(II) To make a secure fit, rivets that are larger than the rivet hole are often used and the rivet is cooled (usually in dry ice) before it is placed in the hole. A steel rivet 1.872cm in diameter is to be placed in a hole 1.870cm in diameter in a metal at 22°C. To what temperature must the rivet be cooled if it is to fit in the hole
Answers
Given:
Rivet diameter, = 1.872 cm
Hole diameter, = 1.870 cm
Temperature, = 22 °C
Formula Used:
where,
= coefficient of linear expansion
= change in diameter =
= change in temperature =
Solution:
we know that coefficient of linear expansion of steel, =
Using the above formula :
= \frac{1.870 - 1.872}{1.872\times \T_{2} - T_{1}}[/tex]
= \frac{1.870 - 1.872}{12\times 10^{-6}}}[/tex]
Therefore, the rivet must be cooled to
Final answer:
The question involves the concept of thermal expansion in Physics. By knowing the initial diameter of the rivet and hole, as well as the ambient temperature, we can use the thermal expansion formula to calculate the temperature to which the steel rivet must be cooled to fit into the hole.
Explanation:
The subject in question pertains to Physics and specifically to the concept of thermal expansion. This indicates how objects (in this case, a steel rivet) tend to change in volume or shape as a response to a change in temperature. The diameter of the rivet when cooled will decrease slightly, allowing it to fit into the smaller hole.
To find the temperature to which the rivet needs to be cooled, we require knowledge of the thermal expansion coefficient of steel, which (for generalization) can be averaged to around 0.000012 (1/°C). The formula to calculate the change in diameter (Δd) is:
Δd = α * d * ΔT
where α is the coefficient of linear expansion, d is the original diameter, and ΔT is the change in temperature. Knowing the initial diameter of the rivet and the hole it must fit into, together with the ambient temperature (22°C), we can rearrange this formula to find the cooling temperature needed for the rivet to fit into the hole.
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Final answer:
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