A car of mass 1.33 103 kg is initially moving on a level road at a speed of 18.0 m/s. Compute the increase in temperature of the brakes, assuming that all the mechanical energy ends up as internal energy in the brake system. Assume a total heat capacity of 10,000 J/C°.
To calculate the increase in temperature of the brakes, we need to find the mechanical energy of the car and then convert it into heat energy using the heat capacity equation.
The mechanical energy (E) of the car is given by the equation:
E = (1/2) * m * v^2
Where:
m = mass of the car = 1.33 * 10^3 kg
v = velocity of the car = 18.0 m/s
Substituting the given values into the equation, we have:
E = (1/2) * (1.33 * 10^3 kg) * (18.0 m/s)^2
Now, we can calculate the mechanical energy:
E = (1/2) * (1.33 * 10^3 kg) * (324 m^2/s^2)
E = 216,324 J
Since all the mechanical energy ends up as internal energy in the brake system, this is the amount of heat energy produced.
Next, we use the heat capacity equation:
Q = m * c * ΔT
Where:
Q = heat energy
m = mass of the substance heated (brake system) (not given)
c = specific heat capacity = 10,000 J/C° given
ΔT = change in temperature (ΔT = Tf - Ti)
We need to find ΔT, so we rearrange the equation:
ΔT = Q / (m * c)
Substituting the values, we have:
ΔT = 216,324 J / (m * 10,000 J/C°)
Since the mass (m) of the brake system is not given, we cannot calculate the exact increase in temperature. We can, however, calculate ΔT if the mass of the brake system is provided.