A chair has a mass of 50 kilograms. What force does the chair’s weight apply to the ground below it?
Okay, so, in this question, we’ve got a chair here placed on the floor. And we’ve been asked to find the force exerted by this chair onto the floor beneath it. Now to do this we can, first of all, recall that the chair has a weight. That’s a downward-acting gravitational force which we’ll call 𝑊. Now this is the force that acts on the chair because it’s been placed in the gravitational field, in this case, of the Earth. Because we’re assuming that the question, when it refers to the ground beneath the chair, is referring to the Earth.
So, we realise that this chair has a weight acting on it. And we also realise that the chair is in contact with the ground, specifically at the chair’s legs. Well, in this situation, in order to stop the chair and the ground from passing straight through each other, the chair and the floor must be exerting a force on each other.
The reasoning for this is as follows. We’ve already seen that the weight force must be acting on the chair. However, the chair is perfectly stationary sitting on the floor. Now the only way that the chair can be perfectly stationery on the floor is if it has a net force of zero acting on it.
In other words, if the weight was the only force acting on the chair, then the chair would be accelerating downwards. But it’s not. So, there must be an upward force exactly cancelling out the weight force that must be also exerted on the chair. And this upward force is the force exerted by the floor onto the chair because the chair is in contact with the floor. This is because of Newton’s first law of motion.
We can recall that any object with an unbalanced force acting on it must change velocity. It must accelerate. However, because the chair is perfectly still, it does not accelerate and, therefore, the forces on the chair are balanced.
Then we can use Newton’s third law of motion to tell us that, if the floor is exerting an upward force of 𝑊 onto the chair, then the chair must exert an equal and opposite reaction force onto the floor. In other words, the chair exerts a downward force onto the floor, and that force must be exactly the same in magnitude, which is 𝑊. Therefore, although the weight of the chair is the force acting on the chair due to the Earth’s gravity, that force, the weight force, has exactly the same magnitude as the force exerted by the chair onto the floor.
So, when we’re asked to find the force that’s exerted by the chair’s weight onto the ground below it, what we really want to find is the weight of the chair. To do this, we can recall that the weight of an object can be found by multiplying the mass of the object by the gravitational field strength of the gravitational field that the object is in. In this case, we’re referring to the gravitational field strength of the Earth because the chair is on Earth.
So, at this point, we can plug in the values, realising that the question tells us that the mass of the chair is 50 kilograms and recalling that the gravitational field strength of the Earth, otherwise known as the acceleration due to gravity on Earth, is 9.8 metres per second squared.
Then we can realise that we’re working in base units, that’s kilogram for mass and metres per second squared for acceleration. And therefore, whatever we find on the right-hand side as the answer is going to be in the base unit of weight. And because weight is a force, we’re going to find the answer on the right-hand side in newtons.
Therefore, evaluating the right-hand side, we find that the weight of the chair is 490 newtons. And hence, we’ve found our final answer. The force exerted by the chair’s weight onto the ground below it is 490 newtons.