Worksheet 5: Rocket Science - Modeling Physics

Impulsive Force Model Worksheet 5:
Rocket Science
1. Read: In working with propulsion due to a fluid, it is very helpful to rearrange the impulsemomentum
theorem from: F net ∆t = ∆(mv) to F net = (∆m/∆t) ∆v, where ∆m/∆t is called the mass
flow rate, i.e. the number of kilograms of propelled fluid per second, ∆v is the change in velocity of the
fluid, and F net is the net force on the fluid, which is equal to the thrust force on the propeller or rocket.
2. A motorboat’s propeller has a diameter of 20 cm.
a. When the boat is cruising at 10 m/s, determine the mass flow rate through the propeller
region. Imagine that the propeller simply accelerates the cylinder of water it passes through. (Water’s
density is 1000 kg/m 3 )
b. Find the water exhaust velocity needed to produce 1200 N of thrust on the boat.
3. An airplane’s propeller has a diameter of 1.8 m.
a. When the plane is cruising at 60 m/s, determine the mass flow rate through the propeller
region. Imagine that the propeller simply accelerates the cylinder of air it passes through. (Air’s
density is 1.16 kg/m 3 )
b. When the incoming air is accelerated from 60 m/s to an exhaust velocity of 150 m/s, find the
thrust on the plane.

4. The space shuttle’s main engines spray out 736,000 kg of water vapor at 4500 m/s by chemically
combining hydrogen and oxygen for 460 seconds. Find the average thrust force provided by the main
engines.
5. A 0.36 kg soda bottle rocket holds 1.5 kg of water as it sits upon the launch pad. The rocket expels
all of the water in 0.7 seconds producing a rocket burnout velocity of 33 m/s. (The burnout velocity is
the rocket’s velocity once thrust ceases.)
a. Draw a force diagram for the 0.7 s thrust phase of the launch.
b. Determine the mass flow rate for the rocket.
c. Determine the rocket’s average acceleration for the 0.7 s thrust phase of the launch. When is
the instantaneous acceleration of the rocket the greatest and the least
d. Determine the average net force on the rocket.
e. Determine the exhaust velocity of the water ejected from the rocket.