Can anyone actually explain to me how this mathematics question was does as I had it in an engineering test?

Question

Can anyone actually explain to me how this mathematics question was does as I had it in an engineering test but couldn't do it:
You need to determain whether the length of copper a copper rod oven will expand by more than 2% of the original length when heated. Information you have suggests that heating to 1500 degrees C, will not result in greater expansion the the required 2%.
1)Is this information correct?
2) If not, what is the maximum temperature the rod can be heated to in order to stay within the expansion limits?
The information you have is:
The equation relating original length 'I*o' and length 'l' at temperature 't'.
l= l*o(1+at) 'a' is the coefficient of linear expansion, and 't' is the temperature.
Values given are 'I*o' = 0.250m, 'a'= 1.7× 10 to the power -5.

I would appreciate any help with this question as a question similar will come up on my JAR 66 aerospace engineering licence.

Thanks

Answer 1

1500* C is not acceptable as copper melts at 1084*C

Answer 2

If the original length is L then the original length + 2 % is expressed as L*( 1 + 2/100 )
Do you understand that ?

Now look at :
l= l*o(1+at)

is at = 2/100 , l will be 2%| longer .

a is given t = 1500 is given fill in in a.t ,
if the value is smaller than 2% , the answer on 1) is NO

for 2) solve the equaltion for t: a.t = 2/100 , with this t the length will be 2|% more than original.

and you should build the next generation of spacestations ?????

Answer 3

The initial length was .250m. Add 2% to this to get .255m. Now set up
.255=(.250)[1+(1.7E-5) T]
and solve for T. This is a linear equation in T. I get T=1176C as the maximum acceptable temperature.

Answer 4

For no more than 2% expansion, you want

l <= 1.02*l_o

(rewriting l*o as l_o to avoid confusing the * with multiplication).

Therefore, you must have l_o(1+at) <= 1.02*l_o, or 1+at <= 1.02, or at <= 0.2.

for a=1.7e-5, you get t <= 0.02/a = 1,176.5 degrees, so 1500 degrees will result in a greater than 2% expansion.