A mass m_{1 }rest on top of another mass , m_{2}, which
is connected to m_{3 }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 m_{2 }is shown to the left .

Color of arrow | black | blue | green | cyan | red | yellow |

force | gravity | normal | tension | friction | friction | Net force
on m |

source | earth | table | rope | m_{1} |
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.

- m
_{1}and m_{2}would not be accelerated? (Net force =0.) - m
_{1}and m_{2 }are accelerated together. - m
_{1}and m_{2 }are accelerated differently. (a_{1}a_{2}which one is larger?)

This is a sample gif picture.

The mass of the blocks are m_{1}, m_{2},
m_{3 }, accelerations are a_{1
}, a_{2 }, a_{3 }.

The normal force between m_{1 }and m_{2} : N_{12
}= m_{1} g, (where g is the gravity field strength
)

so the frictional force f_{12 }
m_{1} g£g .

The normal force between m_{2 }and the table : N_{2
}= (m_{1}+m_{2}) g

so the frictional force f_{2 }(m_{1}+m_{2})
g£g

The tension of the rope is T¡C

For m_{1} ¡G f_{12} = m_{1}
a_{1}

For m_{2}¡GIf T > ( f_{12}
+ f_{2} ) then T - ( f_{12}
+ f_{2} ) = m_{2} a_{2}

otherwise f_{2 }= T and a_{2}
= 0.

For m_{2}¡G T - m_{3} g = m_{3}
a_{3}

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¡GFu-Kwun Hwang, Dept. of physics, National Taiwan Normal University

Last modified :