A student foolishly attempts to stop a steel bar, of length L = 1 m and at a temperature of 20ºC, from thermally expanding by attaching it to a wooden support with a nail at each end. Steel's Young's modulus is Y = 2.9 × 1011 N/m2 and it's linear thermal expansion coefficient is α = 12.1 × 10-6 1/C.

Y = 2.9 × 1011 N/m2
α = 12.1 × 10-6 1/C

a) Enter an expression, in terms of defined variables, for the stress, S, that each nail will need to sustain at a temperature Ts.
b) What is the value of the stress, in pascals, that develops due to a rise of temperature to 21ºC?
c) Assuming the nails have a cross-sectional area of A = 10-5 m2 all of which is perpendicular to the stress force from the bar, what is the force acting on each due to that temperature rise?
d) Do you think it is possible to prevent the bar from expanding using nails?