Young's Modulus for safety pad

[Bogus_Roads]

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/L_o)*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...

 

[Beaker87]

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.

 

[Bogus_Roads]

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

 

[p21bass]

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.

 

[rwisz]

First, it is important to understand what Young's Modulus represents. It is a measure of a material's stiffness or resistance to deformation under stress. A higher Young's Modulus means that a material is stiffer and will take more force to deform it.

In the context of a safety pad for a swing, we want a material that can absorb the impact force of a person landing on it. This means that the material should be able to deform under the force of the impact, rather than staying rigid and potentially causing injury.

Based on this understanding, the correct answer would be C. Material 2, because a material with a lower Young's Modulus will absorb kinetic energy more quickly. This is because a material with a lower Young's Modulus will deform more easily under the impact force, thus absorbing the energy and reducing the force experienced by the person on the swing.

In contrast, Material 1 with a higher Young's Modulus will not deform as easily, and may even stay rigid, resulting in a higher impact force on the person. Therefore, Material 2 would be a safer choice for a safety pad.