"A Decorative Stone Fell Off The Fence. Considering The Presence Of Air, How Does The Kinetic Energy (K) Of The Stone Just Before Striking The Ground
"A decorative stone fell off the fence. Considering the presence of air, how does the kinetic energy (K) of the stone just before striking the ground compare to its potential energy (U) on the fence?
a. K is equal to U.
b. K is greater than U.
c. K is less than U.
d. It is impossible to tell."
Answer:
b. Kinetic Energy is greater than Potential Energy. Just before the decorative stone hits the ground, it will have a greater kinetic energy than its potential energy.
Review:
Before anything else, we need to understand the concepts of kinetic energy and potential energy. Kinetic energy is the work that an object needs to have in order for it to be in action or to accelerate. Basically, kinetic energy is the object's energy triggered by its motion in three dimensional space. The energy is collected through its acceleration and secures its magnitude until a change of speed happens. The kinetic energy of an object will be set to zero once it is put into rest; zero velocity.
On the other side, potential energy is the energy that an object has within itself which is defined by its mass, distance from a relative mass or point of reference, and gravitational force. Knowing its definition, your own potential energy may differ on the point of reference you are using. Example, if you are on the rooftop of a 6-storey establishment, your potential energy will vary from each floor. Your potential energy from the rooftop in reference to the 5th floor will be different from your potential energy if your reference is the 2nd floor.
The formula for the kinetic energy is
The formula for the potential energy is
Explanation:
The given question asks us about the relationship of kinetic energy and potential energy. It is stated that a decorative stone sits on top of the fence. At some time, the presence of air caused the decorative stone to fall off the fence. What is the relationship of the kinetic energy of the stone before it lands to its potential energy at rest on the fence.
Now let us get imaginative and picture out the scenario. Let us assume that in every 1 Time Unit there will be 1 Height Unit; we will make everything one is to one (1:1) to easily clarify things up easily. This will be helpful in visualizing the problem. Moving on, the stone on top of the fence has a potential energy of U. Assuming that the stone fell for 1 Time Unit, then the potential energy would be U - 1. It falls another Time Unit, the potential energy would be U - 2 and so on.
We notice that for every fall further from the original position, the potential energy decreases. This is because height is directly proportional to the potential energy; the height goes down, the potential energy goes down.
Moving on to the kinetic energy, the air pushes the decorative stone to the edge of the fence. This causes the stone to harness kinetic energy. As the stone moves for 1 Time Unit, it moves to the acceleration of 1 Acceleration Unit. As the decorative stone goes further from its source, the velocity or speed increases due to the pull of the given acceleration. The stone at 1 Time Unit becomes K + 1, stone at 2 Time Units becomes K + 2 and so on.
In this situation, the kinetic energy increases as its velocity increases while its height decreases. The reason for this is because kinetic energy is directly proportional to its velocity. The faster it goes, the more kinetic energy it generates. The shorter the distance becomes, the faster it gets due to the horizontal distance and gravity (acceleration).
To conclude, the kinetic energy is significantly higher, before it hits the ground, than its potential energy, while it is on the fence. As the height decreases, the potential energy decreases and the kinetic energy increases. Alternatively, as the height increases, the potential energy increases while the kinetic energy decreases.
Internal links you may visit to help you out regarding kinetic energy and potential energy:
CODE:
9.22.4.2.
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