Chapter 6, Problem 27A

Calculate the acceleration of a 300,000-kg jumbo jet just before takeoff when the thrust for each of its four engines is 30,000 N.

To determine

Theacceleration on a jumbo jet, for a given force on its engines

Answer to Problem 27A

The acceleration of the jet is $0.4{\text{m/s}}^2$

Explanation of Solution

Given:

A jumbo jet of mass 300,000-kg takes off by a force of 30,000 N on each of its four engines

Formula used:

Using Newton’s second law of motion, a body experiencing a force F gets accelerated in the direction of the force and its magnitude a is proportional to magnitude of the applied force. It also holds an inverse relation with the mass of the body m . This can be expressed as,

  $F=ma$

For a given force and mass of the object, the acceleration can be calculated as,

  $a=\frac{F}{m}$

Calculation:

Here, force experienced by each of the four engines is 30,000 N. Thus, the force on the four engines together is given by,

  $\begin{array}{c}F=4\times 30,000\\ =120,000\text{}\text{}\text{ N}\end{array}$

The mass of the jet is given as 300,000-kg . Since it is just before take-off, the effect of gravity is not considered.

Substituting the parameters in the expression for acceleration, its value can be obtained as,

  $\begin{array}{c}a=\frac{120,000}{300,000}\\ =\text{0}{\text{.4 m/s}}^2\end{array}$

Conclusion :

The acceleration of the jumbo jet for a given thrust is $0.4{\text{m/s}}^2$ .