€ = Problem2 Starting at rest, a 2500kg helicopter accelerates straight up at a constant 1.7m/s². The helicopter can be modeled as a 2.6m diameter sphere. [ C= 0.5, p = 1.2 kg/m³] a. Draw a free body diagram u= 0 29 is the helicopter's height at the moment its blades are providing an upward force of 29kN? 29000 a) v=183.2728 1-7 a = 1. v² = u²12aS (183.2720) 2. = 1-3m To A = R₁² = 4= 0 a=1-7 m/s² S = 9879 m b) Zry = Fg - D²³ Ex(3) 169 (66 70 29000 = mg - 1/2 CPAV² ✓29090 2 2 b==
€ = Problem2 Starting at rest, a 2500kg helicopter accelerates straight up at a constant 1.7m/s². The helicopter can be modeled as a 2.6m diameter sphere. [ C= 0.5, p = 1.2 kg/m³] a. Draw a free body diagram u= 0 29 is the helicopter's height at the moment its blades are providing an upward force of 29kN? 29000 a) v=183.2728 1-7 a = 1. v² = u²12aS (183.2720) 2. = 1-3m To A = R₁² = 4= 0 a=1-7 m/s² S = 9879 m b) Zry = Fg - D²³ Ex(3) 169 (66 70 29000 = mg - 1/2 CPAV² ✓29090 2 2 b==
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Is my working method correct? I am also confused ablut the free body diagrams. Do i have to show the net force for that?
![## Problem 2
**Scenario:**
A 2500 kg helicopter accelerates straight up at a constant 1.7 m/s². The helicopter can be modeled as a 2.6 m diameter sphere.
- [C = 0.5, ρ = 1.2 kg/m³]
**Tasks:**
a. **Draw a free body diagram.**
b. **Calculate the helicopter's height when its blades provide an upward force of 29 kN.**
---
### Solution
- **Force Equation:**
\[
\Sigma F_y = F_g - D
\]
\[
29000 = mg - \frac{1}{2}C\rho A v^2
\]
- **Drag Force Equation:**
\[
D = \frac{1}{2} C \rho A v^2
\]
- **Variables and Constants:**
- m = 2500 kg (mass)
- a = 1.7 m/s² (acceleration)
- D = Drag Force
- C = 0.5 (drag coefficient)
- ρ = 1.2 kg/m³ (air density)
- A = πr² = π(1.3)² (area of the sphere with radius 1.3 m)
- v = final velocity
- **Substituting the known values:**
- Rearrange the force equation to find velocity \(v\):
\[
29000 - 2500 \times (9.8 + 1.7) = -\frac{1}{2}(0.5)(1.2)(\pi (1.3)^2)v^2
\]
- Solving for \(v\),
\[
v = 103.27 \, \text{m/s}
\]
- **Kinematic Equation:**
\[
v^2 = u^2 + 2as
\]
\[
(103.27)^2 = 0 + 2 \times 1.7 \times s
\]
\[
s = 9879 \, \text{m}
\]
Therefore, the helicopter's height is approximately **9880 m**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F104d41eb-f02b-4e6d-903d-dd6e6944a268%2F5a6625e9-57cd-43d6-bccc-6a8d1b3e25ec%2Ftsgnc4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Problem 2
**Scenario:**
A 2500 kg helicopter accelerates straight up at a constant 1.7 m/s². The helicopter can be modeled as a 2.6 m diameter sphere.
- [C = 0.5, ρ = 1.2 kg/m³]
**Tasks:**
a. **Draw a free body diagram.**
b. **Calculate the helicopter's height when its blades provide an upward force of 29 kN.**
---
### Solution
- **Force Equation:**
\[
\Sigma F_y = F_g - D
\]
\[
29000 = mg - \frac{1}{2}C\rho A v^2
\]
- **Drag Force Equation:**
\[
D = \frac{1}{2} C \rho A v^2
\]
- **Variables and Constants:**
- m = 2500 kg (mass)
- a = 1.7 m/s² (acceleration)
- D = Drag Force
- C = 0.5 (drag coefficient)
- ρ = 1.2 kg/m³ (air density)
- A = πr² = π(1.3)² (area of the sphere with radius 1.3 m)
- v = final velocity
- **Substituting the known values:**
- Rearrange the force equation to find velocity \(v\):
\[
29000 - 2500 \times (9.8 + 1.7) = -\frac{1}{2}(0.5)(1.2)(\pi (1.3)^2)v^2
\]
- Solving for \(v\),
\[
v = 103.27 \, \text{m/s}
\]
- **Kinematic Equation:**
\[
v^2 = u^2 + 2as
\]
\[
(103.27)^2 = 0 + 2 \times 1.7 \times s
\]
\[
s = 9879 \, \text{m}
\]
Therefore, the helicopter's height is approximately **9880 m**.
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