c. When are kinetic energy and potential energy equal in magnitude (equal in amount)?(1 point)%0D%0AResponses%0D%0A%0D%0AThey are equal at the bottom position.%0D%0AThey are equal at the bottom position.%0D%0A%0D%0AThey are equal at the top position.%0D%0AThey are equal at the top position.%0D%0A%0D%0AThey are equal at every position.%0D%0AThey are equal at every position.%0D%0A%0D%0AThey are equal half-way between the top position and the bottom position.
The correct answer is: They are equal at every position.
Kinetic energy and potential energy are equal in magnitude (equal in amount) at the bottom position.
To determine when kinetic energy and potential energy are equal in magnitude, we need to understand their definitions and how they relate to an object's position.
Kinetic energy is the energy an object possesses due to its motion. It depends on both the mass of the object and its velocity. The formula for kinetic energy is K.E. = (1/2)mv^2, where m is the mass of the object and v is its velocity.
Potential energy, on the other hand, is the energy an object possesses due to its position in a force field, such as gravity. It depends on the mass of the object, the acceleration due to gravity (9.8 m/s^2 on Earth), and the object's height above some reference point. The formula for potential energy is P.E. = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the object's height.
When an object moves vertically in a gravitational field, its potential energy changes due to the change in height, while its kinetic energy changes due to the change in velocity. At any given position, the sum of the object's kinetic and potential energy remains constant, known as the conservation of mechanical energy.
Now, let's consider the options for when kinetic energy and potential energy could be equal in magnitude:
1. They are equal at the bottom position.
At the bottom position, the object typically has the maximum kinetic energy because it is moving at its maximum velocity. Potential energy is minimal or zero because the object is at its lowest height. Therefore, at the bottom position, kinetic energy is usually greater than potential energy.
2. They are equal at the top position.
At the top position, the object typically has the minimum kinetic energy because it momentarily comes to a stop, changing direction. Potential energy is at its maximum because the object is at its highest height. Therefore, at the top position, potential energy is usually greater than kinetic energy.
3. They are equal at every position.
This statement is incorrect. At every position, the sum of kinetic energy and potential energy is constant, but they are not necessarily equal to each other.
4. They are equal halfway between the top position and the bottom position.
This statement is correct. Based on the conservation of mechanical energy, halfway between the top and bottom positions, the object has equal amounts of kinetic and potential energy. At this point, the object's potential energy is decreasing as it descends, while its kinetic energy is increasing.
Therefore, the correct response is: "They are equal halfway between the top position and the bottom position."