Question Video: Finding the Mass of a Person in an Ascending Lift Mathematics

Video Transcript

A lift is ascending with an acceleration of 140 centimeters per square second. Given that a person standing inside the lift is exerting a force of 88 kilogram-weight on the floor, find his mass. Take 𝑔 to be equal to 9.8 meters per square second.

Let’s begin by drawing a free-body diagram. We’ll model the person standing on the floor of the lift as a particle. And we know that since the man moves with the lift, they have an acceleration of 140 centimeters per square second. Now, we’re told that the person who stands inside the lift exerts a force of 88 kilogram-weight on the floor. This means the floor exerts an equal and opposite reaction force on the man. The upward force of the floor on the man is 88 kilogram-weight.

We also need to take into account a second force, and that’s the weight of the man. We model this as being equal to his mass times acceleration due to gravity 𝑚𝑔. And then, we can link all of these characteristics by using the formula 𝐹 equals 𝑚𝑎. If we take the upwards direction as being positive, then we see we need to find the net force acting on the man.

Now, since the downward force of his weight is in newtons, we’re going to convert 88 kilogram-weight into newtons. One kilogram-weight is 9.8 newtons. So, 88 kilogram-weight is 88 times 9.8 newtons. So, 88 kilogram-weight is equal to 862.4 newtons. We can therefore say that the net force acting in this system is 862.4 newtons minus 𝑚𝑔 newtons. But we were told to let 𝑔 be equal to 9.8. So, we can rewrite this as 862.4 minus 9.8𝑚.

Now, we know this is equal to mass times acceleration. But since we’re working in newtons, we need to convert 140 centimeters per square second into meters per square second. We achieve this by dividing by 100. And we get 1.4 meters per square second as being the upward acceleration. And so, this is equal to mass times acceleration. It’s equal to 𝑚 times 1.4, which is 1.4𝑚. We need to solve this equation for 𝑚. So, we’re going to add 9.8𝑚 to both sides. That gives us 862.4 equals 11.2𝑚. The last thing we need to do is divide through by 11.2. So, 𝑚 is 862.4 divided by 11.2, and that’s 77.

The mass of the person standing inside the lift then is 77 kilograms.