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Problem 19.5: Fitting a plate over a ball-bearing

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A plate with a hole in the middle needs to fit around a ball bearing. In the animation, you are looking at a side view of the plate and ball bearing shown below:

The solid blue lines in the animation are the plate on either side of the bearing, and the dotted blue lines represent the part of the plate going over the ball bearing, which sticks out of the screen. Initially, the plate almost fits around the bearing, but to get it to fit around the middle of the ball, the blue plate and gray ball bearing are heated so that the temperature of the plate changes as indicated (position is given in millimeters). The coefficient of expansion of the ball bearing is much smaller than the plate so that you can neglect the expansion of the ball bearing in comparison with the plate.

Determine the coefficient of linear expansion of the plate. Restart.

Problem authored by Anne J. Cox.

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