App. maths (Static& Friction)

2009-10-23 7:49 am

1.A thin uniform wire AB is bent into the form of a semicircle.Find the inclination of AB to the vertical when the wire is freely suspended from A. A particle equal to the weight of the wire is now attached to B, find the new inclination of AB to the vertical.

2.An uniform lamina is in the form of a square ABCD of side 2 m,E is a point on AD such that ED=xm and the portion EDC is removed. Show that if the lamina is places in a vertical plane with AE on a rough horizontal surface it will topple if
x&gt;3- 根3.If x=1.5 and the weight of the lamina is W, find the least force which must be applied to the lamina to stop it toppling.

3.A particle rests on a rough plane inclined at an angle x to the horizontal. The coefficient of friction between the particle and the plane is y.When the weight of the particle is W, a horizontal force of magnitude P just prevents the particle from slipping down the plane. If however a force of magnitude 2P acts parallel to the plane, the particle is on the point of slipping up the plane. The same force acting on a particle of weight 2W just prevents if from slipping down the same plane. find the values of x and y,and express P in terms of W.

回答 (1)

Prof. Physics

2009-10-25 3:05 am

✔ 最佳答案

I suggest you separate it into three posts next time.

2009-10-23 09:03:53 補充：
I should post my answer in two days, because you have asked so many questions.

2009-10-24 19:05:39 補充：

圖片參考：http://i601.photobucket.com/albums/tt95/physicsworld9999/physicsworld06Oct241904.jpg?t=1256382325

3. Maximum frictional force, f = yWcosx

Normal reaction, R = Wcosx

When it is at the point of slipping down the
plane,

Vertical: Rcosx + fsinx = W

Wcos2x + yWsinxcosx = W

cos2x + ysinxcosx = 1

ysinxcosx = 1 – cos2x = sin2x

y = tanx … (1)

Horizontal: Rsinx + fcosx = P

Wsinxcosx + yWcos2x = P

P = Wcosx(sinx + tanxcosx) = 2Wsinxcosx … (2)

When it is at the point of slipping up the plane,

Along the plane: 2P = Wsinx + f

2P = Wsinx + yWcosx = W(sinx + tanxcosx)

P = Wsinx … (3)

Put (3) into (2),

cosx = 1/2,

x = 60*

For (1), y = tan60* = √3

P = Wsin60* = W√3 / 2

參考: Physics king

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