Thursday, May 31, 2018

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

Notes to a video lecture on

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 Fup 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?


Fup = m·g·sin(φ)+μ·m·g·cos(φ)

a = g·sin(φ)−μ·g·cos(φ)


a = 2·g·sin(φ) − Fup/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 μs=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 μs given?

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


(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

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