As the drawing illustrates, a siren can be made by blowing a jet of air through 20 equally spaced holes in a rotating disk. The
time it takes for successive holes to move past the air jet is the period of the sound. The siren is to produce a 2338.6-Hz tone. What must be the angular speed ω (in rad/s) of the disk?
- We can tackle this question by simple direct proportion relation between angular speed for the disk to rotate a cycle that constitutes 20 holes. We will use direct relation with number of holes per cycle to compute the revolution per seconds i.e frequency of speed f.
1rev(20 hole) -> 20(cycle)/rev
2006.2(cycle) -> f ?
f = 2006.2/20 = 100.31rev at second
- The relation between angular frequency and angular speed is given by:
Applying the work-energy theorem, if we can neglect the friction between truck and road, the total change in kinetic energy must be equal to the work done by the external forces.
This work, is just 4,475 J.
So we can write the following equation:
where m= mass of the truck = 2.5*10³ kg.
So, we can find the speed v, as follows:
b)
The work done by the man, is just the horizontal force applied, times the displacement produced by the force horizontally:
