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

__Friction Problems 3__

*Problem A*

An object of mass

**can slide on a horizontal table. Two weights of masses**

*M***and**

*M*_{1}**are attached to it on both sides of a table with weightless thread as on this picture.**

*M*_{2}Assuming mass

**is greater than**

*M*_{1}**, the object will start sliding to the left under a pull of a bigger weight.**

*M*_{2}Tensions

**and**

*T*_{1}**, as well as friction act on an object on a table.**

*T*_{2}Assume that this object, as a result of actions of these forces, moves with acceleration

**.**

*a*What is the friction coefficient

**and magnitudes of tensions**

*μ***and**

*T*_{1}**?**

*T*_{2}*Hint*:

Use the Second Newton's Law for each of three objects (one on a table and two weights) participating in the motion.

*Solution*:

For object on a table:

*T*_{1}− T_{2}− μ·M·g = M·aFor weight on the left:

*M*_{1}·g − T_{1}= M_{1}·aFor weight on the right:

*T*_{2}− M_{2}·g = M_{2}·aGot linear system of three equations with three unknowns: friction coefficient

**and magnitudes of tensions**

*μ***and**

*T*_{1}**.**

*T*_{2}