Final answer:
To calculate the new diameter of the heated brake disk, the linear expansion formula is used considering the initial diameter of 28.00 cm and a temperature increase from 30°C to 190°C. The result gives a new diameter of approximately 28.05376 cm.
Step-by-step explanation:
When a car's brake disks heat up from 30°C to 190°C, the increase in temperature causes the disks to expand. To determine the new diameter after heating, we can use the linear expansion formula ΔL = L₀αΔT, where ΔL is the change in length (or diameter in this case), L₀ is the initial length, α is the coefficient of linear expansion for iron (α ≈ 12 x 10^-6 °C^-1), and ΔT is the change in temperature. Applying this formula, we find that the new diameter D = D₀ + ΔL, where D₀ is the initial diameter.
To calculate the increase in the brake disk's diameter:
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- First, find the change in temperature, which is 190°C - 30°C = 160°C.
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- Then, calculate the change in diameter ΔD using the formula ΔL = L₀αΔT with L₀ = 28.00 cm.
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- Finally, add ΔD to the initial diameter to get the new diameter after heating.
Since the question states the initial diameter is 28.00 cm:
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- ΔD = 28.00 cm * 12 x 10^-6 °C^-1 * 160°C
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- ΔD = 0.05376 cm
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- New diameter D = 28.00 cm + 0.05376 cm = 28.05376 cm
The brake disk's diameter after heating up would thus be approximately 28.05376 cm.