Unizor - Physics4Teens - Mechanics - Dynamics - Friction - Problems 1

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



Friction Problems 1



Problem A



There is an object of mass m on an inclined plane that makes angle φ with horizon.

To move this object up on this inclined plane with constant speed you need to apply a force F_up directed uphill.

The coefficient of friction is unknown.

Let's assume that, left by itself, the object would slide down the
inclined plane under its own weight. The free fall acceleration is g, so the weight of an object of mass m is m·g.

What is the acceleration a of an object when it moves downhill under its own weight?



Hint

F_up = m·g·sin(φ)+μ·m·g·cos(φ)

a = g·sin(φ)−μ·g·cos(φ)



Answer:

a = 2·g·sin(φ) − F_up/m





Problem B



An object is lying on a horizontal platform that moves with acceleration a=10 m/sec².

The coefficient of kinetic friction between an object and a surface of a platform is μ=0.3, while coefficient of static friction is μ_s=0.4.

The free fall acceleration is g=9.8m/sec², so the weight of an object of mass m is m·g, but mass m is unknown.

(a) How the object will behave?

(b) Why was coefficient of static friction μ_s given?

(c) What is the acceleration of the object relative to the ground and relative to the platform?



Answer:

(a) The object will slide back along the platform's surface, but forward relative to the ground.

(b) If the coefficient of static friction is too high, the object will
not change its position relatively to a platform, and the next question
would make no sense.

(c) Relative to the ground acceleration is a₀=g·μ=2.94m/sec².

Relative to the platform acceleration is a₁=a₀−a=−7.06m/sec²