Question

When you apply the brakes on your car, the kinetic energy of your vehicle is transformed into thermal energy in your brake disks. During a mountain descent, a 28.00-cm diameter iron brake disk heats up from 30°C to 190°C. What is the diameter of the disk after it heats up?

Answer 1

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:

1. 
   
3. First, find the change in temperature, which is 190°C - 30°C = 160°C.
4. 
   
6. Then, calculate the change in diameter ΔD using the formula ΔL = L₀αΔT with L₀ = 28.00 cm.
7. 
   
9. 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:

• 
  
• ΔD = 28.00 cm * 12 x 10^-6 °C^-1 * 160°C
• 
  
• ΔD = 0.05376 cm
• 
  
• 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.