You step into an elevator, and it accelerates to a downward speed of 8.2 m/s in 2.2 s . How does your apparent weight during this acceleration time compare with your actual weight?
To understand how your apparent weight during this acceleration compares to your actual weight, we need to analyze the concept of apparent weight and the effects of acceleration.
Apparent weight refers to the force you feel on a scale when standing on an object that is accelerating (in this case, the elevator). It is important to note that apparent weight can differ from your actual weight, which is the force of gravity acting on you.
In this scenario, the elevator is accelerating downward, so the apparent weight will be different from your actual weight.
To calculate your apparent weight, we need to consider the net force acting on you. The net force is the difference between the force of gravity (your weight) and the force exerted due to the acceleration.
The formula to calculate net force is:
Net Force = Mass * Acceleration
In this case, the acceleration of the elevator is given as 8.2 m/s in 2.2 seconds. To find the net force, we need to calculate the acceleration in m/s^2. We can do that by dividing the change in speed by the time taken:
Acceleration = Change in Speed / Time Taken
Given:
Change in Speed = 8.2 m/s
Time Taken = 2.2 s
Acceleration = 8.2 m/s / 2.2 s = 3.727 m/s^2 (approximately)
Now that we have the acceleration, we need to calculate the net force. However, we need to know your mass to do this calculation.
Let's assume your mass is 70 kilograms (kg):
Net Force = Mass * Acceleration
Net Force = 70 kg * 3.727 m/s^2
Net Force = 260.89 N (approximately)
So, during this downward acceleration, your apparent weight would be 260.89 Newtons (N) instead of your actual weight.
To compare the apparent weight with your actual weight, you can calculate the ratio between the two:
Ratio = Apparent Weight / Actual Weight
Assuming your actual weight is 700 Newtons (N):
Ratio = 260.89 N / 700 N
Ratio ≈ 0.3727 (approximately)
Therefore, during this downward acceleration, your apparent weight would be approximately 37.27% of your actual weight.