Final answer:
The scale will read 825 N when the person is accelerating upward at 1.2 m/s² because this is the combination of their actual weight and the additional force caused by the elevator's acceleration.
Step-by-step explanation:
When the elevator is accelerating upwards at 1.2 m/s², we need to calculate the apparent weight of the person standing on the scale, which is the reading the scale will show. The apparent weight is the sum of the actual weight and the force due to the acceleration. Using Newton's second law (F = ma), where ‘F’ is force, ‘m’ is mass, and ‘a’ is acceleration, the additional force due to acceleration can be calculated.
The actual weight (‘W’) of the person is the force due to gravity, which is W = mg, where ‘g’ is the acceleration due to gravity (9.8 m/s²). Given the mass of the person is 75 kg, their weight is 75 kg × 9.8 m/s² = 735 N.
The additional upward force (‘Fa’) due to the elevator's acceleration is Fa = ma = 75 kg × 1.2 m/s² = 90 N. Therefore, the scale reading is the sum of the actual weight and the additional force due to the elevator's acceleration: Scale reading = W + Fa = 735 N + 90 N = 825 N.