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  • The disappearing force

    From Luigi Fortunati@21:1/5 to All on Sat May 14 11:05:28 2022
    In my animation
    https://www.geogebra.org/m/qc9pfvva
    there is the force of gravity <mg> (in black), the component parallel
    to the plane (in blue) and the other component perpendicular to the
    plane (in red).

    Starting the animation, as the inclination of the plane increases, the
    vertical force of gravity (in black) remains unchanged and the force perpendicular to the plane (in red) decreases to zero.

    Is it correct to say that as the inclination of the plane increases,
    the red force disappears but the black force does not disappear at all?

    [[Mod. note -- For anyone unable to view the animation, it shows a block
    on an inclined plane (at an angle $\alpha$ to the horizontal), with the
    block's weight $mg$ (shown in black) resolved into components
    $mg \cos \alpha$ perpendicular to the plane (shown in red)
    and $mg \sin \alpha$ parallel to the plane (shown in blue).

    To answer the author's question: yes, the black force (the block's weight
    $mg) is unchanged as the inclination of the increases, but the red force
    (the component $mg \sin \alpha$ perpendicular to the plane) decreases.
    When the inclination reaches 90 degrees then the red force is zero.
    -- jt]]

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Luigi Fortunati@21:1/5 to All on Mon May 16 15:47:08 2022
    Luigi Fortunati sabato 14/05/2022 alle ore 06:05:28 ha scritto:
    In my animation
    https://www.geogebra.org/m/qc9pfvva
    there is the force of gravity <mg> (in black), the component parallel
    to the plane (in blue) and the other component perpendicular to the
    plane (in red).

    Starting the animation, as the inclination of the plane increases, the vertical force of gravity (in black) remains unchanged and the force perpendicular to the plane (in red) decreases to zero.

    Is it correct to say that as the inclination of the plane increases,
    the red force disappears but the black force does not disappear at all?

    [[Mod. note -- For anyone unable to view the animation, it shows a block
    on an inclined plane (at an angle $\alpha$ to the horizontal), with the block's weight $mg$ (shown in black) resolved into components
    $mg \cos \alpha$ perpendicular to the plane (shown in red)
    and $mg \sin \alpha$ parallel to the plane (shown in blue).

    To answer the author's question: yes, the black force (the block's weight $mg) is unchanged as the inclination of the increases, but the red force
    (the component $mg \sin \alpha$ perpendicular to the plane) decreases.
    When the inclination reaches 90 degrees then the red force is zero.
    -- jt]]

    I added to my animation
    https://www.geogebra.org/m/jkvhjmjv
    the "final position" button and the constraining force (green).

    In the direction perpendicular to the plane, the red force and the
    green force (equal and opposite) are reduced more and more until they
    disappear at 90 degrees of the alpha angle.

    Conversely, the blue force increases more and more until it becomes
    equal to <mg> when the alpha angle reaches 90 degrees.

    Is it correct to say that, if the block slides without friction along
    the plane, its acceleration will increase as the alpha angle increases,
    until it reaches its maximum value <g> at 90 degrees?

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)