Unizor - Physics4Teens - Mechanics - Dynamics - Friction - Problems 2

Notes to a video lecture on http://www.unizor.com



Friction Problems 2



Problem A



There is a ramp of mass M and angle φ to horizon, lying, but not fixed, on a horizontal surface (it's like a triangular prism lying on a side).

An object of mass m slides down this ramp. As it slides, the ramp also moves along the horizontal surface it's lying on.

What is the acceleration of a ramp relative to a horizontal surface, as
object slides down, if the coefficient of friction between an object and
a ramp is μ₀, and the coefficient of friction between a ramp and a horizontal surface is μ₁?

The free fall acceleration is g, so the weight of an object of mass m is m·g.



Hint:

(1) Review Problem B from Mechanics - Dynamics - Superposition of Forces - Inclined Plane of this course.

(2) Take into account that, according to the Third Newton's Law,
friction between an object and a ramp is, on one hand, a force exhorted
by a ramp that pulls object uphill against its sliding downhill and, on
the other hand, is an action of an object on the ramp in an opposite
direction, slowing its horizontal movement.