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Q7.
A metalworking company runs machines at different operating speeds for different thicknesses of the metal sheet they are producing. The formula given is:
S = 3/8T + 0.2
where S is the speed in metres per seconds (m/s) and T is the thickness of the sheet in metres.
(a) What speed will the machine run at for a 3mm steel sheet?
(b) If the machine is running at 0.22m/s, how thick (in mm) is the sheet being produced?
(a) - answer and commentary
The key point to note is that the formula works for thickness in metres and the information given and the required answers are in millimetres.
So, a 3mm sheet is 3÷1000 = 0.003m.
Now we replace T with 0.003 in the formula. To work out 3/8 you can either use the fraction facility on the calculator (if
you know how it works) or do 3÷8 instead.
S = 3/8T + 0.2
SÌý = (3/8x0.003) + 0.2
SÌý = 0.003x3 ÷ 8 + 0.2
SÌý = 0.01125 + 0.2
SÌý = 0.201125
It is reasonable to give answers to 2 significant figures, so we will say 0.20m/s.
Answer:0.20m/s
(b) - answer and commentary
This time we will need to work the formula backwards.
0.22 = 3/8T + 0.2
0.22 - 0.2 = 3/8T
0.02 = 3/8T
0.02x8 = 3T
0.16 = 3T
0.16 ÷ 3 = T
T = 0.053333
Again, we give our answers to 2 significant figures: 0.053 metres. The answer is asked for in millimetres, so
0.053m = 0.053x1000 = 53mm.
Answer: 53mm
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