Video Transcript
A sofa with a mass of 125 kilograms has a base with an area of 2.5 meters squared. What pressure does the sofa apply to the ground beneath it?
Okay, so in this question, we’re told that we have a sofa and that this sofa has a mass of 125 kilograms. We’ll call this mass 𝑚 so that we have 𝑚 is equal to 125 kilograms. We’re also told that the base of this sofa has an area of 2.5 meters squared. The base may look like a rectangle, so we could draw it like this. And we’ll label the area as 𝐴 so that we have 𝐴 is equal to 2.5 meters squared. We’re asked to work out the pressure that the sofa applies to the ground beneath it. So let’s draw in some ground beneath our sofa.
Now, the sofa is only gonna apply pressure to the area directly underneath its base. So that’s the bit of ground in the shape of the base of the sofa, which we know has an area of 2.5 meters squared. We can recall that pressure is defined as force per unit area. Labeling the pressure as 𝑃, the force as 𝐹, and the area as 𝐴, then we can express this statement mathematically as 𝑃 is equal to 𝐹 divided by 𝐴.
In our case, we already know the value of the area 𝐴. So that’s our 2.5-meter-squared area of the base of the sofa. However, at this point, we don’t yet know the value of the force 𝐹. The force acting is the weight of the sofa, so we can draw our force 𝐹 acting vertically downward. This force is going to be equal to the mass of the sofa, which we’ve labeled 𝑚, multiplied by 𝑔, the acceleration due to gravity. We can recall that 𝑔 is equal to 9.8 meters per second squared.
Substituting in our values for the mass 𝑚 and the acceleration due to gravity 𝑔, we get that the force 𝐹 is equal to 125 kilograms multiplied by 9.8 meters per second squared. Since both the mass and the acceleration are expressed in their SI base units, then the force that we calculate will also be in its own SI base unit. The SI base unit of force is the newton. And doing this multiplication, we find that the force is equal to 1225 newtons. This value of 𝐹 is the force applied by the sofa to the ground beneath it.
So now in our expression for the pressure 𝑃, not only do we know the area, but we also know that the force is 1225 newtons. All that we need to do now is to substitute in these values for the force 𝐹 and the area 𝐴 into this expression for 𝑃. Doing this gives us that 𝑃 is equal to 1225 newtons divided by 2.5 meters squared. Since the force is in its SI base unit of newtons and the area is in its SI base unit of meters squared, then our pressure 𝑃 will also be in its own SI base unit. The SI base unit of pressure is the pascal.
And doing the division, we find that 𝑃 is equal to 490 pascals. This value of 𝑃 gives the pressure applied by the sofa to the ground beneath it. And so our answer to the question is that this pressure is 490 pascals.
