极限摩擦

极限摩擦被定义为在彼此接触的两个静态表面之间产生的摩擦。彼此接触的两个静态表面之间可能产生的最大摩擦。一旦施加在两个表面上的力超过极限摩擦，就会发生运动。

对于两个干燥的表面，极限摩擦力是法向反作用力与极限摩擦系数的乘积。换句话说，可以在两个表面之间施加的摩擦量是有限的，并且如果使作用在身体上的力足够大，则将发生运动。

因此，我们可以将极限摩擦定义为当物体刚好在另一个物体的表面上滑动时发挥作用的静摩擦力的最大值。

极限摩擦定律

以下是限制摩擦的定律：

(a)限制摩擦力的方向和运动的方向总是相反的。

(b)极限摩擦力始终与相接触的两个表面相切。

(c)两个表面之间的极限摩擦力大小和法向力成正比。

(d)极限摩擦取决于材料，接触表面的性质以及光滑度。

(e)极限摩擦与表面的形状和面积无关。

极限摩擦的例子

以下是极限摩擦的一些示例：

1. 当我们在路上行走时。
2. 当汽车在悬崖上行驶时。
3. 上游水对游泳者施加的摩擦力。
4. 页面或笔记本在笔上的摩擦力。
5. 在地面上移动物体。
6. 停在山丘上的汽车不会滑下来。这是因为限制摩擦的值足够高以确保轿厢处于静止状态。摩擦的极限力与物体的质量成正比。
7. 由于静摩擦力高，推重车似乎非常困难
8. 当我们推动任何物体时，我们会遇到静摩擦一段时间，直到达到极限摩擦值为止。

公式及其推导

因此，我们可以将极限摩擦定义为当物体刚好在另一个物体的表面上滑动时发挥作用的静摩擦力的最大值。极限摩擦力是法向力与极限摩擦系数的乘积。

以下是数学表示形式：

施加到身体上的摩擦力始终与作用在身体上的法向力成正比。

$F\propto N$

为了删除比例符号，我们引入一个常数$\mu$ 。

现在， $F = \mu \times N$

$F =\mu N$

在哪里，

F is the limiting friction

$\mu$  is the coefficient of limiting friction

N is the normal force

问题：求出施加在摩擦系数为5且极限摩擦为50 N的物体上的法向力。

解决方案：

As we know$F =\mu N$

Where,

F is the limiting friction

$\mu$ is the coefficient of limiting friction

N is the normal force

$N = \frac{F}{\mu} = \frac{50}{5}$

N = 10 N

样题

问题1：限制摩擦的别称是什么?

回答：

It is the maximum value of friction. Thus limiting friction is also called as maximum value of friction.

问题2：静摩擦和极限摩擦有什么区别?

回答：

Static friction is a self-adjusting force because it comes into play when the body is lying over the surface of another body without any motion. When that body overcomes the force of static friction, the maximum value of static friction is reached, which is known as limiting friction.

问题3：动摩擦与极限摩擦之间的关系是什么?

回答：

When the applied force, F, is increased further (beyond the limiting frictional force), the body begins to move, then the force opposing the motion is called the kinetic or sliding friction. The kinetic friction is less than the limiting friction.

问题4：为什么动摩擦小于极限摩擦?

回答：

Initially it requires more force to break the interlock between the irregularities of two surfaces. But once the block is in motion, it takes time to interlock between the irregularities of two surfaces. Also, the body gains the inertia of motion. So, the kinetic friction is less than the limiting friction.

问题5：静摩擦或极限摩擦是否更大?

回答：

In short, static friction is the same as the force being applied because the body isn’t moving.Static friction is acting due to the body tends to move when a force is acting on it.Limiting friction is the friction acting on a body when it is about to start moving.Commonly, limiting friction is the highest.

问题6：极限摩擦力是否可变?

回答：

When that body overcomes the force of static friction, the maximum value of static friction is reached -which is known as limiting friction. After the limiting friction, the frictional force is not going to increase further. At this stage, the object moves overcoming the frictional force which is at a constant value.

数值问题

问题1.如果摩擦系数为0.2，则找到移动5公斤盒子所需的最小力。

解决方案：

Minimum force is nothing but the value of friction force due to frictional surface because if we apply force more then friction force than box can be move.

N = m×g

N = 5kg × 10 = 10 N

F = μ × N

F = 0.2 × 10 = 2 N

So, we require minimum 2N to move the box.

问题2。如果移动桌子所需的最小力为100 N，则当μ = 5时找到桌子的重量。

解决方案：

Minimum force required to move a table (F) =\mu \times N

Given, F = 100 N and \mu = 5

$F =\mu \times N$

$100 N = 5 \times N$

$N = \frac{100 N}{5} = 20 N$

$N = M\times g$

$20 = M \times 10$

$M = 2$

问题3.如果100千克的机器需要10000 N的力才能改变位置，则求出极限摩擦系数。( $g= 10\frac{m}{s^{2}}$ )

解决方案：

F = 10000 N

M = 1000 kg

N = m × g
N = 100 kg × 10
N = 1000 N
F = μ × N
10000 N = μ × 1000 N
μ = 10