Practice using Potential Energy, Kinetic Energy, and Kinematic Equation 1

1) An egg weighing 2.12 ounces is dropped from a second floor window to the ground below. The egg accelerates at 9.81 m/s² for 21 feet before coming to a complete rest on the ground. Assume that the resistance in the air is negligible. (a) What is the final velocity of the egg, in km/h, immediately before impact?, and (b) how long does it take, in seconds, for the egg to travel the distance from the window to the ground?

Step 1: Read and Reread

As we read through the practice problem we note the given. In this example we have this given information:

m_egg = 2.12 oz.,

a = 9.81 m/s², and

h = 21 ft.

Step 2: Draw a Diagram

Next we sketch a quick diagram similar to that as shown in figure 1.

Figure 1 – Draw a diagram of the scenario

Step 3: Indicate the Known Quantities

Be sure to indicate your known quantities including their variables and their units.

Figure 2 – Indicate known quantities on the diagram

Step 4: Determine the Unknown Variables

Our first unknown is potential energy, PE, which can be calculated from our three pieces of given information. The second unknown is velocity, and the third is time.

Figure 3 – Determine and indicate unknown quantities on diagram

Step 5: Select the Appropriate Formulas

For this example we have selected three formulas to facilitate the calculation of our result. The first equation is that of potential energy, the second is kinetic energy, and the third is what I refer to as kinematic equation 1. These three equations are listed in figure 4.

Figure 4 – Select appropriate formulas for use in this scenario

Step 6: Solve the Formulas Algebraically

 Equation (1) is already in the correct form so we will leave it as is:

Equation (2) must be solved for velocity, v, once rearranged it will look like this:

Equation (3) must be solved for time, t, and once rearranged it will look like this:

Step 7: Convert Units for Known Quantities

 Convert the mass of egg from ounces, oz, to kilograms, kg.

Convert the height from feet, ft, to meters, m.

Step 8 & Step 9: Plug Known Values into Solved Formula and Track Units, and calculate your unknown values

Solve for potential energy, PE, using equation (1).

Now we have to realize that the potential energy, PE, of the egg at 21 ft is equal to the kinetic energy, KE, of the egg when it reaches the ground at 0 ft.

Solve for velocity, v, at the point when the egg reaches the ground, ie. at 0 ft. Tracking the units here we see that the kg from J cancels out with the kg from the mass of the egg, leaving (m/s)² which then becomes square rooted to return simply m/s which we then convert to kilometers per hour, km/h.

Finally, we calculate the amount of time this egg took to reach the ground. We assume an initial velocity, v₀, of the egg to be 0 m/s as it was simply dropped and not thrown.

Step 10: Do the Answers Make Sense?

These answers do seem to make sense. In this example, try to visualize what it would look like for an egg to be dropped from the height of 21 feet and picture if the calculated time of 1.14 seconds seems reasonable.

Step 11: Double Check Your Answers with iEquals Formula Solvers

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Thanks and enjoy!