An object with a weight of 250 newtons floats in water. What is the upthrust force that the water exerts on the object? Consider the vertically downward direction to be positive.
So in this question, we’ve got some water. And we have an object floating in the water. We’ve been told that the weight of the object is 250 newtons. And because the object is floating, it’s got to have an upthrust force on it as well. Let’s call this force 𝑇 for thrust.
Now this upthrust force is because water is exerting an upward pressure on the object. And because the object is floating, the forces on the object must be balanced. Or in other words, the total of the two forces, the weight and the thrust, must be zero. And the reasoning for this is that the forces are balanced. Therefore, the net force or the overall resultant force on the object is zero. If it wasn’t zero, then the object would be accelerating in the direction of the net force. However, it’s just floating there. So the net force on the object is zero.
Hence, we say 250 plus 𝑇 is equal to zero. The total of the forces is equal to zero. And when we rearrange this equation, we find that the upthrust force 𝑇 is equal to negative 250 newtons. And this makes sense. The question tells us to consider the downward direction to be positive. So any forces acting in the upward direction, such as the upthrust 𝑇, will be negative forces. And that’s the reason 𝑇 is negative here. But also the size of the force is also 250 newtons. So it balances out exactly the weight of the object. And hence, we found our final answer. The upthrust force that the water exerts on the object is negative 250 newtons.