Former Governor Phil Bredesen takes the elevator down from the Neyland Stadium skyboxes after watching the home opener. Having earned a physics degree from Harvard, he makes some measurements while riding the elevator down. He stands on a scale and notes various readings. The former governor has a mass of 71  kg. The mass of the elevator and the other occupants is 810kg. Let the direction the elevator is travelling be positive. As the elevator starts down, the scale Gov. Bredesen is standing on reads 444  N
  . Determine the acceleration of the elevator.

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.

---

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.

Former Governor Phil Bredesen takes the elevator down from the Neyland Stadium skyboxes after watching the home opener. Having earned a physics degree from Harvard, he makes some measurements while riding the elevator down. He stands on a scale and notes various readings. The former governor has a mass of 71 kg. The mass of the elevator and the other occupants is 810kg. Let the direction the elevator is traveling be positive. As the elevator starts down, the scale Gov. Bredesen is standing on reads 444 N. Determine the acceleration of the elevator.

Determine the downward acceleration of an elevator using Newton's Second Law of Motion. This physics problem involves a governor standing on a scale, noting the reading of 444 N, with his mass at 71 kg and the elevator's mass at 810 kg. Suitable for high school physics students in Grades 11-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation