A 1,000.0 Kg car with a speed of 90.0km/h brakes to stop. How many cal of heat are generated by the brakes as a result?
To calculate the amount of heat generated by the brakes, we'll need to use the formula:
Heat Generated = Kinetic Energy before stopping - Kinetic Energy after stopping
First, let's calculate the initial kinetic energy of the car using the formula:
Kinetic Energy = (1/2) * mass * speed^2
Given:
Mass of the car (m) = 1,000.0 kg
Speed of the car (v) = 90.0 km/h (convert to m/s by dividing by 3.6)
Mass (m) = 1,000.0 kg
Speed (v) = 90.0 km/h รท 3.6 = 25.0 m/s
Now we can calculate the initial kinetic energy (KE_initial):
KE_initial = (1/2) * m * v^2
KE_initial = (1/2) * 1,000.0 kg * (25.0 m/s)^2
KE_initial = 0.5 * 1,000.0 kg * 625.0 m^2/s^2
KE_initial = 312,500 J (Joules)
Next, we need to calculate the final kinetic energy after the car has stopped. Since the car comes to a complete stop, its final kinetic energy is zero.
KE_final = 0 J (as the car has come to a complete stop)
Now, we can calculate the heat generated by the brakes using the formula mentioned earlier:
Heat Generated = KE_initial - KE_final
Heat Generated = 312,500 J - 0 J
Heat Generated = 312,500 J (Joules)
Therefore, the brakes generate 312,500 Joules of heat as a result.