1. Egg Drop Physics
Everything you ever wanted to know about egg drops, but were afraid to ask.

2. Part I: THE FALL

3. Imagine a fall with no air…
Velocity downward t Fg
Slope =
9.8 m/s2 toward earth
= force of gravity
= weight
= mass x acceleration due to gravity = mg

4. But of course, there will be air!
Fair = air resistance or fluid drag
= 1 2 ∙𝜌 ∙𝑉 2 ∙𝐴 ∙𝐶 𝐷 Fg
Fnet = Fair - Fg

5. All About Air Resistance (Drag)
𝐹 𝑎𝑖𝑟 = 1 2 ∙𝜌 ∙𝑉 2 ∙𝐴 ∙𝐶 𝐷
ρ = air density = kg/m3
V = velocity, m/s
A = cross- sectional area, m2
CD = coefficient of drag

6. Drag Coefficient

7. Evaluate their ideas. Do you think either has a valid strategy. Both
Evaluate their ideas. Do you think either has a valid strategy? Both? Neither? Explain
Sponge Bob says: I want my egg drop vehicle to be the slowest. I am going to make it lightweight to increase its air resistance. This will cause it to slow down as it falls.
Patrick says: I want my egg drop vehicle to be the fastest. I am going to make it heavier to “overpower” any air resistance and have a high net unbalanced force. This will cause it to accelerate as fast as possible.

8. How will it fall in air? Remember, F net = F air − F g And F net =ma
So… a = F net m or a = F air − F g m
Notice that as velocity increases, so does the air resistance. So….
What happens if the air resistance is equal to the weight in magnitude?

9. TERMINAL VELOCITY!!
Fnet = 0 if air resistance = weight, so the acceleration is also zero!
The object maintains a constant velocity from that point.

10. What would the graph look like now?

11. Which experiences a greater air resistance, an elephant or a feather?

13. Practice FBDs
Two same size balls, one twice as heavy as the other, no air
Two same size balls, one twice as heavy as the other, each with air resistance ½ their weight
Two same size balls, one twice as heavy as the other, each with air resistance that is equal to their weight.

14. It’s not the fall that is going to hurt the egg!
Part II: THE LANDING
It’s not the fall that is going to hurt the egg!

15. F net =ma The smaller the final deceleration of your egg,
Deceleration of your egg as it comes to a stop
Impact force on your egg
The smaller the final deceleration of your egg,
the smaller the impact force on your egg.

16. How can the final deceleration of the egg be reduced?
Make Δv as small as possible.
a= ∆v ∆t
Make Δt as large as possible.

17. Making Δv Smaller
Anything that you can do to reduce the FALLING acceleration of your vehicle will reduce the speed it has to LOSE when it lands!
High Drag and Low Weight will help achieve a low falling acceleration and possibly a terminal velocity.
Large cross-sectional area and high drag coefficient.

18. Making Δt Larger
This means that you need to allow as long a stopping time as possible.
“Cushion” or “shock absorbers” allow this longer stopping time.
“Crumple zones” or other break-away features can achieve this also.
When writing your analysis for your egg drop, I will DEMAND that you speak about cushioning the egg in terms of extended stopping time, reduced final deceleration, and reduced impact force, all according to Newton’s Second Law.

19. Check for Understanding
Watch the video clip from Moonraker.
Use the principles presented here to explain:
How JB catches up to the gunman who left the plane before him.
How Jaws catches up with JB.
How JB ultimately gets away from Jaws.
How Jaws survives the landing.

20. Part III: OTHER CONSIDERATIONS

21. Other Considerations Orientation Lift The “small fall”
Center of Gravity
Rotational inertia (moment of inertia)
Lift
The “small fall”

22. Orientation
Center of Gravity = the average location of the weight of an object.
Object’s translation through space is tracked by its center of gravity
If free to rotate, objects rotate freely about their centers of gravity

24. Orientation If your Center of Gravity is…
above the geometric center of your egg drop vehicle, it may reorient as it falls due to a torque created by air resistance that will tip it until the center of gravity is as low as possible.
at the geometric center of your egg drop vehicle, it may rotate in any possible direction, since all positions are equally stable.
below the geometric center of your egg drop vehicle, it will have the best chance of maintaining its orientation while it is falling.

25. Rotational Inertia
ROTATING objects resist changing the axis of rotation.
This resistance to change is called ROTATIONAL INERTIA, or Moment of Inertia
It is what helps you balance when riding a bicycle and it is why you spiral a football when throwing it.

26. Lift
Lift occurs when a moving flow of gas is turned by a solid object.
The flow is turned in one direction, and the lift is generated in the opposite direction, according to Newton's Third Law of action and reaction.

28. Lift

29. I built it with…. So that it will…
Extend the stopping time, reduce the final deceleration, and lower the impact force on my egg since acceleration and force are directly proportional (Newton’s second law!)
Increase the drag/air resistance on my vehicle by….
Increased cross sectional area
And/or high drag coefficient
Which lowers its acceleration, which decreases its change in velocity on landing, lowering the final deceleration and force on the egg at impact.
Decrease the drag/air resistance on my vehicle by having
Decreased cross sectional area
And/or low drag coefficient
And keep the acceleration high so that I have one of the fastest egg drops.
Rotate and
Create rotational inertia which will maintain its orientation on landing.
Create lift that will be an additional force acting against gravity to reduce the rate at which my vehicle accelerates.
Create lift by creating higher pressure under the “wing” than over and allow my vehicle to glide.

31. Drag Coefficient for a cone
Half vertex angle in degrees