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Question

Show by a diagram

ScanSolve AI Tutor · Accepted Answer

Here is a diagram illustrating the setup with the forces and accelerations:

\begin{tikzpicture}[scale=0.8, transform shape]
    % Fixed support
    \draw[thick] (-3, 5) -- (3, 5);
    \draw[thick] (-2.5, 5) -- (-2.5, 4.5);
    \draw[thick] (2.5, 5) -- (2.5, 4.5);

    % Fixed pulley (P1)
    \draw[thick, fill=gray!20] (0, 4.5) circle (0.5);
    \node at (0, 4.5) {$P_1$};

    % String 1
    \draw[thick] (-0.5, 4.5) -- (-0.5, 2); % Left side of string
    \draw[thick] (0.5, 4.5) -- (0.5, 2); % Right side of string

    % Mass M1
    \draw[thick] (-1, 1.5) rectangle (0, 2);
    \node at (-0.5, 1.75) {$M_1$};
    \draw[thick] (-0.5, 2) -- (-0.5, 1.5); % Connection to M1

    % Forces on M1
    \draw[->, blue, thick] (-0.75, 1.75) -- (-0.75, 2.25) node[left] {$T_1$};
    \draw[->, red, thick] (-0.75, 1.75) -- (-0.75, 1.25) node[left] {$M_1 g$};
    \draw[->, green, thick] (-0.25, 1.75) -- (-0.25, 1.25) node[right] {$a_1$};

    % Movable pulley (P2)
    \draw[thick, fill=gray!20] (0.5, 1.5) circle (0.5);
    \node at (0.5, 1.5) {$P_2$};
    \draw[thick] (0.5, 2) -- (0.5, 1.5); % Connection to P2 from String 1

    % Acceleration of P2
    \draw[->, green, thick] (0.75, 1.5) -- (0.75, 2) node[right] {$a_{P2}$};

    % String 2 over P2
    \draw[thick] (0, 1.5) -- (0, -1); % Left side of string 2
    \draw[thick] (1, 1.5) -- (1, -1); % Right side of string 2

    % Mass M2
    \draw[thick] (-0.5, -1.5) rectangle (0.5, -1);
    \node at (0, -1.25) {$M_2$};
    \draw[thick] (0, -1) -- (0, -1.5); % Connection to M2

    % Forces on M2
    \draw[->, blue, thick] (-0.25, -1.25) -- (-0.25, -0.75) node[left] {$T_2$};
    \draw[->, red, thick] (-0.25, -1.25) -- (-0.25, -1.75) node[left] {$M_2 g$};
    \draw[->, green, thick] (0.25, -1.25) -- (0.25, -1.75) node[right] {$a_2$};

    % Mass M3
    \draw[thick] (0.5, -1.5) rectangle (1.5, -1);
    \node at (1, -1.25) {$M_3$};
    \draw[thick] (1, -1) -- (1, -1.5); % Connection to M3

    % Forces on M3
    \draw[->, blue, thick] (0.75, -1.25) -- (0.75, -0.75) node[left] {$T_2$};
    \draw[->, red, thick] (0.75, -1.25) -- (0.75, -1.75) node[left] {$M_3 g$};
    \draw[->, green, thick] (1.25, -1.25) -- (1.25, -0.75) node[right] {$a_3$};

\end{tikzpicture}

$M_1, M_2, M_3$ : The masses.
$P_1$ : Fixed pulley.
$P_2$ : Movable pulley.
$T_1$ : Tension in the string connecting $M_1$ and $P_2$ .
$T_2$ : Tension in the string connecting $M_2$ and $M_3$ over $P_2$ .
$M_1 g, M_2 g, M_3 g$ : Gravitational forces acting on the masses.
$a_1, a_2, a_3$ : Absolute accelerations of $M_1, M_2, M_3$ respectively.
$a_{P2}$ : Acceleration of the movable pulley $P_2$ .

2 zimekamilika. Zimebaki 3 leo — tuma inayofuata.

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