Two railroad cars, each of mass 1800 kg and traveling 70.0 km/hr, collide head-on and come to rest. How much thermal energy in joules is produced in this collision?
To calculate the thermal energy produced in this collision, we can use the principle of conservation of mechanical energy. In this case, the initial kinetic energy of the two cars is transformed into thermal energy due to the collision.
First, we need to calculate the initial kinetic energy of the two cars. The kinetic energy formula is given by:
KE = 1/2 * mass * velocity^2
For the first car:
Mass (m1) = 1800 kg
Velocity (v1) = 70.0 km/hr = 19.4 m/s (by converting km/hr to m/s)
Using the kinetic energy formula for the first car, we have:
KE1 = 1/2 * 1800 kg * (19.4 m/s)^2
For the second car, the mass and velocity remain the same, so we have the same kinetic energy:
KE2 = KE1 = 1/2 * 1800 kg * (19.4 m/s)^2
The total initial kinetic energy before the collision is given by the sum of the kinetic energy of both cars:
Initial KE = KE1 + KE2
Now, since the two cars come to rest after the collision, all the initial kinetic energy is converted into thermal energy. Therefore, the thermal energy produced in this collision is equal to the initial kinetic energy.
We can now calculate the thermal energy produced by substituting the values in the appropriate equations:
Thermal Energy = Initial KE
= 1/2 * 1800 kg * (19.4 m/s)^2 + 1/2 * 1800 kg * (19.4 m/s)^2
= 1/2 * 1800 kg * (19.4 m/s)^2 * 2
Now, let's calculate the thermal energy:
Thermal Energy = 1/2 * 1800 kg * (19.4 m/s)^2 * 2
Using a calculator, we can calculate this value to get the answer.