Unizor - Physics4Teens - Mechanics - Dynamics - Friction - Problems 3

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



Friction Problems 3



Problem A



An object of mass M can slide on a horizontal table. Two weights of masses M₁ and M₂ are attached to it on both sides of a table with weightless thread as on this picture.



Assuming mass M₁ is greater than M₂, the object will start sliding to the left under a pull of a bigger weight.

Tensions T₁ and T₂, as well as friction act on an object on a table.

Assume that this object, as a result of actions of these forces, moves with acceleration a.

What is the friction coefficient μ and magnitudes of tensions T₁ and T₂?



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:

T₁ − T₂ − μ·M·g = M·a

For weight on the left:

M₁·g − T₁ = M₁·a

For weight on the right:

T₂ − M₂·g = M₂·a

Got linear system of three equations with three unknowns: friction coefficient μ and magnitudes of tensions T₁ and T₂.