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Question bank: Surface Expansion

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Question 1:

Medium

When an object is heated, its dimensions tend to increase, and this phenomenon is known as spatial expansion. Considering that the linear expansion coefficient of a certain material is equal to 0.00025°C⁻¹, determine the variation in length of a 2 m bar when heated to 50°C.
Surface Expansion
Question 2:

Medium

An engineer is designing a metal component that will be used in a car engine, and temperature variations during engine operation are a concern. The component has a central hole that needs to maintain its proper size. The metal part has a linear expansion coefficient of 11x, and the diameter of the hole is initially 8 mm at 20ºC. The component can reach a maximum temperature of 120ºC due to engine operation. Determine: (a) what will be the linear expansion of the hole when the component reaches the maximum temperature of 120ºC, considering the mentioned initial temperature; (b) the final diameter of the hole at 120ºC; (c) report if there will be assembly problems, considering that the shaft designed to pass through the hole has a maximum diameter of 8.10 mm, and that the expansion of this shaft is negligible.
Surface Expansion
Question 3:

Medium

A metal plate has a circular hole with a radius of 2 cm and is being heated. The plate's temperature increases by 100°C and the metal's linear expansion coefficient is 1.2 * 10^-5 °C^-1. Assuming uniform expansion, what is the new radius of the hole after the temperature rise?
Surface Expansion
Question 4:

Medium

The coefficient of superficial expansion of metals is generally higher than that of non-metallic materials. What would be the effect of this difference on superficial expansion?
Surface Expansion
Question 5:

Easy

A square metal plate with a side of 1 m is uniformly heated, causing it to expand. The metal's surface expansion coefficient is 2 x 10^-5 °C^-1. After heating, a worker needs to make a hole exactly in the center of the plate, but realizes that the hole he originally made when the plate was at 20°C is now at 30°C, resulting in a displaced hole. Considering that the surface expansion is directly proportional to the initial area of the plate and the surface expansion coefficient, and that the area of a square is given by A = L^2 (where L is the side of the square), determine the new area of the plate and the displacement of the hole in centimeters, knowing that the linear expansion of the metal is negligible for the calculation of the hole displacement.
Surface Expansion
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