncertainties are:

What is the percentage uncertainty in x?

A. 5 %

B. 15 %

C. 25 %

D. 30 %

In order to find the uncertainty for $\gamma$, a maximum gradient line would be drawn. On the graph, sketch the maximum gradient line for the data.

In order to find the uncertainty for $\gamma$, a maximum gradient line would be drawn. On the graph, sketch the maximum gradient line for the data.

In order to find the uncertainty for $\gamma$, a maximum gradient line would be drawn. On the graph, sketch the maximum gradient line for the data.

The percentage uncertainty for $\gamma$ is $15\%$. State $\gamma$, with its absolute uncertainty.

The percentage uncertainty for $\gamma$ is $15\%$. State $\gamma$, with its absolute uncertainty.

The percentage uncertainty for $\gamma$ is $15\%$. State $\gamma$, with its absolute uncertainty.

The expected value of $\gamma$ is $0.027$. Comment on your result.

The expected value of $\gamma$ is $0.027$. Comment on your result.

The expected value of $\gamma$ is $0.027$. Comment on your result.

State why the experiment is repeated with different values of $W$.

State why the experiment is repeated with different values of $W$.

State why the experiment is repeated with different values of $W$.

The measurements of $T$ were collected five times. Explain how repeated measurements of $T$ reduced the random error in the final experimental value of $mr$.

The measurements of $T$ were collected five times. Explain how repeated measurements of $T$ reduced the random error in the final experimental value of $mr$.

The measurements of $T$ were collected five times. Explain how repeated measurements of $T$ reduced the random error in the final experimental value of $mr$.

A student measures the length l and width w of a rectangular table top.

What is the absolute uncertainty of the perimeter of the table top?

A.  $0.3 \text{cm}$

B.  $0.6 \text{cm}$

C.  $\text{1.2} \text{cm}$

D.  $\text{2.4} \text{cm}$

A student measures the length l and width w of a rectangular table top.

What is the absolute uncertainty of the perimeter of the table top?

A.  $0.3 \text{cm}$

B.  $0.6 \text{cm}$

C.  $\text{1.2} \text{cm}$

D.  $\text{2.4} \text{cm}$

A ball of mass (50 ± 1) g is moving with a speed of (25 ± 1) m s⁻¹. What is the fractional uncertainty in the momentum of the ball?

A.  0.02

B.  0.04

C.  0.06

D.  0.08

A ball of mass (50 ± 1) g is moving with a speed of (25 ± 1) m s⁻¹. What is the fractional uncertainty in the momentum of the ball?

A.  0.02

B.  0.04

C.  0.06

D.  0.08

The radius of a circle is measured to be (10.0 ± 0.5) cm. What is the area of the circle?

A.  (314.2 ± 0.3) cm²

B.  (314 ± 1) cm²

C.  (314 ± 15) cm²

D.  (314 ± 31) cm²

The radius of a circle is measured to be (10.0 ± 0.5) cm. What is the area of the circle?

A.  (314.2 ± 0.3) cm²

B.  (314 ± 1) cm²

C.  (314 ± 15) cm²

D.  (314 ± 31) cm²

Two different experiments, P and Q, generate two sets of data to confirm the proportionality of variables $x$ and $y$. The graphs for the data from P and Q are shown. The maximum and minimum gradient lines are shown for both sets of data.

What is true about the systematic error and the uncertainty of the gradient when P is compared to Q?

Two different experiments, P and Q, generate two sets of data to confirm the proportionality of variables $x$ and $y$. The graphs for the data from P and Q are shown. The maximum and minimum gradient lines are shown for both sets of data.

What is true about the systematic error and the uncertainty of the gradient when P is compared to Q?

The uncertainty in reading a laboratory thermometer is 0.5 °C. The temperature of a liquid falls from 20 °C to 10 °C as measured by the thermometer. What is the percentage uncertainty in the change in temperature?

A.  2.5 %

B.  5 %

C.  7.5 %

D.  10 %

The uncertainty in reading a laboratory thermometer is 0.5 °C. The temperature of a liquid falls from 20 °C to 10 °C as measured by the thermometer. What is the percentage uncertainty in the change in temperature?

A.  2.5 %

B.  5 %

C.  7.5 %

D.  10 %

Light of frequency $f$ is incident on a metallic surface of work function W. Photoelectrons with a maximum kinetic energy E_max are emitted. The frequency of the incident light is changed to 2$f$.

What is true about the maximum kinetic energy and the work function?

Light of frequency $f$ is incident on a metallic surface of work function W. Photoelectrons with a maximum kinetic energy E_max are emitted. The frequency of the incident light is changed to 2$f$.

What is true about the maximum kinetic energy and the work function?