摩擦力的討論 .

(a) Let Rw and Rg be the normal reactions given by the wall and ground respectively on the ladder.
W be the weight of the ladder, and Ff be the frictional force on ground.

Hence, for equilibrium in the vertical direction:
W = Rg --------------- (1)
For equilibrium in the horizontal direction:
Ff = Rw ---------------- (2)

Taking moment about the foot of the ladder,
(Rw).L.sin(a) = W.(L/2).cos(a)
where L is the length of the ladder (and assume the centre of mass of the ladder is at tits mid-point).
a is the angle at which the ladder makes with the ground.

Hence, Rw = W/(2.tan(a)) ------------ (3)
or Ff = W/(2.tan(a)) [using equation (2)]
When the foot of the ladder is made closer to the wall, angle a will increase. Thus than(a) increases, and W/(2.tan(a)) decreases.
Therefore, Ff, the frictional force, decreases.

(b) From equation (3), Rw, the reaction on the wall, also decreases.

(a)地板對梯子的靜摩擦力, 減少
(b)牆對梯子的力, 減少

這個問題關於torque.
你需知道
the gravity of ladder = the reaction force by ground
friction = the reaction force by wall
因為x-axis and y-axis 的力需相同.
首先你take momnet about the contacting point of wall.
Assume the wall on the left side.
clockwise force: friction, gravity
anti-clockwise force, reaction by ground.
*the moment arm of the reaction force by wall, so can be ignore.

The friction force is to balance the clockwise force to enable the system being stable.

As the ladder is moving to the wall, the moment arm of both the gravity of ladder and the reaction force by ground decrease. Thus, the excess anti-clockwise force decreses. the required friction thus decreases. friction = the reaction force by wall. Thus , (b)牆對梯子的力, 減少