Final answer:
When a 75.0-kg man stands on a scale in an elevator accelerating at 15.0 m/s², the scale reads an unreasonably high value of 1860 N, indicating the premise of the elevator's acceleration might be unrealistic for standard elevators.
Step-by-step explanation:
To calculate the scale reading in newtons when a 75.0-kg man stands on a bathroom scale in an accelerating elevator, we'll need to apply Newton's second law of motion. The man's weight is a force caused by gravity and is given by W = mg, where m is the mass and g is the acceleration due to gravity (9.80 m/s2). So, the man's weight is W = (75.0 kg)(9.80 m/s2) = 735 N.
Next, we calculate the acceleration of the elevator, a, which is given by the change in velocity over time: a = ∆v / t = (30.0 m/s) / (2.00 s) = 15.0 m/s2. The total force on the man, according to Newton's second law, is F = ma, where m is his mass plus his weight for the accelerating system.
The net force acting on the man in the elevator is thus Fnet = ma + mg = m(a + g). Plugging in the values gives us Fnet = (75.0 kg)(15.0 m/s2 + 9.80 m/s2) = (75.0 kg)(24.8 m/s2) = 1860 N.
The scale reading is the normal force exerted by the scale, which is equal to Fnet. Comparing 1860 N to the man's weight of 735 N, we see that the scale reading is much higher than his actual weight due to the acceleration of the elevator.
The unreasonable result here is that the scale reading is over twice the man's weight, which indicates extreme acceleration that is not typical for standard elevators, leading us to question the premises of the problem. Elevators typically have more moderate accelerations to ensure passenger safety and comfort.