Inclined Plane with Friction
المؤلف:
E. R. Huggins
المصدر:
Physics 2000
الجزء والصفحة:
273
24-11-2020
2940
Inclined Plane with Friction
In our analysis of the air cart on the inclined track, we mentioned that a frictionless surface exerts only a normal force on an object. If there is any sideways force, that is supposed to be a friction force 
. In Figure (1) we show a cart on an inclined plane, with a friction force included. The normal force 
is perpendicular to the plane, the friction force is parallel to the plane, and gravity still points down.
Figure 1: Friction force acting on the cart.
To analyze the motion of the cart when acted on by a friction force, we write Newton’s second law in the usual form
..........(1)
The only change is that we have added in the new force .
Since the motion of the cart is still along the plane, it is convenient to take the x axis along the plane as shown in Figure (2). Breaking Equation 1 up into x and y components now gives
...........(2a)
.........(2b)
From 2b we get,
Fn = mg cos θ...........(3)
which is the same result as for the frictionless plane.
The new result comes when we look at motion down the plane. Solving 2a for ax gives
ax = gsinθ – Ff /m.......... (4)
Not surprisingly, the friction force reduces the acceleration down the plane.
Figure 2
الاكثر قراءة في الميكانيك
اخر الاخبار
اخبار العتبة العباسية المقدسة
