Exemplo 8.8 de College Physics, 8.7 Introduction to Rocket Propulsion

Calculating Acceleration: Initial Acceleration of a Moon Launch

Problema e solução em inglês, como no livro original.

A Saturn V’s mass at liftoff was $2 . 80 \times 10^{6} kg$ , its fuel-burn rate was $1 . 40 \times 10^{4} kg/s$ , and the exhaust velocity was $2 . 40 \times 10^{3} m/s$ . Calculate its initial acceleration.

Resolva no papel primeiro. Depois abra a solução um passo de cada vez e pare assim que conseguir terminar sozinho.

Estratégia
This problem is a straightforward application of the expression for acceleration because $a$ is the unknown and all of the terms on the right side of the equation are given.
Solução
Substituting the given values into the equation for acceleration yields
$\begin{array}{l} a & = & \frac{v_{e}}{m} \frac{Δ m}{Δ t} - g \\ = & \frac{2 . 40 \times 10^{3}}{2 . 80 \times 10^{6}} (1 . 40 \times 10^{4} kg/s) - 9 . 80 {m/s}^{2} \\ = & 2.20 {m/s}^{2} . \end{array}$
8.79
Discussão
This value is fairly small, even for an initial acceleration. The acceleration does increase steadily as the rocket burns fuel, because $m$ decreases while $v_{e}$ and $\frac{Δ m}{Δ t}$ remain constant. Knowing this acceleration and the mass of the rocket, you can show that the thrust of the engines was $3 . 36 \times 10^{7} N$ .

0 de 3 passos abertos

Como foi?

Estratégia

Solução

Discussão

Estratégia

Solução

Discussão