A man standing on the ground applies a force of 735 newtons to the ground beneath him due to his weight. What is the mass of the man?
The first thing to do is to underline all of the important information in the question. So we know the man standing on the ground is applying a force of 735 newtons to the ground beneath him. That’s due to his weight. What we’ve been asked to do is to find the mass of the man. We can label the man’s weight as 𝑊 and that’s 735 newtons. And we want to find the mass 𝑚.
In order to do this, we need to find a relationship between the mass of an object and the weight of an object. In this case, obviously, the object is the dude. That relationship specifically is that 𝑊, the weight, is equal to the mass 𝑚 multiplied by the gravitational field strength 𝑔.
Just as a quick aside by the way, this kind of looks like Newton’s second law of motion, which is that the force 𝐹 on an object is equal to the mass of the object 𝑚 multiplied by its acceleration 𝑎. Now, we already know that weight is a force. So these two look alike. The weight is a force. Of course, the masses of the object look alike, which means that the gravitational field strength and acceleration also must be similar. That’s why the gravitational field strength is also sometimes known as the acceleration caused by gravity.
Anyway, let’s go back to the question. We need to apply this equation 𝑊 is equal to 𝑚𝑔 to our scenario here. Since we want to find out the mass of the dude, what we need to do is rearrange the equation until we only have mass on one side. To do this, we can divide both sides of the equation by the gravitational field strength 𝑔, which leaves us with the weight divided by the gravitational field strength being equal to the mass.
Now since we’ve been told in the question that the dude is standing on the ground, we know that the gravitational field strength that we’re looking for is that of the Earth. And the gravitational field strength of the Earth happens to be 9.8 newtons per kilogram. So we’re just substituting the values for the weight of the guy and the gravitational field strength of the Earth.
Once we’ve done that, we can plug the values into our calculator to find the mass of the cheeky chappie. And so we find out that the bloke weighs 75 kilograms and that is the answer to our question.