David Sang and Graham Jones Solutions for Chapter: Practical Skills at AS Level, Exercise 9: Questions

You measure the following quantities:

$A=(1.0\pm 0.4)\mathrm{m} B=(2.0\pm 0.2)\mathrm{m}$

$C=(2.0\pm 0.5){\mathrm{ms}}^{-1} D=(0.20\pm 0.01)\mathrm{s}$

Calculate the result and its uncertainty for each of the following expressions. You may express your uncertainty either as an absolute value or as a percentage.

(a) $A+B$

You measure the following quantities:

$A=(1.0\pm 0.4)\mathrm{m} B=(2.0\pm 0.2)\mathrm{m}$

$C=(2.0\pm 0.5){\mathrm{ms}}^{-1} D=(0.20\pm 0.01)\mathrm{s}$

Calculate the result and its uncertainty for each of the following expressions. You may express your uncertainty either as an absolute value or as a percentage.

(b) $B-A$

You measure the following quantities:

$A=(1.0\pm 0.4)\mathrm{m} B=(2.0\pm 0.2)\mathrm{m}$

$C=(2.0\pm 0.5){\mathrm{ms}}^{-1} D=(0.20\pm 0.01)\mathrm{s}$

Calculate the result and its uncertainty for each of the following expressions. You may express your uncertainty either as an absolute value or as a percentage.

(c) $C\times D$

You measure the following quantities:

$A=(1.0\pm 0.4)\mathrm{m} B=(2.0\pm 0.2)\mathrm{m}$

$C=(2.0\pm 0.5){\mathrm{ms}}^{-1} D=(0.20\pm 0.01)\mathrm{s}$

Calculate the result and its uncertainty for each of the following expressions. You may express your uncertainty either as an absolute value or as a percentage.

(d) $\frac{B}{D}$

You measure the following quantities:

$A=(1.0\pm 0.4)\mathrm{m} B=(2.0\pm 0.2)\mathrm{m}$

$C=(2.0\pm 0.5){\mathrm{ms}}^{-1} D=(0.20\pm 0.01)\mathrm{s}$

Calculate the result and its uncertainty for each of the following expressions. You may express your uncertainty either as an absolute value or as a percentage.

(e) $A^2$

You measure the following quantities:

$A=(1.0\pm 0.4)\mathrm{m} B=(2.0\pm 0.2)\mathrm{m}$

$C=(2.0\pm 0.5){\mathrm{ms}}^{-1} D=(0.20\pm 0.01)\mathrm{s}$

Calculate the result and its uncertainty for each of the following expressions. You may express your uncertainty either as an absolute value or as a percentage.

(f) $2\times A$

You measure the following quantities:

$A=(1.0\pm 0.4)\mathrm{m} B=(2.0\pm 0.2)\mathrm{m}$

$C=(2.0\pm 0.5){\mathrm{ms}}^{-1} D=(0.20\pm 0.01)\mathrm{s}$

Calculate the result and its uncertainty for each of the following expressions. You may express your uncertainty either as an absolute value or as a percentage.

(g) The square root of $(A\times B)$. (Recall that the square root of $x$ can be written as $x^{1/3}$.)

A rifle bullet is photographed in flight using two flashes of light separated by a time interval of $(1.00\pm 0.02)\mathrm{ms}$. The first image of the bullet on the photograph appears to be at a position of $(22.5\pm 0.5)\mathrm{cm}$ on a scale underneath the flight path. The position of the second image is $(37.5\pm 0.7)\mathrm{cm}$ on the same scale. Find the speed of the bullet and its absolute uncertainty.