原帖由 abc666 於 8/4/2009 10:35 AM 發表
當一件物件放在一條斜坡上
normal reaction on 物件by斜坡是(angle to horizontal=X)
R=mg cosX
還是
R=mg / cosX
當物件不動,或向下滑動時
或斜坡有friction或沒friction
或物件在preform circular motion ...
R = mg cosX
in the cases that the inclined plane is smooth or rough, no matter the object is sliding down or not.
Note that there are only 3 forces exerted on the object (weight, normal reaction and friction)
Resolve mg respectively into components along and perpendicular to the inclined plane
Components along the plane=mg cos X
Components perpendicular to the plane=mg sinX
Components along the plane is balanced.Therefore, R = mg cosX
EDIT:匆忙間打錯了
Components perpendicular to the plane=mg cos X
Components along the plane=mg sinX
Components perpendicular to the plane is balanced.Therefore, R = mg cosX
When the object is performing HORIZONTAL circular motion without friction,
components along the plane is NOT balanced.
(The reason is that the resultant force is the centripetal force pointing towards the centre,which can be resolve into components along and perpendicular to the inclined plane)
So R= mg cosX does not hold.
Consider the vertical components of forces.
Note that the object is moving on a horizontal plane.
Therefore, vertical components of forces is balanced.
R cosX = mg
R = mg / cos X
In addition, solving the velocity can be done by the following steps.
Vertical components of forces contribute to centripetal force.R sinX = mv^2/r
v=sqrt(gr tanX) (sqrt=square root)
p.s. circular motion 這部分在今天的 Applied paper I 價值兩分
When the object is performing HORIZONTAL circular motion WITH friction,
Consider the vertical and horizontal components of forces.
EDIT:For v<designated speed,i.e. friction f is pointing upwards
R cosX = mg - f sinX
R sinX - f cosX = mv^2/r
EDIT:For v>designated speed,i.e. friction f is pointing downwards
R cosX = mg + f sinX
R sinX + f cosX = mv^2/r
Obviously,R changes.
Solving the velocity 是我今天不夠時間想的那部分
想到了,原來今早被自己局限了,概念沒錯可是想不下去(淚目*2036)
Only consider the friction point downwards.
For the case surface in contact is small
For the case a plane is in contact
Then take moment about centre of gravity.
Moment about centre of gravity = 0
[ 本帖最後由 超夢夢的夢境 於 8/4/2009 09:01 PM 編輯 ] |
發表於 8/4/2009 10:35 AM 
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