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

basicly 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

 

[asteriatic]

To calculate the pressure exerted by a falling mass, we can use the equation P = F/A, where P is pressure, F is force, and A is area. In this case, we can assume that the mass falls from a certain height and exerts a force on the flat plate. We can then calculate the pressure by dividing this force by the area of the plate.

Since the plate is effectively massless, we can disregard its contribution to the force and focus on the mass of the falling object. We know that the force of gravity acting on the mass is equal to its weight, which can be calculated using the equation W = mg, where W is weight, m is mass, and g is the acceleration due to gravity. In this case, the weight of the falling mass would be 100kg*9.8m/s^2 = 980N.

To calculate the height from which the mass needs to fall to exert a pressure of 30kPa, we can rearrange the equation P = F/A to solve for height. This gives us the equation h = (PA)/mg.

Substituting in the given values, we get h = (30,000N/m^2 * 0.0625m^2)/(980N) = 1.91m. Therefore, the mass would need to fall from a height of approximately 1.91m to exert a pressure of 30kPa on the flat plate.

However, it is important to note that this is a very rough approximation and does not take into account various factors such as air resistance and the body's mitigation. It would be more accurate to conduct a controlled experiment with precise measurements to determine the exact pressure exerted on the grass seeds.