€ = 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**.
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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