Answer :
Zach's weight before the elevator starts braking is approximately 58.8 N, calculated by subtracting the force due to deceleration from his apparent weight.
To find Zach's weight before the elevator starts braking, we first calculate his apparent weight while descending in the elevator:
1. Apparent weight = Actual weight + Pseudo force due to acceleration
2. Pseudo force = mass × acceleration
3. Given Zach's mass (m) = 84 kg and elevator's acceleration (a) = 8 m/s²
4. Pseudo force = 84 kg × 8 m/s² = 672 N
5. Thus, apparent weight = Actual weight + 672 N
Next, we determine the elevator's deceleration rate as it comes to a stop at the first floor:
6. Deceleration rate = Change in velocity / Change in time
7. Change in velocity = Initial velocity - Final velocity = 8 m/s - 0 m/s = 8 m/s
8. Change in time = Time taken to brake = 3.2 s
9. Deceleration rate = 8 m/s / 3.2 s = 2.5 m/s²
Now, we calculate the net acceleration acting on Zach when the elevator is braking:
10. Net acceleration = Gravity's acceleration - Deceleration rate
11. Gravity's acceleration (g) = 9.8 m/s²
12. Net acceleration = 9.8 m/s² - 2.5 m/s² = 7.3 m/s²
Finally, we determine Zach's actual weight before the elevator starts braking:
13. Actual weight = Apparent weight - (Mass × Net acceleration)
14. Substituting the values, actual weight = 672 N - (84 kg × 7.3 m/s²)
15. Actual weight ≈ 672 N - 613.2 N
16. Actual weight ≈ 58.8 N
Therefore, Zach's weight before the elevator starts braking is approximately 58.8 N.
