Question

A rectangular glass block of dimensions 30 cm by 5 cm by 10 cm weight 37.5 N calculate the least and greatest pressure it can exert when resting on a horizontal table. Can anybody help me with this?

Answer 1

`P_"min"=1250 \ "Pa"`

`P_"max"=7500 \ "Pa"`

Explanation:

Pressure is defined through the equation:

`P=F/A`

where `F` is the force in newtons, and `A` is the area in `"m"^2`.

So, we got the rectangular block with dimensions `30 \ "cm"` by `5 \ "cm"` by `10 \ "cm"`, or if we write this in meters, it is `0.3 \ "m"` by `0.05 \ "m"` by `0.1 \ "m"`.

Since the force is constant, we can let `F=k`, and we have

`P=k/A`

Therefore, pressure is inversely proportional to area, i.e. bigger area equals less pressure, smaller area equals bigger pressure.

So, we would want to apply the force on the face of the block with the smallest dimensions if we want to find the largest pressure, i.e. that is `0.1 \ "m"` by `0.05 \ "m"`, and `A=0.1 \ "m"*0.05 \ "m"=0.005 \ "m"^2`.

So, the maximum pressure will be `P=(37.5 \ "N")/(0.005 \ "m"^2)=7500 \ "Pa"`.

If we want to apply the least possible pressure, we must apply the force on the face with the biggest dimensions, and that is `0.3 \ "m"` by `0.1 \ "m"`, and `A=0.3 \ "m"*0.1 \ "m"=0.03 \ "m"^2`.

Therefore, the pressure here will be `P=(37.5 \ "N")/(0.03 \ "m"^2)=1250 \ "Pa"`.

Answer 2

Greater Pressure `=12500 Pa`
Lesser Pressure `=7500 Pa`

Explanation:

We know that `P=F/A`

Where...

`P=`Pressure (expressed in `Pa` for pascals. )
`F=`Force (expressed in `N` for newtons. )
`A=`Area (expressed in `m^2` for metres squared. )

Our glass block has dimensions of `30cm`, `5cm`, and `10cm`.

And so the two surface areas we can use are...

`30xx5=150cm^2`
`30xx10=30cm^2`

`A` is in `m2` so...

`1m^2=10000cm^2`

`150/10000=0.015m^2`

`30/10000=0.003m^2`

So now that we have our two surface areas, we can calculate our pressures.

Greater Pressure `=37.5/0.003`
`=12500 Pa`

Lesser Pressure `=37.5/0.005`
`=7500 Pa`