Two air-track carts move toward one another on an air track. Cart 1 has a mass of 0.336 kg and a speed of 1.16 m/s. Cart 2 has a mass of 0.634 kg. What speed must cart 2 have if the total momentum of the system is is to be zero?
What is the system's kinetic energy?
To find the speed of cart 2 when the total momentum of the system is zero, we need to set up an equation using the principle of conservation of momentum.
Momentum is defined as the product of an object's mass and its velocity:
Momentum = mass * velocity
For cart 1:
Momentum1 = 0.336 kg * 1.16 m/s
For cart 2, let's assume its velocity is V2:
Momentum2 = 0.634 kg * V2
Since the total momentum of the system is zero, we can set up the equation:
Momentum1 + Momentum2 = 0
0.336 kg * 1.16 m/s + 0.634 kg * V2 = 0
Now, let's solve for V2:
0.336 kg * 1.16 m/s + 0.634 kg * V2 = 0
0.38736 kg * m/s + 0.634 kg * V2 = 0
0.634 kg * V2 = - 0.38736 kg * m/s
V2 = (-0.38736 kg * m/s) / 0.634 kg
V2 ≈ -0.61 m/s
Since speed cannot be negative, the speed of cart 2 must be approximately 0.61 m/s for the total momentum of the system to be zero.
Now, let's calculate the system's kinetic energy:
Kinetic energy is defined as 1/2 * mass * (velocity)^2
The kinetic energy of cart 1 is:
KE1 = 1/2 * 0.336 kg * (1.16 m/s)^2
The kinetic energy of cart 2 is:
KE2 = 1/2 * 0.634 kg * (0.61 m/s)^2
The system's kinetic energy is the sum of both kinetic energies:
System's Kinetic Energy = KE1 + KE2
Now you can substitute the values and calculate the system's kinetic energy.