M2~Rigid Body Equilibrium Assignment

百葉

2008-01-21 3:09 pm

A uniform rod AB of mass 20kg and length 1m is smoothly hingrd to a wall at A. AB makes an angle of 40度 to the downward vertical. The rod is held in this position by a light string acting at B, at an angle of 50度 to the upwards vertical.
Find the magnitude of the tension in the string.

回答 (1)

2008-01-21 7:03 pm

✔ 最佳答案

圖片參考：http://i263.photobucket.com/albums/ii157/mathmate/math/RigidBody.jpg
Figure 1
Here there are three forces acting on the rigid bar, namely the reactions at A, the weight of the bar W=20 kg, and tension T of the rope at B.
The problem can be easily solved by taking moments about A, in which case we eliminate the unknown forces due to reactions.
Anti-Clockwise moments=TLsin(90)
Clockwise= 20Lsin(40)/2
So by equating and simplifying,
TLsin(90) = 20Lsin(40)/2
T=20sin(40)/sin(90)/2
=6.428 kg

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