Two air-track carts move toward one another on an air track. Cart 1 has a mass of 0.34 kg and a speed of 1.1 m/s . Cart 2 has a mass of 0.68 kg and a speed of 0.55 m/s. Calculate the system's kinetic energy.
Before or after the collision?
Before the collision, you just add up the separate kinetic energies (mV^2/2) of each.
To calculate the system's kinetic energy, we need to find the individual kinetic energies of each cart and then sum them up.
The kinetic energy of an object can be calculated using the formula:
Kinetic Energy = (1/2) * mass * velocity^2
Let's find the kinetic energy of Cart 1 first:
Mass of Cart 1 = 0.34 kg
Velocity of Cart 1 = 1.1 m/s
Kinetic Energy of Cart 1 = (1/2) * 0.34 kg * (1.1 m/s)^2
= 1/2 * 0.34 kg * 1.21 m^2/s^2
= 0.2054 Joules
Now, let's find the kinetic energy of Cart 2:
Mass of Cart 2 = 0.68 kg
Velocity of Cart 2 = 0.55 m/s
Kinetic Energy of Cart 2 = (1/2) * 0.68 kg * (0.55 m/s)^2
= 1/2 * 0.68 kg * 0.3025 m^2/s^2
= 0.1099 Joules
Finally, let's calculate the system's kinetic energy by summing up the kinetic energies of both carts:
System's Kinetic Energy = Kinetic Energy of Cart 1 + Kinetic Energy of Cart 2
= 0.2054 Joules + 0.1099 Joules
= 0.3153 Joules
Therefore, the system's kinetic energy is 0.3153 Joules.