Final answer:
In a system with no external forces, linear momentum along a specific axis is conserved. For a pendulum and cart at rest, momentum is conserved along the y-axis according to the equation for momentum conservation. A graph of total momentum would show constant momentum over time, whereas kinetic energy would vary depending on the pendulum's position.
Step-by-step explanation:
The subject of the question is the conservation of linear momentum in a system where both a cart and a pendulum have zero initial velocity and the pendulum is released from a certain angle. Assuming there are negligible frictions, the conservation of momentum depends on the external forces acting on the system. If there is no external force in a particular direction, momentum will be conserved in that direction.
As for the y-axis, applying the conservation of linear momentum, the initial momentum must equal the final momentum. Given that the velocities along the y-axis are initially zero, the equation 0 = m₁v₁ sin 0₁ + m₂v₂ sin 0₂ suggests that the linear momentum along the y-axis will be conserved.
However, in cases where external forces (such as gravity) are at play, as in the vertical direction of the pendulum’s movement, momentum would not be conserved due to forces like gravity affecting the system.
In a graph of total momentum vs. time, the momentum would remain constant if no external forces are in the direction of motion.
Conversely, in a graph of total kinetic energy vs. time, the kinetic energy would initially increase as the pendulum is released and decreases when the pendulum reaches its highest point in its swing, reflecting energy conservation in an ideal system with no losses due to friction or air resistance.