Falling mass onto flat plate pressure exerted

[llamedos]

Homework Statement

hi I'm trying to design a small experiment based on soil pressure
i've not had much use of some of the equations and principles for a few years so I'm a little rusty

basically I'm trying to exert pressures onto grass seeds (lolium perenne) in a rough field experiment in order to see how it affects germination rates

effective material
small flat plate 0.25m*0.25m for this purpose it is effectively massless
me approx mass 100kg

i can exert approx 15-16kPa by standing on the plate
but I'm trying to calculate how high i need to jump to exert around 30kPa

looking for a max pressure
i'd assume soil compression to be about 2 cm from surface height
i don't need high precision but a rough and ready approximation

ignore any mitigation by the body i.e knees and ankles

any help gratefully received

Homework Equations

mass m = 100kg
grav = g = 9.8m/s^2
area = a = 0.0625m^2

The Attempt at a Solution

 

[tiny-tim]

welcome to pf!

ih llamedos! welcome to pf!

i can exert approx 15-16kPa by standing on the plate
but I'm trying to calculate how high i need to jump to exert around 30kPa …

jumping will only exert a very temporary pressure, probably totally useless for your purposes

easier would be to erect a frame with a bar going over your head, so that you can push up against it to press down on the plate continuously …

and you can put ordinary bathroom scales on the plate to show you the force

btw, i assume you'll have a control area with an identical plate with no pressure on it? ​

 

[llamedos]

its a form of simulated rolling so effective time period is about 0.1 seconds and lower
which is similar to the exertion period of jumping on it

yes there is a control i don't do anything to it

but i could get lost in the complexities of soil matrix dynamics under compressive forces and incident periods so i don't want to.

also when i say field i literally mean field
cutting a plate with half the area and using it twice could work but then there would be the challenge of compensating for more edge effects

on another note i joined back in 2007 when i was doing my a-levels been lurking ever since but never really needed to ask for assistance

 

[tiny-tim]

its a form of simulated rolling so effective time period is about 0.1 seconds and lower
which is similar to the exertion period of jumping on it

yes there is a control i don't do anything to it

but i could get lost in the complexities of soil matrix dynamics under compressive forces and incident periods so i don't want to.

also when i say field i literally mean field
cutting a plate with half the area and using it twice could work but then there would be the challenge of compensating for more edge effects

on another note i joined back in 2007 when i was doing my a-levels been lurking ever since but never really needed to ask for assistance

(if you want to simulate rolling, why not use an actual roller? )

let's see … if a roller with mass M passes over the area of a plate in time t,

then that's an impulse (force times time) of Mgt​

if your own mass is m, and your centre of mass rises by a height h (from crouch position to maximum position), then the impulse is the initial change in momentum, = mv_i, = m√(2gh)

(if you both jump from the plate and land on the plate, then that's multiplied by 2)

so for the same effect you need h to be (M/m)²t²g/2