A 79.2-kg person stands on a scale in an elevator. What is the apparent weight when the elevator is (a) accelerating upward with an acceleration of 1.92 m/s2, (b) moving upward at a constant speed, and (c) accelerating downward with an acceleration of 1.89 m/s2

I was going to use the equation
FN = mg + ma in which we are given a and mg but I was not sure what to use for m.

(a) ma = - mg + N

N = ma+mg

(b) 0= - mg + N
N =mg.

(c) -ma = - mg + N
N =mg - ma

A) a=1.92m/s^2

N-mg=ma
N=m(g+a)=79.2(10+1.92)=944 N
B) V=const, a=0
N-mg=0
N=mg=79.2*10=792 N
C) a=1.89m/s^2
N-mg=-ma
N=m(g-a) =79.2(10-1.89)=642.3 N

so is 79.2 kg the value for mass(m) or mg?

Mass [s meeasured in kg.

Force (mg) - in Newtons.
m = 79.2 kg

To find the apparent weight of a person in different elevator scenarios, we can use the equation:

Apparent Weight (FW) = weight due to gravity (mg) + weight due to acceleration (ma),

where m is the mass of the person, g is the acceleration due to gravity (approximately 9.8 m/s^2), and a is the acceleration of the elevator.

(a) Accelerating upward:
In this case, the acceleration of the elevator is directed upward and is given as 1.92 m/s^2. To calculate the apparent weight, we can use the equation:

FW = mg + ma.

Given that the mass of the person is 79.2 kg, we can substitute the values:

FW = (79.2 kg)(9.8 m/s^2) + (79.2 kg)(1.92 m/s^2).

(b) Constant speed:
When the elevator is moving upward at a constant speed, there is no acceleration. Therefore, the apparent weight is equal to the weight due to gravity, since there is no additional weight due to acceleration:

FW = mg.

Using the same mass value, we have:

FW = (79.2 kg)(9.8 m/s^2).

(c) Accelerating downward:
Here, the elevator is accelerating downward with an acceleration of 1.89 m/s^2. Again, we can use the same equation:

FW = mg + ma.

Substituting the values, we get:

FW = (79.2 kg)(9.8 m/s^2) + (79.2 kg)(-1.89 m/s^2).

Remember that when the elevator accelerates downward, it contributes a negative value to the equation because it opposes the gravitational force.

Now you can calculate the apparent weights in each scenario using these equations.