Solution:
Given the information in the question:
Temperature, T= 27 °C
The outer diameter of the shaft at 27 °C is d1 = 8.70 cm
The diameter of the central hole in the wheel at 27 °C is d2 = 8.69 cm
Coefficient of linear expansion of steel,
Let temperature at which the wheel will slip on the shaft =
Calculation:
Change due to cooling
d2= d1(1+αΔT)
d2 = d1[1+α(T1 – T)]
We are evaluating the value of
d2 – d1 = d1 α(T1 – T)
8.69 – 8.70 = 8.70 x x (T1 – 27)
-0.01 = 10.44 x (T1 – 27)
-0.01/ (10.44 ) = T1 – 27
T1 = 27 – [0.01/ (10.44 )]
T1 = 27 – 95.7 = -68.7
Answer: Therefore, the wheel will slip on the shaft when the temperature of the shaft is -68.7 0.