一道英文物理题A sign has a mass of 1050 kg,a height h = 1 m,and a w

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一道英文物理题

A sign has a mass of 1050 kg,a height h = 1 m,and a width W = 4 m.It
is held by a light rod of length 5 m that is perpendicular to a rough
wall.A guy wire at 23° to the horizontal holds the sign to the wall.
Note that the distance from the left edge of the sign to the wall is 1
m.

Suppose we rely upon friction between the wall and the rod to hold up
the sign (there is no hinge attaching the rod to the wall).What is the
smallest value of the coefficient of friction μ such that the sign will
remain in place?

由于墙面的支点不动,可以用力矩平衡
而N,f都是过支点的,所以对力矩贡献为0
所以
T*Lsin23=G*(L-W/2)
T=G(3/5)/sin23
然后你把N,f合成为F,那么这就是一个三力平衡问题
而且T和G大小方向都已经确定
所以F的大小和方向也已经确定
如果摩擦系数不够大
那么角a就达不到
因为tan a= f/N=μ
所以摩擦系数的临界值为tan a
μ>=tan a=f/N=(G-Tsin23)/Tcos23
=(G-G(3/5))/[G(3/5)cot 23]
=(1-(3/5))/[(3/5)cot23]
=(2/3)tan 23
约等于
0.283

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