Chapter 4, Problem 81GP

(a)

To determine

The lift force exerted by the air on the rotor of helicopter.

Answer to Problem 81GP

The lift force exerted by the air on the rotor of helicopter is $94340\text{N}$ .

Explanation of Solution

Given info:

The mass of the helicopter is, $m_h=7650\text{kg}$ .

The upward acceleration of the helicopter is, $a=0.80\text{m}/{\text{s}}^2$ .

The mass of the frame is, $m_f=1250\text{kg}$ .

Formula Used:

The expression to calculate the lift force exerted by the air on the rotor of helicopter is,

  $F_l=\left(m_h+m_f\right)\left(g+a\right)$

Calculation:

Substitute all the values in the above expression.

  $\begin{array}{c}{F}_l=\left(7650\text{kg}+1250\text{kg}\right)\left(9.8\text{m}/{\text{s}}^2+0.80\text{m}/{\text{s}}^2\right)\\ =94340\text{N}\end{array}$

Conclusion:

Thus, the lift force exerted by the air on the rotor of helicopter is $94340\text{N}$ .

(b)

To determine

The tension in the cable.

Answer to Problem 81GP

The tension in the cable is $13250\text{N}$ .

Explanation of Solution

Formula Used:

The expression to calculate the tension in the cable is,

  $F_t=m_f\left(g+a\right)$

Calculation:

Substitute all the values in the above expression.

  $\begin{array}{c}{F}_t=\left(1250\text{kg}\right)\left(9.8\text{m}/{\text{s}}^2+0.80\text{m}/{\text{s}}^2\right)\\ =13250\text{N}\end{array}$

Conclusion:

Thus, the tension in the cable is $13250\text{N}$ .

(c)

To determine

The force exerted by the cable on the helicopter.

Answer to Problem 81GP

The force exerted by the cable on the helicopter is $13250\text{N}$ .

Explanation of Solution

Formula Used:

The expression to calculate theforce exerted by the cable on the helicopter is,

  $F=F_t$

Calculation:

Substitute all the values in the above expression.

  $F=13250\text{N}$

Conclusion:

Thus, the force exerted by the cable on the helicopter is $13250\text{N}$ .