Chapter 6, Problem 14P

A 17,000-kg jet takes off from an aircraft carrier via a catapult (Fig. 6-39a). The gases thrust out from the jet's engines exert a constant force of 130 kN on the jet; the force exerted on the jet by the catapult is plotted in Fig. 6-39b. Determine the work done on the jet: (a) by the gases expelled by its engines during launch of the jet; and (b) by the catapult during launch of the jet.

Figure 6-39

To determine

The work done on the jet by the gases expelled by its engines during the launch of the jet.

Answer to Problem 14P

Solution: $\text{1}{\text{.1×10}}^{\text{7}}\text{J}$

Explanation of Solution

Area under force-displacement graph gives work done by the force.

Given:The gases thrust out from the jet’s engines exert a constant force of $\text{13}0\text{ kN}$ and a graph of force as a function of displacement

Formula used: Work done:

  $W=F\cdot d$

Where, F is the applied force and d is the displacement.

Work done = Area under F-x curve

Calculation:

The gases thrust out from the jet’s engines and exert a constant force.

Therefore, work done by the gas is:

  $W=\text{ Fdcos}\theta$

  $\begin{array}{c}W=\text{ 130}\times {\text{10}}^{\text{3}}\times 85\times \cos 0\\ =\text{1}{\text{.1×10}}^{\text{7}}\text{J}\end{array}$

Conclusion:The work done on the jetby the gases expelled by its engines during the launch of the jet is $\text{1}{\text{.1×10}}^{\text{7}}\text{J}$ .

To determine

To Determine the work done on the jet by the catapult during the launch of the jet.

Answer to Problem 14P

Solution:The work done on the jet by the catapult during the launch of the jet is ${\text{5×10}}^{\text{7}}\text{J}$

Explanation of Solution

Area under force-displacement graph gives work done by the force.Given:The gases thrust out from the jet’s engines exert a constant force of $\text{13}0\text{ kN}$ and a graph of force as a function of displacement

Formula used:

Work done:

  $W=F\cdot d$

Where, F is the applied force and d is the displacement.

Work done = Area under F-x curve

Calculation:

The work done by the catapult during the launch of the jet is:

Work done = Area under F-x curve

  $\begin{array}{c}W=\frac{\text{1}}{\text{2}}\times 85\left(1100+65\right){10}^3\\ =4.95\times {10}^7\\ \simeq {\text{5×10}}^{\text{7}}\text{J}\end{array}$

Conclusion:The work done on the jet by the catapult during the launch of the jet is ${\text{5×10}}^{\text{7}}\text{J}$ .