The speed of the load A is equal to v_A. What is the speed of load B?

Solutions of Savchenko Problems in Physics

Aliaksandr Melnichenka
October 2023

    <h3 id="back-link"><a href="/#1.5">$\leftarrow$Back</a></h3>

    <h3> Statement </h3>
    <p>
        $1.5.1.$ The speed of the load $A$ is equal to $v_A$. What is the speed of load $B$?

    <h3>Solution</h3>
    <p>
        <p>Since the thread is rigid and inextensible, its length is preserved during the movement of the loads.</p>

Let load $B$ rise a distance equal to $L$ in time $\Delta t$, then load $A$ will fall a distance $\frac{L}{2}$ in the same time.

This follows from the fact that on both sides of block $1$ the thread will lengthen by $\frac{L}{2}$, which means that the center of the block will fall the same distance. In this case, the length of the thread is preserved.

Then on one side

$$L = v_B \cdot \Delta t$$

and on the other

$$\frac{L}{2} = v_A \cdot \Delta t$$

Therefore,

$$v_B \cdot \Delta t = 2v_A \cdot \Delta t$$

The speed of load $B$ is

$$\fbox{$v_B = 2v_A$}$$

    <h4>Answer</h4>
    <p>
        $$v_B = 2v_A$$
    </p>


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