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 determine the acceleration of the elevator, we need to use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.

(a) Let's consider the forces acting on the mass when the elevator is at rest. The only force acting on the mass is its weight, which is equal to the gravitational force acting on it. We can use the equation F = m * g, where F is the force (weight), m is the mass, and g is the acceleration due to gravity (approximately 9.8 m/s²).

When at rest, the force (weight) is 98N, so we have:
98N = m * 9.8 m/s²

Similarly, when the elevator is moving, the force (weight) is 93N. Hence, we have:
93N = m * 9.8 m/s²

We can solve both equations for the mass (m):
m = 98N / 9.8 m/s² = 10 kg
m = 93N / 9.8 m/s² = 9.49 kg

Since the mass does not change, we assume that the acceleration of the elevator causes the difference in forces.

Using Newton's second law, we can find the acceleration (a):
a = (Force when moving - Force at rest) / mass
a = (93N - 98N) / 10 kg
a = -0.5 m/s²

Therefore, the acceleration of the elevator is -0.5 m/s². The negative sign indicates that the elevator is accelerating downwards.

(b) The direction of the elevator's acceleration can be inferred based on the change in force. As the force decreases from 98N to 93N, we can conclude that the elevator is accelerating downward since the weight (force) on the mass is decreasing.