Answer to Question #141197 in Mechanics | Relativity for Jackson

Question

The first stage of the Saturn V space vehicle consumed fuel and oxidizer at the rate of 1.50 x 10^4 kg/s with an exhaust speed of 2.60 x 10^3 m/s. (a) Calculate the thrust produced by this engine. (b) Find the acceleration the vehicle had just as it lifted off the launch pad on the Earth, taking the vehicle’s initial mass as 3.00 x 10^6 kg.

Answer 1

a) thrust could be calculated using mass of fuel and oxidizer and exhaust speed. Engine accelerates substance with mass 1.5 x 10^4 kg to speed 2.6 x 10^3 every 1 second. And according to 3rd Newton's law same force impacts vehicle:

$F=m\times a=m\times\frac{V}{t}=1.5\times10^4\times \frac{2.6\times10^3}{1}=3.9\times10^7N$

b)

$F=m\times a;$

$a = \frac{F}{m}=\frac{3.9\times 10^7}{3\times 10^6}=13m/s$