A Saturn V’s mass at liftoff was 2.80×10^6 kg , its fuel-burn rate was 1.40×10^4 kg/s , and the exhaust velocity was 2.40×10^3 m/s . Calculate its initial acceleration.

Question

A Saturn V’s mass at liftoff was [latex] 2.80×10^6 [/latex] kg , its fuel-burn rate was [latex] 1.40×10^4 [/latex] kg/s , and the exhaust velocity was [latex] 2.40×10^3 [/latex] m/s . Calculate its initial acceleration.

Strategy
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.

Accepted Answer

Substituting the given values into the equation for acceleration yields

[latex] a = \frac{v_e}{m} \frac{Δm}{Δt} − g[/latex] (8.79)

[latex] = \frac{2.40×10^3 m/s}{2.80×10^6 kg} (1.40×10^4 kg/s) − 9.80 m/s^2[/latex]

[latex] = 2.20 m/s^2 .[/latex]

Discussion

This value is fairly small, even for an initial acceleration. The acceleration does increase steadily as the rocket burns fuel, because m decreases while [latex] v_e and \frac{Δm}{Δt} [/latex] remain constant. Knowing this acceleration and the mass of the rocket, you can show that the thrust of the engines was [latex] 3.36×10^7 N [/latex] .

Question 8.8: A Saturn V’s mass at liftoff was 2.80×10^6 kg , its fuel-bur...

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