Question

Answer any 4 of the 5 questions. Work out your solutions neatly and completely just as you would in a class test. Draw pictures and use English where appropriate. SHOW ALL YOUR WORK to receive full credit. Draw a box around each of your final answers to identify them to me. Make sure to give proper units for all your answers, and to round all your answers (except question 5) to 3 significant figures.

5. A machine in a factory in a very cold place (T = 26.00 °F) cuts out a flat rectangle sheet of polyethylene, exactly 75.00 cm x 95.50 cm. Calculate the area of the rectangle when it is installed on a roof and reaches a temperature of 117.0 °F. You must round your answer to 4 significant digits for full credit on this problem.

Answer 1

change in area of rectangle sheet due to change in temperature is given by:

dA = 2**A0*dT

dA = change in area = A - A0

A - A0 = 2*A0*dT

A = A0*(1 + 2*dT)

A0 = Initial Area of sheet at cold place = 75.00*95.50 cm^2 = 7162.5*10^-4 m^2 = 0.71625 m^2

A = Area of sheet at the roof = ?

dT = change in temperature = Tf - Ti

Ti = Initial temperature = 26.00 F = (26 - 32)*5/9 = -3.33 C

Tf = final temperature = 117.0 F = (117 - 32)*5/9 = 47.22 C

= linear thermal expansion coefficient of polyethylene = 160*10^-6 /C

So,

A = 0.71625*(1 + 2*160*10^-6*(47.22 - (-3.33))

A = 0.727836 = 7278.36*10^-4 m^2 = 7278.36 cm^2

Let me know if you've any query.