Consider a small rocket engine attached to a rotating disk as shown above. You c
ID: 1515761 • Letter: C
Question
Consider a small rocket engine attached to a rotating disk as shown above. You can also see this experiment in action:
Rocket Wheel
Note: We're NOT using the data from the video.
The engine is mounted to the wheel at an angle ? = 15 degrees from a line tangent to the edge of the wheel as shown.
You find that when you light the rocket, the wheel will spin a total of 5.00 revolutions in a time 2.2 seconds while the rocket is still burning. What is the force (thrust) of the rocket, assuming the thrust is constant while it is burning?
The spinning wheel has a mass of 3.5 kg and a radius of 0.40 m, is a uniform disk, and the mass of the rocket can be neglected.
Give you answer in Newtons to at least three significant digits. You won't be graded on the number of digits you provide, this is just to be sure you don't get points deducted due to rounding errors.
Explanation / Answer
T = I alpha
rF sin theta = I alpha
rF sintheta = 1/2 * mr^2 alpha
theta = 5 revolutions = 5( 2pi rad/ 1 rev) = 31.4 rad
theta = 1/2* alpha* t ^2= (0.5) alpha (2.2)^2 = 2.42 alpha
alpha = 31.4/2.42 = 12.97 rad/s^2
F = 1/2 * 3.5 kg ( 0.4)^2 ( 12.97)/ 0.4 sin15
=70.2N