# Young's Modulus for safety pad

In summary, the conversation is discussing the best material for a safety pad below a swing. Material 1 has a higher Young's Modulus than Material 2, but it is argued that Material 2 should be chosen because it has a larger length over which the impact force acts, resulting in a lower average impact force. The concept of absorption of kinetic energy is also brought up, with the conclusion that a material with a lower Young's Modulus will absorb kinetic energy more quickly. The idea of impulse is then introduced, stating that a small force applied over a longer time can have the same momentum change as a large force applied briefly. Therefore, the longer the collision takes, the less force is applied.

## Homework Statement

Two different materials are being considered for a safety pad below a swing. Material 1 has a Young's Modulus twice that of Material 2. Which should be chosen?

A. Material 2, because the length over which the impact force acts is larger, resulting in a lower average impact force.
B. Material 1, because the length over which the impact force acts is larger, resulting in a lower average impact force.
C. Material 2, because a material with a lower Young's Modulus will absorb kinetic energy more quickly.
D. Material 1, because a material with a higher Young's Modulus will absorb kinetic energy more quickly.

## Homework Equations

($$\Delta$$L/Lo)*E=F/A.

## The Attempt at a Solution

$$\Delta$$L is clearly larger with a smaller YM, but does the mean the length over which the impact force acts is larger. Does that then mean that it's lower impact? I've never even come across the idea of absorption of kinetic energy, and I don't think it's obvious that something that is "squishy" should absorb kinetic energy more quickly...

Try to think of force in a collision as the change in momentum divided by the amount of time it takes.

Therefore, the longer a collision takes, the less force is applied.

How do you know greater length acted over=greater time?

It's based upon impulse. It's defined better here than I could do myself, so I'll just quote...

In classical mechanics, an impulse is defined as the integral of a force with respect to time. When a force is applied to a rigid body it changes the momentum of that body. A small force applied for a long time can produce the same momentum change as a large force applied briefly, because it is the product of the force and the time for which it is applied that is important. The impulse is equal to the change of momentum.