A model of a helicopter rotor has four blades, each of length 3.50 m from the central shaft to the blade tip. The model is rotated in a wind tunnel at a rotational speed of 580 rev/min .
a) What is the linear speed of the blade tip?
_____ m/s
b) What is the radial acceleration of the blade tip expressed as a multiple of the acceleration of gravity, g?
______g
thanks in advance guys!
2007-02-06 19:20:08 · 6 answers · asked by Anonymous in Science & Mathematics ➔ Physics
try to wikipedia my dear
2007-02-06 19:29:30 · answer #1 · answered by Edrew c 2 · 0⤊ 2⤋
a) One revolution has a distance of C = 2πr = 2π(3.50) = 22.0 m, and takes time 60 / 580 = 0.103 seconds. So the linear speed is 22.0 / 0.103 = 213 m/s.
b) a = v^2 / r = 213^2 / 3.50 = 1.29 x 10^4 m/s^2 = (1.29 x 10^4 / 9.81) g = 1.32 x 10^3 g.
2007-02-06 19:27:12 · answer #2 · answered by Scarlet Manuka 7 · 2⤊ 0⤋
linear speed of the blade tip is equal to
v = r * w
r = 3.50 meters
w is the angular velocity in radians per second
1 rad /s = 9.549 rev per min ( 1 rpm = 2pi rad / min = 2pi / 60 rad / sec )
thus
1 rpm = 1 / 9.549 rad / s
580 rpm = 580 / 9.549 rad / s
w = 60.73 rad / s
v = 3.5 * 60.73 = 212.58 m /s
radial acceleration is given by
ar = v^2 / r
ar = 212.58 * 212.58 / 3.5 = 12911.501 m / sec^2
ar ( g ) = 12911.501 / 9.8 = 1317.5gs
2007-02-06 19:44:47 · answer #3 · answered by raza_matrix 1 · 1⤊ 0⤋
(a)V=wR,where V=velocity
w=rotational speed
R=radius
V=(580/60)x2x3.142x3.5
=212.6m/s
(b)a=v^2/R,where a=acceleration
v=velocity
R=radius
a=212.6^2/3.5
=12915m/s^2
so when express in multiple of g
=1291.5g
2007-02-06 19:31:48 · answer #4 · answered by yan 2 · 0⤊ 0⤋
I checked. Your method and final answer are correct. Why do you think your answer is wrong? Did you enter the answer in some online site? If so, then are you sure that the site expects the answer in kg?
2016-05-24 02:17:56 · answer #5 · answered by Anonymous · 0⤊ 0⤋
This is a good question, and one that intrigued me for quite a long time.
2016-08-23 17:18:40 · answer #6 · answered by ? 4 · 0⤊ 0⤋