再黎 app math。Statics & Friction

用戶250680

2009-03-04 6:58 am

A uniform rod AB of weight 2W is freely hinged at A. The rod is in equillibrium at an angle θ to the vertical when a horizontal force W acts at B.

Calculate θ and the reaction of the hinge on the rod.

Answer: 45 degree, sqrt(5) W

回答 (1)

Prof. Physics

2009-03-04 4:03 pm

✔ 最佳答案

Please have a look of the following link:

http://i601.photobucket.com/albums/tt95/physicsworld9999/physicsworld01Mar040759.jpg

Let X, Y be the horizontal component and vertical component of the reaction of the hinge on the rod at A respectively.

Since the system is in equilibrium, hence the resultant force and the resultant torque on the system is zero.

Horizontal: X = W

Vertical: Y = 2W

So, the reaction of the hinge on the rod, R

= √[W^2 + (2W)^2]

= W√5

To calculate the value of θ, take moment about point A. (to eliminate as much forces as possible, to simply the calculation.)

2Wasinθ = W(2a)cosθ

tanθ = 1

θ = 45˚

參考: Physics king

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