Question

7. An aluminum Bolt with diameter 0.5 in is to be inserted into a hole 0.499 in diameter cut in a steel plate. Both bolt and plate are initially at 22 C. Coefficient of thermal expansion (contraction) of aluminum is 26 x 10-6 and of steel 11 x 10-6. a) In order to insert the bolt into the hole, both must be heated or cooled to the same temperature? ANS b) Find this temperature ANS

Answer 1

Initial area of the Bolt of aluminum > initial area of the hole of the steel plate coefficient of thermal expansion of aluminum (alpha_A) > coefficient of thermal expansion of steel plate (alpha_s) so, if we want to insert the bolt in to the steel plate, then both the areas should be at least equal. So, we have to increase the area of the hole or we have to decrease the area of the aluminum Bolt. As, alpha_A > , so heating is not possible, because if we heat both the metals, then always area of the aluminum Bolt will be greater than the area of the steel plate's hole. So, we have to cool both the metals, so that area of the aluminum Bolt will decrease faster than the area of the hole of the steel plate. So, at a particular temperature area of the aluminum bolt will be