Answer :
The force exerted on Zach during the braking process is approximately 3276 Newtons.After finding the acceleration, we multiply it by Zach's mass to get the force exerted, which amounts to approximately 3276 Newtons.
To calculate the force exerted on Zach during the braking process, we can use Newton's second law, which states that force is equal to mass times acceleration (F = ma). Since the elevator is braking, the acceleration is negative, which means we'll need to use the absolute value of the acceleration.
First, we need to find the acceleration of the elevator during braking. We know that the elevator's initial velocity is 8 m/s and it comes to a stop in 3.2 seconds. Using the formula for acceleration (a = Δv / Δt), where Δv is the change in velocity and Δt is the time taken, we can find the acceleration:
[tex]\[ a = \frac{0 - 8}{3.2} = -2.5 \, \text{m/s}^2 \][/tex]
Now, we have the acceleration. Next, we use Newton's second law to find the force:
[tex]\[ F = ma = 84 \times |-2.5| = 3276 \, \text{N} \][/tex]
Therefore, the force exerted on Zach during the braking process is approximately 3276 Newtons.
The force exerted on Zach can be calculated using Newton's second law, which relates force, mass, and acceleration. By first finding the acceleration of the elevator during braking and then applying it to Zach's mass, we determine the force exerted.
Here, the elevator's acceleration is negative because it's braking, but we consider the absolute value for calculation. After finding the acceleration, we multiply it by Zach's mass to get the force exerted, which amounts to approximately 3276 Newtons.
