A person stands on a bathroom scale in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.71 of the person's regular weight. Calculate the acceleration of the elevator, and find the direction of acceleration.

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To calculate the acceleration of the elevator, we can use the concept of apparent weight, which is the weight measured by the scale. The scale reads 0.71 of the person's regular weight, meaning the apparent weight is smaller than the actual weight.

Let's assume the person's regular weight is W. Therefore, the scale reading is 0.71W.

The apparent weight of an object in an elevator can be represented by the equation:

Apparent weight = Actual weight - Buoyant force

In this case, the person is standing inside a motionless elevator. Therefore, the buoyant force is zero. Thus, we have:

0.71W = W - 0

Now, let's consider what happens when the elevator begins to move. When the elevator accelerates, an upward force is exerted on the person, reducing the normal force acting on the person. This decrease in normal force leads to a decrease in the apparent weight measured by the scale.

The equation for the apparent weight during acceleration is:

Apparent weight = Actual weight - Normal force

Since the apparent weight is given as 0.71W, we can rewrite the equation as:

0.71W = W - Normal force

To calculate the normal force, we need to determine the acceleration of the elevator. Here's how we can do that:

First, we need to determine the net force acting on the person. The net force is the difference between the actual weight and the normal force:

Net force = Actual weight - Normal force

Since force is equal to mass multiplied by acceleration (F = ma), we can rewrite the equation as:

ma = W - Normal force

In this case, the mass of the person cancels out from both sides of the equation, so:

a = (W - Normal force) / m

Since the normal force is the force experienced by the person due to the elevator's acceleration, we can substitute it with m * a (Newton's second law: F=ma):

a = (W - m * a) / m

Now we can solve this equation for 'a' by substituting the given value for the scale reading (0.71W) and rearranging the equation:

a = (W - m * a) / m
am = W - m * a
am + m * a = W
a(m + m) = W
a(2m) = W
a = W / (2m)

Therefore, the acceleration of the elevator is a = W / (2m).

To determine the direction of acceleration, we need to consider the apparent weight. Since the scale reading decreases, the person experiences a smaller force normal to the scale, which means the acceleration is upward. Thus, the direction of acceleration is upward.