Math Is Fun Forum

missbossyy

Member

Registered: 2008-02-01

Posts: 38

Phys~~

A wind farm generator uses a two-bladed propeller mounted on a pylon at a height of 20
meters. The length of each propeller blade is 12 m. A tip of the propeller breaks off when
the propeller is vertical. At that instant, the period of rotation of the propeller is 1.2 sec.
The fragment flies off horizontally and strikes the ground at point P.
(A) Calculate the initial speed v0 of the tip as it is launched from the propeller.
(B) Calculate the horizontal distance from the base to point P.
(C) Calculate the angle from the vertical at which the tip strikes point P.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Phys~~

(A) The tangential speed of an object moving in circular motion is

, where T is the period and r the radius of its circular orbit. In this case, T is given to you as 1.2 s and r is the propellor-blade length, which is 12 m.

(B) Ignoring the horizontal motion for the time being, first find the time t[sub]0[/sub] it takes to drop vertically to the ground. Since it drops from rest, the equation of motion is

where h = 20 + 12 = 32 m.

Solve for t[sub]0[/sub]. Then the horizontal distance travelled is D = v[sub]0[/sub]t[sub]0[/sub], where v[sub]0[/sub] is as found in part (A).

(C) Let y be the vertical height of the tip at time t and x be the horizontal distance it has moved in this time. Then

Differentiate y with respect to x. Substituting x = D into the differentiated expression will give you the gradient of y with respect to x at the point the tip hit the ground. This is equal to the tangent of the angle to the horizontal at which the tip struck the ground. Hence the angle to vertical at which the tip struck the ground is the inverse cotangent of this gradient.

Last edited by JaneFairfax (2008-02-09 05:00:19)

missbossyy

Member

Registered: 2008-02-01

Posts: 38

Re: Phys~~

thank u so so so much