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 between any two surfaces are the same. Force diagram for mass m₂ is shown to the left .

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, (where g is the gravity field strength)

so the frictional force f₁₂ m₁ gu .

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

so the frictional force f₂ (m₁+m₂)gu

The tension of the rope is T.

For m₁ : f₁₂ = m₁a₁

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

otherwise f₂ = T and a₂= 0.

For m₂ : T - m₃ g = m₃a₃

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.