Question Video: Calculating the Weight of a Woman inside a Descending Elevator Physics

Video Transcript

A woman with a mass of 55 kilograms stands on a weighing scale that is on the floor of a descending elevator as shown in the diagram. The elevator is descending with an acceleration of 9.8 meters per second squared. What is the reading on the weighing scale?

The diagram shows a woman standing on an elevator with a scale at the bottom on the floor and an arrow representing the acceleration downwards. Let’s label the information from our problem on our diagram. The problem told us that the woman on the elevator has a mass of 55 kilograms and that the value of the acceleration is 9.8 meters per second squared in a downward direction. We’re being asked to find the reading on the scale, which is labeled as our normal force in the diagram. This is the reaction force of the scale on the woman. And it’s pointing in an upward direction. We have also included the weight of the woman or the force due to gravity pointing downwards as it points towards the center of the Earth.

To determine what the reading is on the weighing scale, we need to begin with Newton’s second law. Newton’s second law says that the net force on an object is equal to the mass of the object times the acceleration of the object. To find the net force, we add our two forces together as represented by the left side of our equation. The normal force or the reading on the scale is positive as it’s in an upward direction. And we typically choose upwards to be positive. The force of gravity is negative as it is in the opposite direction pointing downwards.

On the right side of the equation, our mass was given to us as 55 kilograms and our acceleration was negative 9.8 meters per second squared, where the negative is because the acceleration is in a downward direction. Multiplying out the right-hand side of the equation, we get negative 539 newtons. To continue solving our problem, we’ll need to replace the weight of the woman with an expression based on the values. We need to remember the weight or the force due to gravity is equal to the mass of the object times the acceleration due to gravity. For this problem, the mass of the woman is 55 kilograms and the acceleration due to gravity is 9.8 meters per second squared.

Multiplying out our two values, we once again get 539 newtons. To solve for the reaction force of the scale on the woman, we need to add 539 newtons to both the left side of the equation as well as the right side of the equation. This cancels out the 539 newtons on the left side equation as well as on the right side of the equation, leaving us with zero newtons. The reading on the weighing scale on the floor of a descending elevator at a rate of 9.8 meters per second squared is zero newtons. As the elevator is falling at the same rate as 𝑔, it is in free fall, and the woman inside is weightless, which is why the contact force 𝐹 𝑁 is measured to be zero.