Edit to “Solution”

giorgiotinashvili edited Aug 11, 2025, 8:34 PM

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			### Statement

			$2.1.13.$ A system of three identical balls connected by identical springs is suspended on a thread. The thread is burned out. Find the acceleration of the balls immediately after burning the thread.

			### Solution

			![ Forces acting on the system \|842x756, 46%](../../img/2.1.13/draw.png)

			Let's write the equilibrium condition for the two lower balls on the vertical and horizontal axes

			$$
		@@ -12,7 +12,6 @@Solution
			\left\\{\begin{matrix} mg = F_1 \sin\alpha\\\ F_x = F_1 \cos\alpha& \end{matrix}\right.
			$$

		−	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

			![ Falling Slinky \|345x351, 46%](../../img/2.1.13/slinki.gif)

			I recommend an interesting problem about Slinky [IPhO 2019 "Springs and Slinky"](https://s3.eu-central-1.amazonaws.com/physprob.com/files/ipho/2019_Israel_p1.pdf)

			#### Answer

			The acceleration of the upper ball is $3g$, and the acceleration of the lower balls is zero.
		unchanged lines 31

	### Statement		### Statement

	$2.1.13.$ A system of three identical balls connected by identical springs is suspended on a thread. The thread is burned out. Find the acceleration of the balls immediately after burning the thread.		$2.1.13.$ A system of three identical balls connected by identical springs is suspended on a thread. The thread is burned out. Find the acceleration of the balls immediately after burning the thread.

	### Solution		### Solution

	![ Forces acting on the system \|842x756, 46%](../../img/2.1.13/draw.png)		![ Forces acting on the system \|842x756, 46%](../../img/2.1.13/draw.png)

	Let's write the equilibrium condition for the two lower balls on the vertical and horizontal axes		Let's write the equilibrium condition for the two lower balls on the vertical and horizontal axes

	$$		$$
	@@ -12,7 +12,6 @@Solution
	\left\\{\begin{matrix} mg = F_1 \sin\alpha\\\ F_x = F_1 \cos\alpha& \end{matrix}\right.		\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		And for the upper ball

	$$		$$
	T = mg + 2F_1 \sin\alpha		T = mg + 2F_1 \sin\alpha
	$$		$$

	$$		$$
	T = 3mg		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		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		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 $mg$ — $F_1 \sin\alpha$		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		Thus, the lower balls will be in zero gravity

	$$		$$
	a=0		a=0
	$$		$$

	__NO__: Something similar happens when a Slinky falls		__NO__: Something similar happens when a Slinky falls

	![ Falling Slinky \|345x351, 46%](../../img/2.1.13/slinki.gif)		![ Falling Slinky \|345x351, 46%](../../img/2.1.13/slinki.gif)

	I recommend an interesting problem about Slinky [IPhO 2019 "Springs and Slinky"](https://s3.eu-central-1.amazonaws.com/physprob.com/files/ipho/2019_Israel_p1.pdf)		I recommend an interesting problem about Slinky [IPhO 2019 "Springs and Slinky"](https://s3.eu-central-1.amazonaws.com/physprob.com/files/ipho/2019_Israel_p1.pdf)

	#### Answer		#### Answer

	The acceleration of the upper ball is $3g$, and the acceleration of the lower balls is zero.		The acceleration of the upper ball is $3g$, and the acceleration of the lower balls is zero.
	unchanged lines 31