To determine the acceleration of the elevator, we can use Newton's second law of motion, which states:

$F_{\text{net}} = m \cdot a$

Where:

• $F_{\text{net}}$ is the net force acting on Governor Bredesen.
• $m$ is his mass.
• $a$ is the acceleration of the elevator.

Let's break this down into steps:

1. Forces acting on the Governor

There are two forces acting on Governor Bredesen:

• His weight, which is the force due to gravity: $F_{\text{gravity}} = m \cdot g = 71 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 695.8 \, \text{N}$ This force points downward.

• The normal force (the force exerted by the scale), which is the scale reading: $F_{\text{normal}} = 444 \, \text{N}$ This force points upward (because the scale pushes upward on him).

2. Net force on the Governor

The net force is the difference between the force of gravity and the normal force: $F_{\text{net}} = F_{\text{normal}} - F_{\text{gravity}} = 444 \, \text{N} - 695.8 \, \text{N} = -251.8 \, \text{N}$ Since the result is negative, it indicates the elevator is accelerating downward.

3. Acceleration of the elevator

Using Newton's second law, we can solve for the acceleration of the elevator: $F_{\text{net}} = m \cdot a$ $-251.8 \, \text{N} = 71 \, \text{kg} \cdot a$ $a = \frac{-251.8 \, \text{N}}{71 \, \text{kg}} = -3.55 \, \text{m/s}^2$

Conclusion

The acceleration of the elevator is $-3.55 \, \text{m/s}^2$, indicating that the elevator is accelerating downward.

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Would you like more details on any part of this solution? Here are some related questions you might be interested in:

1. How does the direction of acceleration affect the forces in an elevator?
2. What happens if the elevator accelerates upward instead?
3. How can we calculate the tension in the elevator cable?
4. What would the scale read if the elevator were in free fall?
5. How does the total mass of the elevator system affect its acceleration?

Tip: Remember, a negative acceleration in this context means the elevator is either speeding up while going down or slowing down while going up.