Final answer:
The reading on the scale, when a person with a mass of 50 kg is in an elevator that is accelerating upwards at 3 m/s², would be 640 N.
Step-by-step explanation:
When you are standing on a scale in an elevator that is accelerating upwards, the scale measures not only your weight but also the additional force required to accelerate you. This additional force comes from the fact that the elevator is increasing its speed at a rate (or acceleration) of 3 m/s². The reading on the scale will be the sum of your weight and the force due to the elevator's acceleration.
First, let's calculate your weight. Your mass is 50 kg, so your weight (W) is the mass (m) times the acceleration due to gravity (g), which is approximately 9.8 m/s². This calculation is as follows:
W = m × g = 50 kg × 9.8 m/s² = 490 N.
Next, to find the additional force due to the elevator's acceleration upwards (Fa), we use Newton's second law, which states that F = ma:
Fa = m × a = 50 kg × 3 m/s² = 150 N.
The total force that the scale must exert, and thus the scale reading (Fscale), is the sum of your weight and the additional force:
Fscale = W + Fa = 490 N + 150 N = 640 N.
Therefore, the reading on the scale would be 640 N, which corresponds to option b.