A man measures the acceleration of an elevator using a spring balance. He fastens the scale to the roof, and suspends a mass from it. If the scale reads 98N when the elevator is at rest, and 93N when the elevator is moving.

a) what is the acceleration of the elevator?

b) in which direction is the elevator accelerating?

To find the acceleration of the elevator, we can apply Newton's second law of motion, which states that force equals mass multiplied by acceleration (F = ma).

a) First, let's calculate the net force acting on the mass when the elevator is at rest. According to the given information, the reading on the scale is 98N. Since the elevator is at rest, the net force equals the weight of the mass. Therefore, we can determine the mass using the formula weight = mass * gravitational acceleration.

Weight = 98N
Gravitational acceleration (g) = 9.8 m/s^2 (approximate value)

Using the formula weight = mass * g, we can rearrange the equation to find m:

Mass (m) = Weight / g
m = 98N / 9.8 m/s^2
m ≈ 10 kg

Now, let's calculate the net force acting on the mass when the elevator is in motion. According to the given information, the reading on the scale is 93N. This time, though, the net force acting on the mass is the difference between the weight of the mass and the reading on the scale. The force difference is equal to mass multiplied by acceleration:

Net force = Weight - Scale reading
Net force = ma

Simplifying, we have:
ma = Weight - Scale reading
10 kg * a = 98N - 93N
10 kg * a = 5N

Finally, we can determine the acceleration (a) by rearranging the equation:

a = (5N) / (10 kg)
a = 0.5 m/s^2

Therefore, the acceleration of the elevator is 0.5 m/s^2.

b) To determine the direction of acceleration, we need to consider the force acting on the mass. If the net force is positive, the direction of acceleration is upward; if negative, the direction of acceleration is downward.

In this case, the net force is 5N, which is positive. Therefore, the elevator is accelerating upwards.