In the context of mechanical energy, which of the following situations is clearly exhibiting kinetic energy because the object is in actual motion?

Introduction / Context:
Mechanical energy appears mainly as potential energy and kinetic energy. Potential energy is stored due to position or configuration, while kinetic energy is associated with motion. Many everyday situations involve combinations of both, but it is important to be able to identify which situations clearly involve kinetic energy due to objects actually moving. This question asks you to pick the example that is definitely showing kinetic energy.

Given Data / Assumptions:

• Kinetic energy depends on mass and the square of speed, given by KE = 1/2 * m * v^2.
• An archer with a flexed bow has stored elastic potential energy, but the arrow may still be at rest.
• A person sitting on a couch is at rest with respect to the room.
• A space station in orbit is moving at very high speed around Earth.

Concept / Approach:
Kinetic energy exists only when an object has non zero speed in a chosen frame of reference. If the object is at rest in that frame, its kinetic energy is zero, although it may still have potential energy. In the case of the archer, the bow stores elastic potential energy when flexed, but until the arrow is released, there is no significant kinetic energy for the arrow or bow. A person sitting still on a couch has no macroscopic kinetic energy in the room frame. In contrast, a space station orbiting Earth is moving at several kilometres per second, and therefore clearly has a large amount of kinetic energy associated with its motion. Thus, the space station example is the one definitely exhibiting kinetic energy.

Step-by-Step Solution:
Step 1: Recall the formula for kinetic energy: KE = 1/2 * m * v^2, which requires non zero speed v.Step 2: Examine the archer with a flexed bow: the bow arms and string are under tension, storing potential energy, but nothing is moving significantly.Step 3: Examine the person sitting on a couch: the person is at rest relative to the couch and the room, so kinetic energy in that frame is zero.Step 4: Examine the space station orbiting Earth: it is moving rapidly along its orbital path, so its speed v is large and the kinetic energy is significant.Step 5: Recognise that option D claiming all of the above are exhibiting kinetic energy cannot be correct, because in two cases there is no visible motion.Step 6: Conclude that the space station orbiting Earth is the correct choice as a clear example of kinetic energy.

Verification / Alternative check:
Physically, the orbit of a space station is maintained by the balance between gravitational attraction and the station kinetic energy of motion. If its kinetic energy changed too much, the orbit would change or the station would fall back to Earth. Engineers calculate orbital energy using the station mass and velocity. In contrast, when an archer holds a drawn bow, the energy is stored in the deformation of the bow, and if you release the string, this potential energy becomes kinetic energy of the arrow. The sitting person example involves no motion relative to the surroundings, so there is no kinetic energy at that scale.

Why Other Options Are Wrong:
An archer with a flexed bow mainly demonstrates elastic potential energy stored in the bow limbs and string, not kinetic energy, because there is no significant motion until the arrow is released. A person sitting on a couch is stationary, so there is no macroscopic kinetic energy in the room frame. The option stating that all of the above exhibit kinetic energy is wrong because at most one of the situations clearly involves motion of the entire object.

Common Pitfalls:
Some students may confuse potential energy with kinetic energy and assume that any energy in a system means kinetic energy. Others may think that because on a deeper level Earth and everything on it are moving through space, all objects always have kinetic energy, but in basic problems the reference frame is usually the room or Earth surface. To avoid confusion, always ask whether the object in question is actually moving in the chosen frame. If it is, kinetic energy is present; if it is not, kinetic energy is zero and the energy may be stored as potential energy instead.

Final Answer:
The situation clearly exhibiting kinetic energy is a space station orbiting Earth at high speed.