An elevator is moving vertically upward at a constant speed. A man of mass 150 kilograms is standing inside. Determine the reaction force of the floor on the man. Take 𝑔 to be equal to 9.8 metres per square second.
To answer this question, let’s identify what we’ve been given and what we’re looking to find. Firstly, we’re dealing with an elevator, and this elevator is moving vertically upward at a constant speed. Here is our elevator. It’s moving upward, but its speed is constant. So, that means its acceleration is zero metres per square second. We then have a man who has a mass of 150 kilograms inside. And we’re looking to find the reaction force of the floor on the man.
Now, we know that the man himself exerts a force on the floor of the lift. That force is equal to his mass multiplied by acceleration due to gravity. Well, his mass is 150 kilograms.And so, his force acting downwards on the lift is 150 𝑔, or 150 times 9.8 since we’re told 𝑔 is equal to 9.8 metres per square second. Newton’s third law says that for every action, there’s an equal and opposite reaction. So in this case, the floor exerts a force on the man. Let’s call that 𝑅. We now go back to Newton’s second law, which generally says that force is equal to mass times acceleration.
Now, we’re interested in the overall force acting upon the man. That’s going to be the difference of the two forces. And since the lift is moving upwards, we can say that the overall force is 𝑅 minus 150 times 9.8. We’re going to make that equal to mass times acceleration. And we know that the mass of the man is 150. But acceleration, we said, was zero. Simplifying a little then, we get 𝑅 minus 1470 equals zero. And then, we add 1470 to both sides to solve for 𝑅. And since this is a force, we measure in newtons. The reaction force of the floor on the man is therefore 1470 newtons.