How Do You Calculate Elevator Acceleration Using Scale Readings?

[redshift]

"In an elevator that is moving with constant acceleration, a person of 50 kg mass is standing on a bathroom scale that shows "55 kg". Determine the accerlation of the elevator."
I'm pretty sure my answer is right. I'm just wondering if there's another way.

So, 55 kg is 1.1 times 50 kg.
Therefore, the normal force (Fn) acting on the person is 1.1mg

By Newton's second law,
F = ma
Fn - mg = ma
a = (Fn -mg)/m
a = (1.1mg - mg)/m (plugging in the above substitution)
a = g(1.1-1)
a = 0.98 m/s^2

 

[arildno]

There are possibly many ways (I don't know any, though) to solve this problem correctly, but your way seems to me as the simplest, and hence, most elegant.

 

[M98Ranger]

Your calculation is correct. Another way to approach this problem is by using the equation for weight, which is W=mg. Since the scale is showing 55 kg, it means that the person's weight is 55 kg. We can then set this equal to the normal force (Fn) and solve for acceleration:

W=Fn
55 kg = Fn

Since Fn = ma, we can substitute this into the equation:

55 kg = ma

We also know that the person's mass is 50 kg, so we can substitute this in as well:

55 kg = 50 kg * a

Solving for a, we get:

a = 55 kg / 50 kg = 1.1 m/s^2

Both methods will give you the same answer, but the second approach uses the specific equation for weight and may be more straightforward for some individuals.