Mathematical tools for scientists

Order Description

TASK SCENARIO

Task 1

The lab you have been assigned to is full of equipment of all ages. Some equipment uses the metric system of units and some the imperial measurement system.

a) Give examples (one each for Biology, Chemistry & Physics) of quantities and the units (both metric and imperial) they are measured in together with the conversion factor used.
For each example in a) above produce your own worked example of converting from metric to imperial units and vice-versa. The calculations should involve decimal numbers and you should leave calculations to an appropriate number of significant figures.

Task 2

You have been asked to design a poster for the lab illustrating the use of standard form to solve problems in science. Your poster should be A4 size and should include worked examples (one each from Biology, Chemistry & Physics) of calculations using standard form.

Task 3

a) A scientist who works in the lab has forgotten how many white blood cells there are in the average human body, he can remember that there are 25,000,000,000,000 red blood cells and that there are 800 times as many red blood cells as white blood cells. Using ratios work out the answer for him.
b) Whilst checking the storage cupboard you find a jar for vitamin C unfortunately the chemical formula has been rubbed off! Vitamin C contains three elements: carbon, hydrogen, and oxygen. You work out that the number of moles of each element are 3.41 mol C, 4.53 mol H & 3.41 mol O, Knowing that the numbers of moles of each element are in the same ratio as the number of atoms, use ratios and fractions to find the simplest formula for vitamin C.
You have also noticed that the storage cupboard is lit by two 100 Watt old fashioned light bulbs. You want to convince your supervisor to change these. You know that light bulbs are 95% inefficient. Work out how much energy is wasted in heat if both bulbs are left on continuously for a period of one day. (Power in Watts = Joules/second).

Task 4

Your supervisor has told you that you will need to use mensuration and algebra to solve some problems for her. You decide to revise your basic algebra skills by doing the following problems:

a) An approximate method of converting from degrees Celcius to degrees Fahrenheit is given by the rule: Multiply by 2 and add 30. Using C to stand for degrees Celcius and F to stand for degrees Fahrenheit, complete the formula. F = …
b) Simplify by collecting like terms: 2??3??+?2+5?+2??
c) Simplify as far as possible 3t2x4t3
d) Expand the brackets and collect like terms: 3??2(2?+5)
e) The formula ?=2?? gives the velocity v of an object where h is the height from which it dropped (in metres) and g is approximately 9.81 ms-1. Calculate the velocity of a stone dropped from a height of 30m.

Task 5

a) You have been given a picture of the CMS detector which is part of the Large Hadron Collider at CERN.

The picture gives the overall diameter of the CMS as 15m and its length as 21.5m. Assuming the overall shape approximates to a cylinder use formulae to calculate it’s a) cross-sectional area and b) overall volume.

b) White blood cells have a diameter of approximately 6µm, assuming they are roughly spherical in shape, calculate the volume of a single cell in m3.

c) A chemist in the lab is investigating the rate of reaction of a chemical with copper plate. She has decided to increase the surface area available for the reaction by shaping the copper plate into an opened ended cylinder. Being very busy she has asked you to do the calculation! You measure the (inner) diameter as 3 mm and the length as 9.4 cm. What is the internal surface area in m2.

Task 6

Your supervisor has given you three tasks from three of the scientists working in the lab.
a) The Physicist has been building a pendulum clock, he wants each full swing of the pendulum to last 1 second. Using the formula ?=2??? where T is the time for one swing, l is the length of the pendulum and g is the acceleration due to gravity find the required length. Rearrange the formula to make l the subject.

b) The chemist asks you to calculate the molarity of 0.4 moles of H2SO4 in 750cm3 of water. Using appropriate formulae work this out.

The biologist is trying to estimate the density of a sample of bone she has been sent. You measure the bone to be 25.6 cm long and 2.3 cm in diameter. It weighs 650 grams. By using appropriate formulae find the density in kgm-3 .