The painter works in a suspended cradle. He needed to get up quickly. He begins to pull the rope with such force that the force of his pressure on the floor of the cradle is reduced to 400 H. Cradle weight 12 kg, painter weight 72 kg. What is the acceleration of the cradle?

Solutions of Savchenko Problems in Physics

Aliaksandr Melnichenka
October 2023

    <h3 id="back-link"><a href="/#2.1">$\leftarrow$Back</a></h3>

    <h3> Statement </h3>
    <p>
        $2.1.13.$ The painter works in a suspended cradle. He needed to get up quickly. He begins to pull the rope with such force that the force of his pressure on the floor of the cradle is reduced to $400$ H. Cradle weight $12$ kg, painter weight $72$ kg. What is the acceleration of the cradle?
    </p>

    <h3>Solution</h3>
    <p>
        <center>

Let's write the equilibrium condition for the two lower balls on the vertical and horizontal axes $$\left\{\begin{matrix} mg = F_1 \sin \alpha \\ F_x = F_1 \cos \alpha & \end{matrix}\right.$$ where $P$ is the painter's pressure force on the chair.

And for the upper ball $$T = mg + 2F_1 \sin \alpha$$

$$T = 3mg$$
Accordingly, when the thread burns out, the upper ball will be acted upon downwards by a force of $T=3mg$. From Newton's second law, we find its initial acceleration as
$$a = \frac{T}{m} = 3g$$
The lower balls will be acted upon in the horizontal direction by the force $F_x$, which will be compensated by the force $F_1 \cos \alpha$, and the force of gravity $mg$ — $F_1 \sin \alpha$

Thus, the lower balls will be in zero gravity $$a=0$$ NO: Something similar happens when a Slinky falls

I recommend an interesting problem about Slinky IPhO 2019 "Springs and Slinky"

    <h4>Answer</h4>
    <p>
        The acceleration of the upper ball is $3g$, and the acceleration of the lower balls is zero.
    </p>


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