Zach, whose mass is 76 kgkg, is in an elevator descending at 9 m/sm/s. The elevator takes 2.6 ss to brake to a stop at the first floor. What is Zach's weight while the elevator is braking?

To determine Zach's weight while the elevator is braking, we need to account for the additional force exerted due to the elevator's deceleration. Zach's apparent weight will be affected by the elevator's deceleration, which changes the net force acting on him.

### Step-by-step solution:

1. **Zach's mass** \( m = 76 \, \text{kg} \).
2. **Initial velocity of the elevator** \( v_i = 9 \, \text{m/s} \).
3. **Final velocity of the elevator** \( v_f = 0 \, \text{m/s} \) (the elevator stops).
4. **Time taken to brake** \( t = 2.6 \, \text{s} \).
5. **Gravitational acceleration** \( g = 9.8 \, \text{m/s}^2 \).

### Step 1: Calculate the elevator's deceleration

The elevator's deceleration \( a \) can be found using the kinematic equation:

\[
v_f = v_i + at
\]

Rearranging for \( a \):

\[
a = \frac{v_f - v_i}{t} = \frac{0 - 9}{2.6} = -3.46 \, \text{m/s}^2
\]

(Note: The negative sign indicates that the elevator is decelerating.)

### Step 2: Apparent weight calculation

The apparent weight is the normal force \( F_N \) acting on Zach, which is modified by the deceleration of the elevator. The equation for apparent weight is:

\[
F_N = m(g + a)
\]

Substituting the values:

\[
F_N = 76 \times (9.8 + (-3.46)) = 76 \times 6.34 = 481.84 \, \text{N}
\]

So, Zach's apparent weight while the elevator is braking is approximately **481.84 N**.

### Conclusion:
Zach's weight while the elevator is braking is about **481.84 N**. This is lower than his normal weight because the elevator is decelerating while descending.

Do you want further details on any step or have any questions?

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Here are five related questions to expand on this:

1. How would Zach's weight change if the elevator were accelerating upwards instead of braking?
2. What would Zach's apparent weight be if the elevator were in free fall?
3. How would Zach's weight change if the elevator descended at a constant speed?
4. How do we calculate the total distance the elevator traveled while braking?
5. How would the problem change if Zach's mass was different?

**Tip**: The normal force (apparent weight) varies depending on the acceleration or deceleration of the system you're in!

Zach, whose mass is 76 kg, is in an elevator descending at 9 m/s. The elevator takes 2.6 s to brake to a stop at the first floor. What is Zach's weight while the elevator is braking?

Explore how to determine the apparent weight of a person in an elevator that is braking. This physics problem involves concepts like deceleration, forces, and apparent weight, using formulas such as Newton's Second Law. Suitable for high school students in Grades 10-12.

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