[size=150][b]三、摩擦力的大小[/b][/size][br][br][b]1、静摩擦力的大小[br][br][/b]静摩擦力的产生是为了阻碍物体之间的分离。[br][br]假设我们给A物体一个大小为10N的向右的外力F，A受到外力必然想要运动，B为了阻止A运动，就会给A一个10N的反向的力，这就是B对A的静摩擦力。[br][br]对于B来说，这个摩擦力的大小只要[color=#980000]刚好[/color]能让A[color=#980000]保持和自己相对静止[/color]就可以了，所以静摩擦力的大小和外力的大小一样，即[math]f_静=F[/math]。

但接触面之间的齿能够提供的摩擦力是有限度的，这个摩擦力的最大值叫最大静摩擦力[math]f_{max}[/math]，外力超过[math]f_{max}[/math]后，物体就会滑动起来。[br][br]物体表面越粗糙，坑洼程度越大，最大静摩擦力会越大。[br][br]另外我们从微观角度可以看到，两个物体压得越紧，即正压力[math]F_N[/math]越大，啮合越深，物体越不容易被推动，最大静摩擦力[math]f_{max}[/math]也越大。

[br]通过实验我们得知，对于同一接触面，最大静摩擦力正比于压力，即[math]f_{max}\propto F_N[/math]。[br][br][math]f_{max}[/math]和[math]F_N[/math]之间的比例系数[math]\frac{f_{max}}{F_N}[/math]因两个接触物体的种类和接触面粗糙程度而异，我们称之为[color=#980000]静摩擦因数[/color]，记为[math]μ_0[/math]。[math]μ_0[/math]可以反映出物体的粗糙程度。[br][br][math]f_{max}[/math]和[math]μ_0[/math]同样是正比关系，[math]μ_0[/math]越大，[math]f_{max}[/math]也越大。[br][br]我们可以在实验室测出两个物体之间的静摩擦因数[math]μ_0[/math]并记录下来，下次碰到就可以直接使用[math]f_{max}=μ_0F_N[/math]计算出最大静摩擦力。[br][br]注意，静摩擦力的大小只取决于平行于接触面方向上的外力，增大压力只会增大最大静摩擦力，不会改变静摩擦力本身的大小。[br][br]需要注意：[math]F_N[/math]是接触面上的正压力，不是重力，只有在水平面上，[math]F_N[/math]的大小才等于重力[math]G[/math]的大小。[br][img]data:image/png;base64,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[/img]

[color=#0000ff][b]例1[/b]：小明同学用右手竖直握着一个玻璃瓶向右匀速走去，下列的说法正确的是（　　）[br][br][img width=120px,height=95px]https://img.xkw.com/dksih/QBM/editorImg/2024/10/22/9357b158-5ca5-4448-988f-e7a5c2533558.png[/img][br][table][tr][td]A．玻璃瓶是运动的，所以不会受到静摩擦力[/td][/tr][tr][td]B．玻璃瓶受的静摩擦力的方向一定向左[/td][/tr][tr][td]C．握力增大时，玻璃瓶受的静摩擦力增大[/td][/tr][tr][td]D．小明同学的右手一定受到向下的静摩擦力[/td][/tr][/table][/color][br][color=#ff0000]解析：[br]玻璃瓶处于平衡状态，受力平衡。[br]静摩擦力沿着接触面方向，在竖直方向上。[br]它要平衡重力，所以静摩擦力的大小f=G，方向竖直向上。[br]增大握力，瓶子重力也不会改变，此时所需的静摩擦力大小仍为G。[br]瓶子受到向上的静摩擦力，反过来，小明的右手一定受向下的静摩擦力。[br]故选D[/color]

[color=#0000ff][b]例2[/b]:如图所示，重力为20N的物体置于水平桌面上，物体与桌面间的动摩擦因数为0.5， 现用8N的水平拉力[i]F[/i]拉物体，则物体所受摩擦力大小为（　　）[br][img]data:image/png;base64,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[/img][br]A．8N    B．0       C．2N    D．10N[br][br][/color][color=#ff0000]解析：[br]最大静摩擦力[math]f_{max}\geμG=10N[/math]，用8N的拉力F拉不动物块，此时物块所受摩擦力为静摩擦力，静摩擦力[math]f=F=8N[/math]，故选A。[/color]

[b]2、滑动摩擦力的大小[br][br][/b]滑动摩擦力是两物体相对滑动，因为齿面间的相互碰撞而产生的。[br][br]它的大小和最大静摩擦力一样和两个因素有关：物体表面间的粗糙程度和正表面的压力[math]F_N[/math]。表面越粗糙，压得越紧，滑动时越费劲，此时滑动摩擦力越大。

滑动摩擦力[math]f[/math]与[math]F_N[/math]的比例系数[math]\frac{f}{F_N}[/math]我们叫做[color=#980000]动摩擦因数[/color]，记为[math]μ[/math]。[br][br]动摩擦因素同样与物体表面的种类和粗糙程度有关，有了动摩擦因数，我们就可以根据压力计算出滑动摩擦力：[math]f=μF_N[/math][br][br]动摩擦因素[math]μ[/math]一般略小于静摩擦因数[math]μ_0[/math]，滑动摩擦力[math]f[/math]也会略小于最大静摩擦力[math]f_{max}[/math]。但一般情况下我们可以认为[math]μ[/math]和[math]μ_0[/math]一样大，滑动摩擦力[math]f[/math]大小就等于最大静摩擦力[math]f_{max}[/math]。[br][br]滑动摩擦力的大小[color=#980000]和物体滑动的速度以及是否受其他外力无关[/color]。物体只要在滑动，动摩擦因数[math]μ[/math]和压力[math]F_N[/math]不变，滑动摩擦力[math]f[/math]就不会变。

[color=#0000ff][b]例1[/b]：如图所示，质量为m=10kg的物体在粗糙水平面上向左运动，物体与水平面间的动摩擦因数μ=0.1，物体同时还受到大小为10N，方向向右的水平拉力[i]F[/i]的作用，则水平面对物体的摩擦力（[math]g取10m/s^2[/math]）（　　）[br][img]https://www.helloimg.com/i/2024/11/09/672f43e4effce.png[/img][br]A．大小是10N，方向水平向右                                                   B．大小是10N，方向水平向左[br]C．大小是20N，方向水平向右                                                   D．大小是20N，方向水平向左[br][br][/color][color=#ff0000]解析:[br]物体的滑动摩擦力大小与物体本身的速度和其他平行于接触面的外力无关，f=μmg=10N。[br]物体相对地面向左运动，摩擦力的方向水平向右，选A。[/color]

[color=#0000ff][b]例2：[/b]（多选）如图所示，用水平力[i]F[/i]将同种材料不同质量的物体压到一竖直墙壁上，下列说法正确的是（　　）[br][img width=108px,height=177px]https://img.xkw.com/dksih/QBM/editorImg/2024/11/5/a6405733-699b-4bc1-be0d-c441b9d95a37.png[/img][br][/color][table][tr][td][color=#0000ff]A．若物体保持静止，则[i]F[/i]越大，物体所受摩擦力越大[/color][/td][/tr][tr][td][color=#0000ff]B．若物体保持静止，则质量越大，物体所受摩擦力越小[/color][/td][/tr][tr][td][color=#0000ff]C．若物体沿墙壁向下滑动，则质量越大，物体所受摩擦力越大[/color][/td][/tr][tr][td][color=#0000ff]D．若物体沿墙壁向下滑动，则[i]F[/i]越大，物体所受摩擦力越大[/color][br][br][/td][/tr][/table][color=#ff0000]解析：[br]物体保持静止时，是静摩擦力，这个静摩擦力是为了平衡重力产生的，与压力无关，重力越大，这个静摩擦力越大，A错B对；[br]物体向下滑动时，是滑动摩擦力，滑动摩擦力和压力是正比关系，压力越大，摩擦力越大，此时重力不会影响摩擦力，C错D对。[/color]