Question

Single Stage 0.0/3.0 points (graded) Consider a rocket carrying 100,000 kg of propellant, 10,000 kg of structure, and 5000 kg of payload. What is the propellant fraction of this rocket? Round your answer to at least 2 decimal places (i.e., enter 0.25 to represent 25%) incorrect 1.100 What is the payload fraction of this rocket? Round your answer to at least 2 decimal places. incorrect 0.05 Recall that the relationship between specific impulse and exhaust velocity is: Vex=g0Isp . Assuming that Isp=450s and g0=9.81m/s2 , what is the value of ΔV in m/s that this rocket will produce if all the propellant is consumed in one stage? incorrect 4414

Answer 1

Answer: The Propellant fraction is 0.87.

The payload fraction is 0.04.

Δv = 8991.81 m/s

Explanation: To determine the fractions, first, calculate the total mass of the rocket:

`m_(t) = m_(prop) + m_(str) + m_(pay)`

`m_(t) = 100,000 + 10,000 + 5,000`

`m_(t) = 115,000`

The Propellant Fraction will be

`m_(prop) = (m_(prop))/(m_(t))`

`m_(prop) = (100,000)/(115,000)`

`m_(prop) =` 0.87

The Payload Fraction is:

`m_(pay) = (m_(pay))/(m_(t))`

`m_(pay) = (5,000)/(115,000)`

`m_(pay) =` 0.04

The value of Δv is calculated by the formula:

Δv =
`-V_(e). ln((m_(final))/(m_(initial)) )`

The exhaust velocity (
`V_(e)`) is:

`V_(e) = g_(0).Isp`

`V_(e) =` 9.81*450

`V_(e) =` 4414.5

`m_(final)` is the total mass after the rocket consume all the propellant and
`m_(initial)` is the total mass before the action.

Δv =
`-V_(e). ln((m_(final))/(m_(initial)) )`

Δv =
`-4414.5.ln((15,000)/(115,000) )`

Δv = - 4414.5.ln(0.13)

Δv = 8991.81

Δv will be 8991.81 m/s.