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4. To make a secure fit, rivets that are larger than the rivet hole are often used and the rivet is cooled before it is placed in the hole. A steel rivet `1.871\ cm` in diameter is to be placed in a hole `1.869\ cm` in diameter at `20°C`, To What temperature must the rivet be cooled if it is to fit in the hole? (`beta` of steel `= 12times10^(-6) //C°`)
4. To make a secure fit, rivets that are larger than the rivet hole are often used and the rivet is cooled before it is placed in the hole. A steel rivet 1.871\ cm in diameter is to be placed in a hole 1.869\ cm in diameter at 20°C, To What temperature must the rivet be cooled if it is to fit in the hole? (beta of steel = 12times10^(-6) //C°) `∆L = alphaL_0∆T `
`T = -69°C`
Given:
`L_0 = 1.871\ cm`
`L = 1.869\ cm`
`α = 12times10^(-6) //C°`
Equation:
`∆L = alphaL_0∆T `
Solution:
`∆L = αL_0∆T `
`=>`
`L - L_0 = αL_0(T-T_0)`
`=>`
`T = T_0 +(L-L_0)/(αL_0)`
`T = 20°C + (1.869\ cm-1.871\ cm)/((12times10^(-6) //C°)(1.871\ cm))`
`T = -69°C` |