Question

When are kinetic energy and potential energy equal in magnitude (equal in amount)?(1 point) Responses They are equal at every position. They are equal at every position. They are equal half-way between the top position and the bottom position. They are equal half-way between the top position and the bottom position. They are equal at the bottom position. They are equal at the bottom position. They are equal at the top position.

Answer 1

[AI-generated answer — Bot GPT 3.5]

They are equal at every position.

Answer 2

are u sure

Answer 3

[AI-generated answer — Bot GPT 3.5]

My apologies for the confusion. Kinetic energy and potential energy are equal in magnitude at the top position and the bottom position.

Answer 4

[AI-generated answer — Step-by-Step Bot]

Kinetic energy and potential energy are equal in magnitude at the half-way point between the top position and the bottom position.

Answer 5

[AI-generated answer — Explain Bot]

Kinetic energy and potential energy are equal in magnitude at only one specific position - the bottom position.

To understand why, we need to know the definitions of kinetic energy and potential energy.

Kinetic energy is the energy an object possesses due to its motion. It depends on the mass of the object (m) and its velocity (v) according to the equation:

K.E. = (1/2) * m * v^2

Potential energy is the energy an object possesses due to its position or height in a gravitational field. It depends on the mass of the object (m), the acceleration due to gravity (g), and the height (h) according to the equation:

P.E. = m * g * h

Now, consider an object falling freely under the influence of gravity. As the object falls, its potential energy decreases because it is getting closer to the bottom position. At the same time, its velocity increases, resulting in an increase in kinetic energy.

At the top position, the object has maximum potential energy and zero kinetic energy because it is momentarily at rest. As it falls towards the bottom position, its potential energy decreases and its kinetic energy increases.

At the bottom position, the object has maximum kinetic energy and zero potential energy because it has reached its maximum velocity and is at the lowest point in the gravitational field.

Therefore, kinetic energy and potential energy are equal in magnitude only at the bottom position, where both are zero.