about fiction compensated runway
a trolley slide down on the fiction compensated runway,why the frictional force acting on the trolley is not zero??
according to your answer,you mean there is 2 forces acting on the tolley?
one is the accelaration due to gravity,another is the mg(sinX).and mg(sinX) have already balance by the friction,but the accelaration due to gravity is not yet balance.
- 1 十年前最愛解答
frictional force acting on the trolley still exists.
but it is COMPENSATED by the acceleration of gravity acting on the trolley
so the trolley slides with a constant speed
- 魏王將張遼Lv 71 十年前
In fact, the component of the trolley's weight down the inclined plane is equally balanced out by the friction on the plane (which is up the inclined plane).
Suppose the angle of inclination of the plane is x, friction is F and the mass of trolley is m, then:
Component of the trolley's weight down the inclined plane = mg sin x
Component of the trolley's weight normal to the inclined plane = mg cos x
By the rule of friction compensated, F = mg sin x (in magnitude)
Moreover, if u is the coefficient of the plane, then u(mg cos x) = F since the magnitude of the normal reaction on the trolley by the plane is equal to the component of the trolley's weight normal to it.
u(mg cos x) = mg sin x
u = tan x資料來源： My Physics knowledge