Final answer:
Using Newton's second law, we find that the only scenario that is not possible for the elevator is it accelerating downwards, as this would result in a scale reading of less than the weight of the mass (less than 19.6 N), which contradicts the observed 20 N.
Step-by-step explanation:
To determine which motion is not possible for the elevator, we first need to analyze the situation using 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 (F = ma). If the spring scale reads 20 N for a 2 kg mass, the acceleration can be calculated by rearranging the equation to a = F/m.
- (1) If the elevator is at rest or (2) moving upward with constant velocity, the only force acting on the mass is gravity, producing a weight of w = mg, where g is the acceleration due to gravity (approximately 9.8 m/s2). The scale should then read the weight of the mass, which is 19.6 N (2 kg * 9.8 m/s2). Since the scale reads 20 N, both of these scenarios are possible but imply that there is a slight upward acceleration or an upward force additional to just gravity.
- (3) If the elevator is moving downward with constant velocity, the same reasoning applies, and the scale should also read the weight of the mass (19.6 N).
- (4) If the elevator is accelerating downward, the net force on the mass would be less than its weight because the acceleration of the elevator would subtract from the gravitational acceleration. In this case, the spring scale would read less than 19.6 N, making this scenario impossible as it does not align with the observed scale reading of 20 N.
Therefore, the fourth option, the elevator accelerating downward, is not possible as it would result in a scale reading less than the actual weight of the mass (less than 19.6 N), contrary to the observed 20 N.