Here is the unit’s question: if momentum is always conserved, why does a dropped egg break but a well-packed one doesn’t? The answer is that conservation of momentum was never the problem. In both cases the egg’s momentum goes from mv to zero, and it passes into the Earth, which barely notices. The change in momentum, Δp = mv, is the same either way.
What differs is how fast the change happens. From Activity 5-1-2, F = Δp ÷ Δt. A bare egg stops in a few milliseconds against the floor and takes a huge force. A packed egg stops over a longer time, and since Δp is fixed, the force shrinks in proportion. Your container can’t change the egg’s momentum. It can only buy time.
🔑A cushion buys time by giving the egg distance to stop in. The more distance the egg travels while slowing down, the longer the stop takes, and the smaller the force.
BMath
Force, Travel, and Energy
A good cushion crushes at a roughly steady force F, which is called a plateau. As the egg sinks in by a distance d, that force does work F × d, and that work has to absorb all of the egg’s energy, which at impact is mgH. By the work-energy theorem from Unit 4:
F × d = m g H → d = m g H ÷ F
For a 0.058 kg egg dropped from 3.0 m, mgH = 0.058 × 9.8 × 3.0 = 1.7 J. Here is how much travel different cushion forces would need:
Cushion force
Travel needed (H = 3.0 m)
Verdict
10 N
17 cm
Gentle, but far too much travel to fit
20 N
8.5 cm
Works, but a tight fit
30 N
5.7 cm
Works well
40 N
4.3 cm
The ideal: the shortest travel that is still safe
60 N
2.8 cm
Short travel, but over the egg’s limit, so it breaks
🔑The best cushion is one that pushes back at just under the egg’s limit for as long as it can. A softer cushion is gentler but needs more travel than a 15 cm container can hold. A stiffer one fits easily but breaks the egg. Design for the sweet spot.
CMath
Measuring a Material’s Force
You can’t look up the force of a pile of cotton or a bundle of straws, so you measure it. Drop the dummy egg onto a sample from a modest height h and measure the maximum compression d. The energy mgh is absorbed over d, so:
F = m g h ÷ d
Testing a foam pad
Given
Dummy egg m = 0.058 kg, dropped from h = 0.50 m
Maximum compression d = 1.2 cm = 0.012 m
The real drop will be H = 3.0 m
Solve
F = m g h ÷ d = 0.058 × 9.8 × 0.50 ÷ 0.012
F = 0.284 ÷ 0.012 = 23.7 N
d_needed = m g H ÷ F = 1.705 ÷ 23.7 = 0.072 m
(shortcut: d_needed = d × H ÷ h = 1.2 × 3.0 ÷ 0.50 = 7.2 cm)
✓ The foam pushes with about 24 N, which is safe, but it needs 7.2 cm of travel at 3.0 m.
⚠️Read the maximum compression, the dummy’s lowest point. Many cushions spring back, so the thickness afterward looks like less crushing than really happened. Slow-motion video against a ruler is the reliable way to read it. Also check that the force is really a plateau: test a second height. If the force comes out about the same, the model holds.
DExample
Cushion Designer
Try a few cushions. Set the force, then set the travel your design provides and the drop height. Watch what happens when the cushion runs out of room.
Design a cushion on paper for the 0.058 kg egg. The graph shows the force the cushion applies as the egg sinks into it. The shaded area is the energy the cushion absorbs, and it has to equal the egg’s energy, mgH. The dashed line is the egg’s rough 40 N limit.
Egg energy mgH = 1.71 J · v = 7.67 m/s Travel needed d = mgH ÷ F = 7.1 cm
Survives. The egg stops over 7.1 cm in about 18.5 ms, at an average of 24 N.
EConcept
Layers, Cradles, and Choosing Materials
Real containers combine materials. Two rules cover most cases:
Layers in a row (in series): the weakest layer crushes first and sets the force. The stiffer layers don’t crush until the weak one is used up. Use a soft layer to do the work and a firmer one as backup.
Pieces side by side (in parallel): their forces add. A bundle of ten straws that each crush at about 2.8 N behaves like one 28 N cushion.
Two more design points matter. First, a cushion only works if the egg actually uses all its travel, so keep the egg centered and held so it can’t slide to the side. Second, an egg’s shell breaks under a concentrated load far more easily than under a spread-out one, so cradle it so the force is shared over a wide area instead of a point.
💡A bouncy container is a worse idea than it sounds. From Activity 5-1-2, a rebound reverses the egg’s momentum, which takes more impulse than just stopping it. You want the cushion to absorb the energy, not give it back.
FMath
Estimating Impact Force and Time
Your report needs an estimate of the impact time and the average force, before and after the drop. From the crush distance d and the impact speed v = √(2gH), a steady stop gives:
Δt = 2d ÷ v F = mgH ÷ d
Before the drop, d is the travel you calculated (d_needed) and F is the cushion’s tested force. After the drop, d is the crush distance you actually measured, and the equations give the actual force and time. The two are compared with percent error: |actual − predicted| ÷ actual × 100.
Predicted vs. actual
Given
Predicted from tests: F = 23.7 N and d = 7.2 cm, so Δt = 18.8 ms
The egg actually sank 6.0 cm into the cushion
H = 3.0 m, so v = 7.67 m/s
Solve
Actual force = mgH ÷ d = 1.705 ÷ 0.060 = 28.4 N
Actual time = 2d ÷ v = 2(0.060) ÷ 7.67 = 15.6 ms
Force error = |28.4 − 23.7| ÷ 28.4 × 100 = 17%
Time error = |15.6 − 18.8| ÷ 15.6 × 100 = 20%
✓ The cushion was a little stiffer than the test suggested, so the egg stopped in a shorter distance and a bit harder. Both are still under the 40 N limit, so the egg survives.
⚠️These are average forces under a steady-force model. A real cushion’s peak force is higher, the container isn’t perfectly rigid, and 40 N is a rough limit, not a law of nature. Treat your results as estimates, and report the gap honestly. That’s the skill this project is testing.
GWatch Out
Three Common Mix-Ups
⚠️“A heavier, tougher container protects better.” The egg’s momentum change depends only on its own mass and speed. Extra container mass doesn’t reduce it, and it can add to the load the cushion has to handle. Travel is what protects the egg.
⚠️“Softer is always better.” A very soft cushion is gentle but bottoms out before the egg has stopped, and the leftover energy hits as a hard stop. The cushion has to be as firm as the egg allows, and no softer.
⚠️“Momentum is destroyed by the cushion.” It isn’t. The egg’s momentum is transferred to the container and the Earth. The cushion only controls how quickly that transfer happens.
HConcept
Quick Check
Four questions. They are not graded. Answer them to find out what still needs work.
Q1A 0.058 kg dummy egg is dropped from 0.50 m and sinks 2.0 cm into a pad. What is the pad’s average stopping force?
Q2An egg (limit about 40 N) is dropped from 3.0 m onto a cushion that pushes with exactly 40 N. What is the least travel it needs?
Q3Your cushion provides 3 cm of travel but needs 7 cm at the design drop height. What happens?
Q4Which statement best answers “If momentum is always conserved, why does a dropped egg break but a well-packed one doesn’t?”
Score: 0 of 4
IConcept
Looking Ahead
You’ve used impulse to protect an egg. Next you’ll look at the other side of collisions, what happens to the kinetic energy, and then put it all to work on a real crash.