Example ## - CHAMPAGNE CORK TRAJECTORY We have an energy equation with the sum of system energies (kinetic and potential) being set equal to work. There being three terms, two must be known, to solve for the third. The simplest energy analyses are those for which work need not be evaluated directly. These are cases where the work is, or can be argued to be, zero or the cases for which kinetic and potential energy changes are known and work is to be calculated, indirecrly.

Champagne Cork TrajectoryAfter the speeches at the "Professors Emeritis Banquet," the student bartenders opening champagne bottles observed a one-gram, cork to fly upward about to meters, just over a rafter in the gym. Calculate the least speed of the cork as it "popped," from the bottle of bubbly.

♦  The event involves energy changes. A good practice is to write the energy equation then modify it to suit the system and event under consideration.

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Inspecting the equation we realize the event will involve change of velocity and elevation change so the kinetic and potential energy will not be zero.

Next we inspecting the "sum of works." We realize during flight the cork experienced a drag force, friction, as it moved through air. That constitutes friction work. But since we cannot calculate that effect, we are obliged to assume it is negligibly small - zero. In addition a gravity force acts on the cork but the effect of that force equals its change of potential energy. Work is associated with surface forces only ( learning now and explained later). Hence, ignoring the drag force its movement through air - the sum of works for the event is set to set equal to zero.

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Next write the energy equation for the cork explicitly:

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Usually the first (some say "initial") state of a system is known. For the cork, 1 is the immediate instant in time the cork goes "pop." Just exploded from the bottle, it has a speed (straight-up, we assume). We seek an approximation of this speed. The elevation of the cork at that instance, is level with the upheld bottle, which we don't know.

STATE (1):   Elevation:  zcork,1 = ?   and    Speed: Vcork,1 = ?.

We choose our event to end at the precise (imagined) time that the cork passed over the beam. Some call this the final State, or we might just label it as 2. In the event-ending condition, the cork has an elevation greater by 10 meters thaninitially. But its speed, at the very top of its flight becomes zero. We don't know the final elevation of the cork, so we write it as an "increase from the initial elevation."

STATE (2):    Elevation:  zcork,1 + 10 m   and    Speed :Vcork,2 = 0

We enter these conditions into the equation to see what it will tell us.

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A calculation shows: V1 = 14 m/s. But we have made many assumptions. We assumed no friction and a vertical flight. Our number is is a minimum value. To be precise, we realize the actual, initial speed of the cork had to be greater.

Our answer: vcork,1 > 14.0 m/s.