The LGM-118 Peacekeeper rocket: The exhaust velocity for solid rocket fuels is ~

Question

The LGM-118 Peacekeeper rocket:

The exhaust velocity for solid rocket fuels is ~3100 m/s. The first stage of this rocket burned for only 40 seconds. How much of the 49,000 kg of the first stage was fuel? What was the mass fraction (f) of the stage? What is the velocity at t = 40 seconds? What is the average acceleration during those forty seconds?

Here is the diagram that goes with this problem:

Stage | mass(kg) | T(MN) | Altitude (km)

1 49,000 2.20 23

--------------------------------------------------------------

2 27,000 1.20 58

--------------------------------------------------------------

3 7,700 0.29 213

--------------------------------------------------------------

payload 4,750 ------ 1120

Explanation / Answer

Payload = 4,750 Kg = Mass of rocket with empty fuel tanks

Mass of fuel = 49,000 - 4,750 = 44,250 kg

Mass Fraction = Mass of fuel/mass of Rocket with empty fuel tanks + 1 = 44250/4750 + 1= 10.3157

Velocity at end of stage 1 = 3100 * ln(10.3157) = 3100 * 2.333 = 7232.3 m/s

Average Accleration = Change in Velocity/Time = 7232.3/40 = 180.8075 m/s^2

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.