Systems of Objects with Friction Video Lessons

Concept

# Problem: A small box of mass m1 is sitting on a board of mass m2 and length L. The board rests on a frictionless horizontal surface. The coefficient of static friction between the board and the box is μs. The coefficient of kinetic friction between the board and the box is, as usual, less than μs.Throughout the problem, use g for the magnitude of the acceleration due to gravity. In the hints, use Ff for the magnitude of the friction force between the board and the box.Find Fmin, the constant force with the least magnitude that must be applied to the board in order to pull the board out from under the the box (which will then fall off of the opposite end of the board).Express your answer in terms of some or all of the variables mus, m1, m2, g, and L. Do not include Ff in your answer.

###### FREE Expert Solution

In this problem, the surface is frictionless.

The frictional force, Fr is acting between the board and the box.

We also need to note that the system is being accelerated from the applied force.

The box will experience a force that acts against friction, given by:

$\overline{){{\mathbf{F}}}_{{\mathbf{r}}}{\mathbf{=}}{{\mathbf{m}}}_{{\mathbf{1}}}{\mathbf{a}}}$

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###### Problem Details

A small box of mass m1 is sitting on a board of mass m2 and length L. The board rests on a frictionless horizontal surface. The coefficient of static friction between the board and the box is μs. The coefficient of kinetic friction between the board and the box is, as usual, less than μs.

Throughout the problem, use g for the magnitude of the acceleration due to gravity. In the hints, use Ff for the magnitude of the friction force between the board and the box.

Find Fmin, the constant force with the least magnitude that must be applied to the board in order to pull the board out from under the the box (which will then fall off of the opposite end of the board).

Express your answer in terms of some or all of the variables mus, m1, m2, g, and L. Do not include Ff in your answer.