What is the Pressure of Falling Sand on a Sticky Surface?

In summary, the problem involves grains of sand of known mass and rate of fall, landing on a sticky surface with no air resistance. To find the pressure exerted on the surface, we can use the equation P = F/A, where F is equal to the force required to accelerate the mass of sand by the velocity of each grain in one second. We can also use F = Δp / Δt, where p is momentum, to find the total change in momentum for all grains of sand landing on a square cm of the surface in one second.
  • #1
dmark312
1
0

Homework Statement



Grains of sand of mass 2.90x10^-3 g each, fall from a height of 0.5 m on a sticky surface at a rate of 45 grains per second per cm^2. What pressure does this shower of sand exert on the surface, assuming that air resistance can be neglected?

Homework Equations



p=F/A=mv^2(N/V)

The Attempt at a Solution


I don't know where to start. Anyone care to point me in the right direction?
 
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  • #2
You can work out the velocity with which every grain of sand lands. You also know what total mass of sand falls per second. Your force, [itex]F[/itex], is equal to the force required to accelerate that certain mass of sand by that certain velocity in one second.
 
  • #3
Welcome to PF :smile:

P = F / A is definitely useful here.

Also of use is

F = Δp / Δt

where little p is momentum (not pressure). You'll need to figure out the change in momentum, for the total of all grains of sand that hit a square cm of the surface, in 1 second.
 

Related to What is the Pressure of Falling Sand on a Sticky Surface?

What is pressure of falling sand?

Pressure of falling sand is a measure of the force exerted by a column of sand as it falls. It is a result of the weight of the sand particles and the acceleration due to gravity.

How is pressure of falling sand related to sand dunes?

The pressure of falling sand is a key factor in the formation and movement of sand dunes. As sand particles fall down a dune, they exert pressure on the particles below, causing them to shift and move.

What factors affect the pressure of falling sand?

The pressure of falling sand is affected by the height of the sand column, the density and size of the sand particles, and the speed of the falling sand. Other factors such as wind and moisture can also play a role.

How is the pressure of falling sand measured?

The pressure of falling sand can be measured using a device called a penetrometer, which measures the resistance of the sand column as it falls. The pressure is then calculated using the weight of the sand column and the area of the penetrometer.

What are the practical applications of studying the pressure of falling sand?

Studying the pressure of falling sand can provide insights into natural phenomena such as sand dune formation and erosion. It can also have practical applications in fields such as civil engineering, where the pressure of falling sand can affect the stability of structures built on or in sand. Additionally, understanding the pressure of falling sand can help in the design and maintenance of agricultural and industrial equipment that handles sand or other granular materials.

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