Question

analyze the energy of the ball-earth system throughout this process to complete the table. assume air resistance is small enough to ignore.

event\ttotal energy of ball-earth system

the cable raises the ball\t

the ball swings down after the cable is released\t

the ball smashes into the wall\t

Explanation:

Step1: Analyze "the cable raises the ball"

When the cable raises the ball, an external force (from the cable) does work on the ball - Earth system. The work done by the cable increases the mechanical energy (potential energy, as the height of the ball increases) of the system. Also, if we consider the system including the cable's energy source (like the motor), but in the ball - Earth system, the cable is an external agent. However, since we are to analyze the ball - Earth system, the work done by the cable (external force) will increase the total energy of the ball - Earth system. So the total energy of the ball - Earth system increases.

Step2: Analyze "the ball swings down after the cable is released"

After the cable is released, we assume air resistance is negligible. In the ball - Earth system, only conservative forces (gravity) act. For a system with only conservative forces, the total mechanical energy (kinetic + potential) is conserved. So as the ball swings down, gravitational potential energy is converted into kinetic energy, but the total energy of the ball - Earth system remains constant.

Step3: Analyze "the ball smashes into the wall"

When the ball smashes into the wall, there is a non - conservative force (the normal force from the wall) acting on the ball. But we are considering the ball - Earth system. The collision with the wall will involve energy transfer (like sound, heat, deformation energy). However, if we consider the system, the total energy (including the energy dissipated as heat, sound, etc.) should be conserved in the universe, but for the ball - Earth system, the impact with the wall (an external force from the wall) will cause a change? Wait, no. Wait, the ball - Earth system: when the ball hits the wall, the wall exerts a force on the ball. But the Earth is part of the system, and the wall is external? Wait, no, the wall is attached to the Earth? If the wall is part of the Earth (like a building on Earth), then the ball - Earth (including the wall) system. In that case, the collision is an internal force (between the ball and the wall, both part of the Earth - ball system). But during the collision, energy is converted into other forms (heat, sound, elastic potential energy of deformation). But the total energy of the ball - Earth system (including the wall) should be conserved? Wait, no, the problem says "ball - Earth system". If the wall is not part of the Earth - ball system, then the wall is an external object. But usually, in such problems, when the ball hits the wall (which is on Earth), we can consider the Earth - ball - wall system, but the problem says "ball - Earth system". So when the ball smashes into the wall, the wall exerts an external force on the ball. But the work done by the wall's force: during the collision, the force from the wall is a non - conservative force. However, the total energy of the ball - Earth system: the ball's kinetic energy is converted into other forms (like heat, sound, and the energy of deformation of the ball and wall). But if we consider the ball - Earth system, and the wall is external, then the total energy of the ball - Earth system will decrease? Wait, no, the law of conservation of energy says that energy is conserved in an isolated system. The ball - Earth system is not isolated when the wall (external) exerts a force. But the problem says "assume air resistance is small enough to ignore". Wait, maybe the problem considers that during the collision, the total energy (including the energy gained by the wall and the ball's deformation) is still conserved in the sense that the energy is just transformed. But in the context of a typical physics problem, when the ball swings down (only gravity, conservative force, energy conserved), when the cable raises the ball (external work, energy increases), and when the ball hits the wall, if we consider the ball - Earth system, and the wall is part of the Earth (like the Earth's structure), then the collision is an internal interaction, and the total energy of the ball - Earth system (including the wall) is conserved. But maybe the problem is simpler:

- For "the cable raises the ball": external work is done on the system (cable does work), so total energy increases.
- For "the ball swings down after the cable is released": only conservative forces (gravity) act, so total energy is constant.
- For "the ball smashes into the wall": if we consider that the collision is an inelastic collision, but within the ball - Earth system (assuming the wall is part of the Earth), the total energy (mechanical + internal energy) is conserved. But maybe the problem expects us to consider that when the ball hits the wall, the energy is still conserved (since energy is just transformed into other forms like heat, sound, etc., within the system). Wait, but the first event: cable raises the ball - external force (cable) does work, so energy increases. Second event: swinging down - only gravity (conservative), so energy constant. Third event: smashing into wall - if the wall is external, then the system is not isolated, but if the wall is part of the Earth, then it's internal, and energy is conserved. But maybe the problem has the following logic:

1. the cable raises the ball: The cable applies a force and does work on the ball - Earth system. So the total energy of the system increases (because work is done on the system by an external force).
2. the ball swings down after the cable is released: No non - conservative forces (air resistance is ignored), so the total mechanical energy (kinetic + potential) of the ball - Earth system is conserved. So total energy is constant.
3. the ball smashes into the wall: When the ball hits the wall, the collision is an inelastic collision. But if we consider the ball - Earth system (and the wall is part of the Earth), the energy is still conserved (it's just converted into other forms like heat, sound, and deformation energy). So total energy is constant? Wait, no, maybe the problem considers that when the ball hits the wall, the external force (wall) does work? No, the wall is at rest (assuming), and the ball is moving. The force from the wall on the ball is a normal force, and during the collision, the displacement of the point of application of the force is zero (or very small), so the work done by the wall is zero? Wait, maybe I made a mistake. Let's recall:

- **Cable raises the ball**: External work (cable) → total energy increases.
- **Ball swings down (cable released)**: Only gravity (conservative) → total energy (mechanical) conserved → total energy constant.
- **Ball smashes into wall**: If we consider the ball - Earth system, and the wall is an external object, then the system is not isolated, but the problem says "assume air resistance is small enough to ignore". Maybe the problem considers that the total energy of the ball - Earth system is conserved in all cases except when an external force does work. When the cable raises the ball, external work is done, so energy increases. When swinging down, no external work (only gravity, internal to the system), so energy constant. When smashing into the wall, if the wall is part of the Earth (so the force is internal), then energy is conserved. So:

- the cable raises the ball: increases
- the ball swings down after the cable is released: constant
- the ball smashes into the wall: constant (or maybe decreases? No, energy is conserved, it's just transformed. So the total energy of the system (including all forms) is constant. But maybe the problem has options like "increases", "decreases", "remains constant".

Assuming the options are "increases", "decreases", "remains constant":

1. the cable raises the ball: The cable does work on the system, so total energy **increases**.
2. the ball swings down after the cable is released: Only conservative forces (gravity) act, so total energy **remains constant**.
3. the ball smashes into the wall: Even though there is a collision, the total energy of the ball - Earth system (including the energy transformed into heat, sound, etc.) **remains constant** (since energy is conserved, just transformed from kinetic energy into other forms within the system, assuming the wall is part of the Earth - ball system).

Answer:

• the cable raises the ball: increases
• the ball swings down after the cable is released: remains constant
• the ball smashes into the wall: remains constant