Why Does the Scale Show 76 kg in the Elevator?

[drewdiddy]

Homework Statement

Normal mass is 65kg. I get into an elevator, on a scale in the elevator and it reads 76 kg. Find a along with direction.

Homework Equations

w = mg + ma

The Attempt at a Solution

Obviously the elevator is accelerating upwards due to the apparent increase in mass. However, for the life of me I am having issues setting up this basic problem. I don't need any answers, just a shove in the right direction. How do I correlate the actual mass with the 76 kg? Thank you.

 

[alphysicist]

Hi drewdiddy,

What force (acting on you) does the reading of 76kg represent?

In other words, you can find a force from the 76kg reading by multiplying it by g, and that force is acting on you. What force is it?

 

[baba89]

Firstly, it is important to note that the mass of an object does not change due to its location or motion. Therefore, the actual mass of the person remains 65kg, regardless of their location (in this case, in an elevator) or the reading on the scale.

To solve this problem, we can use Newton's second law of motion, which states that the net force acting on an object is equal to its mass times its acceleration (F=ma). In this case, the person's weight (or apparent mass) is equal to the sum of two forces: their actual mass (65kg) multiplied by the acceleration due to gravity (9.8m/s^2) and the additional force due to the elevator's acceleration (F=ma).

Using this information, we can set up the following equation:

76kg = 65kg x 9.8m/s^2 + ma

Solving for the acceleration (a), we get:

a = (76kg - 65kg x 9.8m/s^2)/65kg

a = 1.69m/s^2

Therefore, the elevator is accelerating upwards at a rate of 1.69m/s^2. The direction of the acceleration is upwards, as indicated by the positive value of acceleration in our equation.