Final answer:
Using the conservation of energy principle, the potential energy at point B is calculated by subtracting the cart's kinetic energy (3 J) from the total energy of the system (15 J), which results in 12 J of potential energy.
Step-by-step explanation:
The question asks how much potential energy a cart labeled 'B' would have if it had 3 J of kinetic energy, given that the total energy of the system is 15 J. This is a conservation of energy problem, where the total mechanical energy of the system (which is the sum of potential and kinetic energies) remains constant if no external work is done on the system. In this case, the potential energy at point B can be found by subtracting the kinetic energy of the cart at that point from the total energy of the system.
Using the conservation of energy formula: Total Energy = Potential Energy + Kinetic Energy, we rearrange to find the Potential Energy:
Potential Energy = Total Energy - Kinetic Energy
Potential Energy at B = 15 J (Total Energy) - 3 J (Kinetic Energy of cart at B)
Potential Energy at B = 12 J
Therefore, the cart at letter B would have 12 J of potential energy.