若一梯子長L 重可不計

用戶37276

2013-01-06 7:19 am

若一梯子長L 重可不計靠在牆與地上梯與斜牆傾斜西搭牆面光滑一個重W的人站立於梯的中間問梯子與牆和地面作用力各為若干若人稍往上爬梯子便開始下滑由此計算梯子與地面的靜摩擦係數

更新1:

梯子與牆和地面作用力各為 W/2tan西搭以及W*根號1/4tan平方西搭+1 梯子與地面的靜摩擦係數為1/2tan西搭

回答 (1)

天同

2013-01-06 8:58 am

✔ 最佳答案

At equilibrium,
vertical forces are balanced: W = R2, where R2 is the normal reaction at foot of ladder.
horizontal forces are balanced: R1 = Ff
where R1 is the normal reaction on the wall and Ff is friction on ground

But Ff = u.(R2) where u is the coefficient of static friction(靜摩擦係數 )
hence, R1 = u(R2) = uW
u = R1/W ---------------- (1)

Take moment about foot of ladder,
(R1).L.sin(a) = W.(L/2).sin(a) where a is the angle at which the ladder makes with the ground
R1 = W/2

From equation (1),
u = (W/2)/W = 1/2

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