https://file.aiquickdraw.com/mathbot/file/1729786860066qb5enbxt.jpg

The problem reads:

"If the same person in problem 5 rides the elevator back up to the 5th floor, accelerating up at \(2 \, \text{m/s}^2\), then moving at a constant rate, then slowing down at the top at a rate \(2 \, \text{m/s}^2\), finally reaching the 5th floor, what does the person weigh during each interval going back up?"

---

### **Solution Outline**
To solve this, we need to determine the **apparent weight** of the person during the three phases:  
1. **Acceleration up at \(2 \, \text{m/s}^2\)**  
2. **Constant velocity** (no acceleration)  
3. **Deceleration (slowing down) at \(2 \, \text{m/s}^2\)**

The **apparent weight** \(W_{\text{apparent}}\) felt by the person is determined by:
\[
W_{\text{apparent}} = m (g + a)
\]
where:  
- \(m\) is the mass of the person  
- \(g = 9.8 \, \text{m/s}^2\) is the gravitational acceleration  
- \(a\) is the elevator’s acceleration (positive when accelerating upwards, negative when slowing down).

---

### **Case-by-Case Analysis**

#### 1. **During upward acceleration (\(a = +2 \, \text{m/s}^2\))**:
\[
W_{\text{apparent}} = m (9.8 + 2) = m (11.8) \, \text{N}
\]
The person will feel **heavier** during this phase.

---

#### 2. **During constant velocity (\(a = 0\))**:
\[
W_{\text{apparent}} = m (9.8 + 0) = m (9.8) \, \text{N}
\]
The person will feel their **normal weight** here, as there is no additional acceleration.

---

#### 3. **During deceleration (slowing down, \(a = -2 \, \text{m/s}^2\))**:
\[
W_{\text{apparent}} = m (9.8 - 2) = m (7.8) \, \text{N}
\]
The person will feel **lighter** during this phase.

---

### **Summary of Apparent Weight in Each Interval**
1. **Acceleration phase:** \(11.8 \, m \, \text{N}\)
2. **Constant velocity phase:** \(9.8 \, m \, \text{N}\)
3. **Deceleration phase:** \(7.8 \, m \, \text{N}\)

---

### **Conclusion**
- When the elevator is **accelerating up**, the person feels heavier.
- When moving at a **constant velocity**, the person feels their normal weight.
- When the elevator is **slowing down**, the person feels lighter.

---

Would you like a follow-up calculation with specific mass values or additional clarification?

---

### **Related Questions**
1. How would the apparent weight change if the elevator accelerated at \(3 \, \text{m/s}^2\)?
2. What

If the same person in problem 5 rides the elevator back up to the 5th floor, accelerating up at 2 m/s², then moving at a constant rate, then slowing down at the top at a rate 2 m/s², finally reaching the 5th floor, what does the person weigh during each interval going back up?

Solve a kinematics problem to find the apparent weight of a person in an elevator during upward acceleration, constant velocity, and deceleration. Includes step-by-step use of Newton's Second Law and key concepts of motion. Suitable for high school students (Grades 10-12).

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation