The Stanford linear accelerator contains hundreds of brass disks tightly fitted into a steel tube (see figure).The coefficient of linear expansion of the brass is 2.00 x 10^-5 per C°.The system was assembled by cooling the disks in dry ice (-57°C)to enable them to just slide into the close-fitting tube.If the diameter of a disk is 80.00 mm at 43°C, what is its diameter in the dry ice?

Question

Quizplus · Accepted Answer

We can use the formula ΔL = αLΔT to find the change in diameter of the disk. Since the disk is tightly fitted into the steel tube, any change in its diameter will also result in a change in the diameter of the tube.

First, we need to find the change in temperature of the disk as it is cooled from 43°C to -57°C:

ΔT = (-57°C) - (43°C) = -100°C

Next, we can use the given coefficient of linear expansion to find the change in length of the disk:

ΔL = αLΔT = (2.00 x 10^-5)(80.00 mm)(-100°C) = -0.160 mm

Note that the negative sign indicates that the length (and diameter) of the disk has decreased.

Finally, we can calculate the new diameter of the disk:

New diameter = 80.00 mm - 0.160 mm = 79.840 mm

Therefore, the answer is (D) 79.840 mm.

The Stanford Linear Accelerator Contains Hundreds of Brass Disks Tightly