Question

Model rocket engines are sized by thrust, thrust duration, and total impulse, among other characteristics. A size C5 model rocket engine has an average thrust of 5.26 N, a fuel mass of 12.7 g, and an initial mass of 25.5 g. The duration of its burn is 1.90 s. i. What is the average exhaust speed of the engine? (2 marks) ii. If this engine is placed in a rocket body of mass 53.5 g, what is the final velocity of the rocket if it is fired in outer space? Assume the fuel burns at a constant rate.

Answer 1

The average exhaust speed of the C5 model rocket engine is approximately 787.40 m/s, and when placed in a rocket body of 53.5 g in outer space, the final velocity of the rocket would be about 22.2 m/s, assuming constant burn rate and no external forces.

Step-by-step explanation:

Calculating the Average Exhaust Speed
To find the average exhaust speed (ve) for the C5 model rocket engine, we use the rocket equation (Tsiolkovsky rocket equation) which is ve = (Thrust × Burn time) / Mass of fuel. Substituting in the given values (Thrust = 5.26 N, Burn time = 1.90 s, Mass of fuel = 0.0127 kg), we calculate the average exhaust speed as follows: ve = (5.26 N × 1.90 s) / 0.0127 kg which gives an average exhaust speed of approximately 787.40 m/s.

Finding the Final Velocity in Outer Space
Using the conservation of momentum and assuming constant exhaust velocity, we apply the rocket equation Δv = ve × ln(m_initial/m_final), where the total initial mass is the rocket body plus the initial engine mass and the final mass is just the rocket body. With the given data (Rocket body mass = 0.0535 kg, Initial engine mass = 0.0255 kg, Exhaust velocity from previous calculation = 787.40 m/s), we find the final velocity Δv = 787.40 m/s × ln((0.0535 kg + 0.0255 kg)/0.0535 kg). This results in a final velocity of approximately 22.2 m/s.