A student stands on a bathroom scale in an elevator at rest on the 64th floor of a building. The scale reads 845 N. As the elevator moves up,the scale reading increases to 940N,then decreases back to 845N. The acceleration of gravity is 9.8 m/s^2.

Find the acceleration of the elevator. Answer in units of m/s^2.

As the elevator approaches the 74th floor, the scale reading drops as low as 789N.
What is the acceleration of the elevator? Answer in m/s^2

Hint: A newton is a kilogram per m/s^2.

Figure out the mass of the student.

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To find the acceleration of the elevator in both scenarios, we need to consider the forces acting on the student.

When the elevator is at rest and the scale reads 845N, there are two forces at play: the gravitational force and the normal force exerted by the scale. Since the elevator is at rest, these forces must be equal in magnitude but opposite in direction:

Gravitational force = Normal force

The gravitational force is given by the formula:

Gravitational force = mass * acceleration due to gravity

Here, we are given the acceleration due to gravity, which is 9.8 m/s^2. Let's assume the mass of the student is 'm'.

Therefore, the gravitational force is:

Gravitational force = m * 9.8

Since the scale reading is 845N, we can set up the following equation:

845 = m * 9.8

Now we can solve for 'm'. Dividing both sides of the equation by 9.8, we get:

m = 845 / 9.8 ≈ 86 kg

Now, let's move on to the next scenario where the scale reading drops to 789N. The forces acting on the student are still the gravitational force and the normal force exerted by the scale. However, this time there is an additional force acting on the student due to the acceleration of the elevator.

Using the same approach as before, we can set up the equation:

789 = m * (9.8 + acceleration of the elevator)

Since we have the value of 'm' (86 kg) and we know the acceleration due to gravity (9.8 m/s^2), we can rearrange the equation to solve for the acceleration of the elevator:

789 = 86 * (9.8 + acceleration of the elevator)

Dividing both sides by 86, we get:

9.16 ≈ 9.8 + acceleration of the elevator

Subtracting 9.8 from both sides, we find:

acceleration of the elevator ≈ 9.16 - 9.8 ≈ -0.64 m/s^2

Therefore, the acceleration of the elevator in this scenario is approximately -0.64 m/s^2.