Frictional force

A mass m1 rest on top of another mass , m2, which is connected to m3 by a light rope

(passes over a frictionless pulley).

This java applet show the force diagram and the motion of the system when the frictional forces are present.

The mass of each block is shown at the lower-right corner.

Assume the coefficients of friction μ between any two surfaces are the same.

Force diagram for mass m2 is shown to the left .

（不同來源的作用力以各色箭頭代表）:

 Color of arrow black blue green cyan red yellow force gravity normal tension friction friction Net force on m2 source earth table rope m1 table

Click within the white area of each block to change its mass.

Click right mouse button to increase one mass unit,

click left mouse button to decrease one mass unit.

Press Start will start the animation,

click mouse button to suspend the animation, click it again to resume.

Press Reset for default parameters.

• Play it! and find out under what kind of condition:
1. m1 and m2 would not be accelerated? (Net force =0.)
2. m1 and m2 are accelerated together.
3. m1 and m2 are accelerated differently. (a1 ≠ a2 which one is larger?)

This is a sample gif picture.

The mass of the blocks are m1, m2, m3 , accelerations are a1 , a2 , a3 .

The normal force between m1 and m2 : N12= m1 g,

so the frictional force f12 ≦ m1 .

The normal force between m2 and the table : N2= (m1+m2) g

so the frictional force f2 ≦ (m1+m2) gμ

The tension of the rope is T

For m1f12 = m1 a1

For m2：If T > ( f12 + f2 ) then T - ( f12 + f2 ) = m2 a2

otherwise f2= T and a2 = 0.

For m2T - m3 g = m3 a3

From the above equations, we can find out the accelerations.

I did that calculation already! It is your turn to do it now! O.K.

Your suggestions are highly appreciated! Please click hwang@phy03.phy.ntnu.edu.tw

`Author：Fu-Kwun Hwang, Dept. of physics, National Taiwan Normal University`

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