a student stands on an elevator scale at rest on the 64th floor of a building. the scale reads 847 N. As the elevator moves up the scales increases to 923 N, then decreases back to 847 N. the acceleration of gravity is 9.8m/s^2. Answer in units of m/s^2

What question? Do they want the rate of acceleration when it is accelerating? It accelerates and then continues at constant velocity.

To find the acceleration of the elevator, we need to analyze the forces acting on the student's body at different moments.

When the elevator is at rest on the 64th floor, the scale reads a force of 847 N. This force represents the combined weight of the student and the elevator, acting downward. Since the elevator is not accelerating, the net force acting on the student is zero. Therefore, the normal force (or the scale reading) is equal to the gravitational force acting on the student.

However, when the elevator starts moving upwards, there is an additional force acting on the student - the acceleration force of the elevator. This force is also directed upwards, and it causes an increase in the scale reading because the normal force needs to be greater to counteract the upward acceleration. The scale reading reaches a maximum of 923 N.

At any given moment, we can calculate the net force acting on the student by subtracting the weight from the scale reading. Let's call this net force Fnet.

Fnet = Scale reading - Weight

Now, considering that the weight is equal to the mass of the student multiplied by the acceleration due to gravity (mg), we can rewrite the equation as:

Fnet = Scale reading - mg

During the upward acceleration, the net force Fnet is equal to the mass of the student multiplied by the acceleration of the elevator (ma). Thus, we have:

ma = Scale reading - mg

Simplifying further, we get:

a = (Scale reading - mg) / m

Plugging in the given values:

Scale reading = 923 N
mg = mass * 9.8 m/s^2
m = mass (unknown)

We are missing the mass of the student, which we cannot determine from the given information. Therefore, we cannot calculate the acceleration of the elevator without this missing value.

Hence, the answer is the acceleration of the elevator cannot be determined without knowing the mass of the student.