Calculate the acceleration of the elevator

[bpw91284]

Homework Statement

A person stands on a bathroom scale in a motionless elevator. When the elevator begins to move, the scale briefly reads
only 0.78 of the person’s regular weight.
a. Calculate the acceleration of the elevator.
b. Find the direction of acceleration.

Homework Equations

Sum of forces.

The Attempt at a Solution

I know the equation is F_normal-mg=ma but don't understand how it was derived.

 

[Decan]

The normal force points in the y direction and is opposite to the weight of the person (mg). Newtons law says that the sum of all forces = ma. Since the elevator is only moving in y direction, the only component of the net force is the component in the y direction. Put the 2 together and you have F_n -mg = ma

Now that you know this...what are your thoughts on the problem?

 

[m2003]

As a scientist, it is important to understand the derivation of equations in order to fully comprehend their applications. In this case, the equation F_normal-mg=ma is derived from Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration (F=ma).

In this problem, the person's weight is represented by the force of gravity (mg), which is acting downwards. The normal force (F_normal) from the bathroom scale is acting upwards to support the person's weight. When the elevator begins to move, there is a change in the forces acting on the person. The normal force from the scale is still acting upwards, but now there is also an additional force (ma) acting upwards due to the acceleration of the elevator.

To calculate the acceleration of the elevator, we can rearrange the equation F_normal-mg=ma to solve for a: a = (F_normal-mg)/m.

Now, to find the direction of acceleration, we need to look at the direction of the net force acting on the person. Since the normal force and the force of gravity are acting in opposite directions, the net force is in the direction of the acceleration of the elevator, which is upwards. Therefore, the direction of acceleration is upwards.