Iniital KE=1/2 m v^2
heat in the stopping process: Initial KE
massiron*specificheatiron*(deltaTemp)=heat
solve for deltatemp
What was the car’s original kinetic energy and after the car has stopped, what is the change in temperature of the brakes and wheels?
heat in the stopping process: Initial KE
massiron*specificheatiron*(deltaTemp)=heat
solve for deltatemp
Kinetic Energy (KE) = 0.5 * mass * velocity^2
Given that the mass of the car is 1200kg and the velocity is 25m/s, we can calculate the original kinetic energy:
KE = 0.5 * 1200kg * (25m/s)^2
KE = 0.5 * 1200kg * 625m^2/s^2
KE = 375,000 Joules
Therefore, the car's original kinetic energy is 375,000 Joules.
To find the change in temperature of the brakes and wheels, we need to calculate the amount of heat produced by friction. We know that approximately 20kg of iron absorbs this heat.
The heat produced by friction can be calculated using the formula:
Heat = mass * specific heat capacity * temperature change
The specific heat capacity of iron is 450 J/kg°C. Let's assume the car comes to a stop, so its final velocity is 0 m/s. The change in kinetic energy is equal to the heat produced by friction.
Change in Kinetic Energy (ΔKE) = Heat = mass * specific heat capacity * temperature change
Since the final kinetic energy is zero, the change in kinetic energy from the initial value (375,000J) to zero is -375,000J.
-375,000J = 20kg * 450J/kg°C * temperature change
To calculate the change in temperature, we rearrange the equation:
temperature change = (-375,000J) / (20kg * 450J/kg°C)
temperature change = -41.67°C
Therefore, the change in temperature of the brakes and wheels is approximately -41.67°C.