An object with a weight of 600 newtons floats in water because its weight is compensated for by an equal-magnitude upthrust force. The area of the object that the upthrust for acts on is 1.5 meters squared. What is the magnitude of the pressure of the water on the object?
Okay, so in this question, we’ve got some water. And we’ve got an object floating in that water. Now we’re told that the weight of the object is 600 newtons. However, the reason that the object floats and doesn’t sink is because its weight is compensated for by an equal-magnitude upthrust force. In other words, there’s a 600-newton upthrust force on the object. And that upthrust force is because water is applying a pressure on the object.
So in this question, we already know the force with which water is acting on the object. It’s 600 newtons. And we’ve been told that the area of the object that the force acts on is 1.5 meters squared. And what we need to do is to find the magnitude or size of the pressure of the water on the object.
To do this, we’ll recall that pressure 𝑝 is defined as the force per unit area. In other words, it’s how much force is exerted for every meter squared of area. And since we already know the force exerted by the water on the object — that’s 600 newtons — and we know the area on which it acts — that’s 1.5 meters squared — we can work out the pressure exerted by the water on the object. So we say that 𝑝, the pressure, is equal to 600 newtons, the force, divided by 1.5 meters squared, the area.
And luckily for us, we already have standard units. The standard unit of force is newtons. And the standard unit of area is meters squared. So we have the force and the area in its standard units. Therefore, the pressure that we’ll find is also going to be in its standard unit. And this is the pascal. So when we evaluate the right-hand side of the equation, we’ll find that the pressure is in pascals. And so 600 divided by 1.5 is 400. So our pressure is 400 pascals.