Question

1. upon reaching the top of the building, the elevator accelerates downward at 3.0 m/s².

a. construct a force diagram for the 85 kg passenger.
b. calculate the force the floor exerts on the passenger.

Explanation:

Step1: Identify forces and apply Newton's second law

The forces acting on the passenger are the gravitational force \(F_g = mg\) (downward) and the normal force \(N\) (upward). Let the downward direction be positive. According to Newton's second law \(F_{net}=ma\), so \(mg - N=ma\).

Step2: Solve for the normal force \(N\)

We know \(m = 85\space kg\), \(g = 9.8\space m/s^{2}\), \(a=3.0\space m/s^{2}\). Rearranging the equation \(mg - N=ma\) for \(N\), we get \(N=m(g - a)\).
Substitute the values: \(N = 85\times(9.8 - 3.0)\)

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Answer:

The force the floor exerts on the passenger is \(578\space N\)