A person weighing 82.0kg rides an elevator using an accelerometer app on a mobile phone during the elevator ride. They find acceleration happens to be +1.72 m/s^2. What is the force exerted by the legs on the person's upper body, assuming that the legs are 32% of the person's mass?

Question

A person weighing 82.0kg rides an elevator  using an accelerometer app on a mobile phone during the elevator ride. They find acceleration happens to be +1.72 m/s^2. What is the force exerted by the legs on the person's upper body, assuming that the legs are 32% of the person's mass?

loser66 · Answer

@ybarrap

ybarrap · Answer

I see it like this. Break the problem into two parts. 

Part I: The body as a system
Part II: The body made up of 2 systems, upper and lower body.

Part I: The Body

The mobile application can not measure the acceleration due to gravity, so it is relative to gravity. Since it is positive, it is exerting a force on the body, meaning that the elevator is going up. The total acceleration taking into account gravity is g+1.72 m/s^2.

Do you agree?

Once you have total acceleration, multiply  time mass to get total force (it should be greater than his normal weight).

Part II: The body made up of two parts.

All parts of the body are accelerating at the same rate as the  elevator as a system. Therefore, the legs (L) and upper body (U)  are accelerating at the same rate. The forces of one against the other are proportional to their masses. so $F_{U} = m_U\times a_{total}$, where $m_U$ is mass of upper part of body, $F_U$ is the force required to lift the Upper part of the body and $a_{total}$ is the total acceleration we found in Part I.

This is the force excreted by the lower body on the upper.

ybarrap · Answer

Let me know if you have any questions.

anonymous · Answer

No, thank you very much for your Help