Chapter 5: Q92P (page 123)

Compute the initial upward acceleration of a rocket of mass $1.3 \times 10^{4} kg$ if the initial upward force produced by its engine (the thrust) is $2.6 \times 10^{5} N$ . Do not neglect the gravitational force on the rocket.

Short Answer

Expert verified

The initial upward acceleration of the rocket is $10 m / s^{2}$ .

Step by step solution

Given information

$m = 1.3 \times 10^{4} k g$
role="math" localid="1660908233149" $T = 2.6 \times 10^{5} N$

Understanding the concept

Acceleration of an object produced by a net force is directly proportional to the product of mass and acceleration is known as Newton’s second law of motion. So, to calculate net force use the mass of the object and acceleration of the object.

Formula

$F_{n e t} = m \times a$

Here, $F_{net}$ is the force, m is the mass of the object, and a is the acceleration of the object.

Calculate the initial upward acceleration of the rocket

The net force acting on the rocket is given as,

$F_{n e t} = T - m \times g$

But according to Newton’s second law,

$F_{n e t} = m \times a$

So,

$m \times a = T - m \times g 1.3 \times 10^{4} k g \times a = 2.6 \times 10^{5} N - 1.3 \times 10^{4} k g \times 9.81 m / s^{2} a = \frac{2.6 \times 10^{5} N - 1.3 \times 10^{4} k g \times 9.81 m / s^{2}}{1.3 \times 10^{4} k g} = 10 m / s^{2}$