兩個物件接觸時，接觸表面面積越大係唔係代表兩物之間摩擦力越大

摩擦力係同接觸面積無關的！！！

如果有讀到AL Phy的話，一定會學到一條式：f = kR。

f 是摩擦力；k 是摩擦系數；R 是法線作用力(Normal Reaction)。

摩擦系數是一個常數constant，視乎２件接觸物的表面構造／物質而定，比如說表面愈粗糙的東西摩擦系數會愈大，所以其摩擦力亦愈大。這就可解釋到為甚麼有底紋的鞋更不易滑到了。

至於R，通常等於其物件之重量，故２件相同物質及表面構造的東西在同一個平面上重一點的那個會難推，因為其與地面的摩擦力更大。

You have mixed up the frictional force due to sliding between two surfaces with the "gripping force" produced by the grooves at the bottom of your shoes.

No surface is perfectly smooth. There are tiny humps and bumps on any surface. When you walk on a surface with shoes that have deep grooves, these grooves, in fact, lock onto the tiny humps and bumps, thus preventing you from slipping. Such "locking effect" is more prominent if you walk on rugged muddy road.

根據你嘅理論,船同滑雪板等應該都行5到先arm........
除左摩擦系數之外,
鞋底有底紋嘅另外一個目的就系加重向地面下壓嘅力量
因為下壓越大,摩擦力(抓地力)都會越大

比多條formula你(你嘅case應該系滑動摩擦)
滑動摩擦
F= µ x Fn
滑動摩擦力總是比最大靜摩擦力要小。它由垂直於摩擦面的力FN和滑動摩擦係數µ決定，它與滑動面之間的相對速度和面積無關。摩擦係數由滑動面的物質、粗糙度和（可能存在的）潤滑劑所決定。

滑動摩擦力可以做正功也可以做負功，取決於滑動摩擦力的方向與物體對參考系的位移之間的夾角。滑動摩擦力作用所產生的內能（通常表現為溫度升高）則為滑動摩擦力與兩物體相對的位移的乘積。

Frictional force is independent of the contact surface area. Generally, the frictional force is given by the equation
F = uN , u = coefficient of static friction,
N = reaction force given by the ground
u is determined by the nature of the surface (i.e. what the surface is made of)
Actually, the reason why the frictional force is independent of area can be explained as follows:
When two surface joins, friction arises due to the tiny bumps of the surface (no surface is completely smooth!). Let the area be A0. And actually, frictional force is not evenly distributed through out the surface (as the bumps are not evenly distributed). So let the frctional force be distributed in k0 points.
Now with the same object but a larger contact surface area A (A > A0), there are k1 (k1 > k0) number of points. However, with more points, the force on each point is smaller. So the fricitonal force on the whole stays the same.