<meta name="description" content="Two bodies of mass m_1 and m_2 are connected by a stretched thread of length l and move along a smooth horizontal surface. At some point in time, it turned out that the first body is stationary, and the velocity of the second body, equal to v, is perpendicular to the thread. Determine the tension force of the thread.">
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<meta property="og:title" content="Two bodies of mass m_1 and m_2 are connected by a stretched thread of length l and move along a smooth horizontal surface. At some point in time, it turned out that the first body is stationary, and the velocity of the second body, equal to v, is perpendicular to the thread. Determine the tension force of the thread.">
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<meta property="og:description" content="Two bodies of mass m_1 and m_2 are connected by a stretched thread of length l and move along a smooth horizontal surface. At some point in time, it turned out that the first body is stationary, and the velocity of the second body, equal to v, is perpendicular to the thread. Determine the tension force of the thread.">
<title>Two bodies of mass m_1 and m_2 are connected by a stretched thread of length l and move along a smooth horizontal surface. At some point in time, it turned out that the first body is stationary, and the velocity of the second body, equal to v, is perpendicular to the thread. Determine the tension force of the thread.</title>
Two bodies of mass $m_1$ and $m_2$ are connected by a stretched thread of length $l$ and move along a smooth horizontal surface. At some point in time, it turned out that the first body is stationary, and the velocity of the second body, equal to $v$, is perpendicular to the thread. Determine the tension force of the thread.
</p>
<center>
<figure>
<img src="statement.png"
loading="lazy" width="230" />
<figcaption>
For problem $2.2.24^*$
</figcaption>
</figure>
</center>
<h3>Solution</h3>
<p>
</p>
<center>
<figure>
<img src="draw4.png"
loading="lazy" width="170" />
<figcaption>
Forces acting on the system
</figcaption>
</figure>
</center>
<p>
Since point $1$ is at rest, it follows that the forces acting on it are compensated
$$\vec{F}_{c1}=-\vec{T}_{1}$$
$$T_1=m_1\omega ^2 x$$
Where distance $x$ between point $1$ and center of mass
$$x=l\frac{m_2}{m_1+m_2}$$
</p>
<center>
<figure>
<img src="draw3.png"
loading="lazy" width="170" />
<figcaption>
Direction of forces and velocity of the centre of mass
</figcaption>
</figure>
</center>
<p>
Since point $1$ is at rest, the motion is around it. Then the angular velocity of rotation is found through the velocity $v$ of the point $2$
$$\omega = \frac{v}{l}$$
Now, substitute all of this into the expression for $T_1$
According to Newton's third law, since the thread is weightless, the absolute value of tension force of the thread at point $1$ and point $2$ are equal.
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<meta name="description" content="Two bodies of mass m_1 and m_2 are connected by a stretched thread of length l and move along a smooth horizontal surface. At some point in time, it turned out that the first body is stationary, and the velocity of the second body, equal to v, is perpendicular to the thread. Determine the tension force of the thread.">
<meta property="og:title" content="Two bodies of mass m_1 and m_2 are connected by a stretched thread of length l and move along a smooth horizontal surface. At some point in time, it turned out that the first body is stationary, and the velocity of the second body, equal to v, is perpendicular to the thread. Determine the tension force of the thread.">
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<meta property="og:description" content="Two bodies of mass m_1 and m_2 are connected by a stretched thread of length l and move along a smooth horizontal surface. At some point in time, it turned out that the first body is stationary, and the velocity of the second body, equal to v, is perpendicular to the thread. Determine the tension force of the thread.">
<title>Two bodies of mass m_1 and m_2 are connected by a stretched thread of length l and move along a smooth horizontal surface. At some point in time, it turned out that the first body is stationary, and the velocity of the second body, equal to v, is perpendicular to the thread. Determine the tension force of the thread.</title>
Two bodies of mass $m_1$ and $m_2$ are connected by a stretched thread of length $l$ and move along a smooth horizontal surface. At some point in time, it turned out that the first body is stationary, and the velocity of the second body, equal to $v$, is perpendicular to the thread. Determine the tension force of the thread.
Two bodies of mass $m_1$ and $m_2$ are connected by a stretched thread of length $l$ and move along a smooth horizontal surface. At some point in time, it turned out that the first body is stationary, and the velocity of the second body, equal to $v$, is perpendicular to the thread. Determine the tension force of the thread.
</p>
</p>
<center>
<center>
<figure>
<figure>
<img src="statement.png"
<img src="statement.png"
loading="lazy" width="230" />
loading="lazy" width="230" />
<figcaption>
<figcaption>
For problem $2.2.24^*$
For problem $2.2.24^*$
</figcaption>
</figcaption>
</figure>
</figure>
</center>
</center>
<h3>Solution</h3>
<h3>Solution</h3>
<p>
<p>
</p>
</p>
<center>
<center>
<figure>
<figure>
<img src="draw4.png"
<img src="draw4.png"
loading="lazy" width="170" />
loading="lazy" width="170" />
<figcaption>
<figcaption>
Forces acting on the system
Forces acting on the system
</figcaption>
</figcaption>
</figure>
</figure>
</center>
</center>
<p>
<p>
Since point $1$ is at rest, it follows that the forces acting on it are compensated
Since point $1$ is at rest, it follows that the forces acting on it are compensated
$$\vec{F}_{c1}=-\vec{T}_{1}$$
$$\vec{F}_{c1}=-\vec{T}_{1}$$
$$T_1=m_1\omega ^2 x$$
$$T_1=m_1\omega ^2 x$$
Where distance $x$ between point $1$ and center of mass
Where distance $x$ between point $1$ and center of mass
$$x=l\frac{m_2}{m_1+m_2}$$
$$x=l\frac{m_2}{m_1+m_2}$$
</p>
</p>
<center>
<center>
<figure>
<figure>
<img src="draw3.png"
<img src="draw3.png"
loading="lazy" width="170" />
loading="lazy" width="170" />
<figcaption>
<figcaption>
Direction of forces and velocity of the centre of mass
Direction of forces and velocity of the centre of mass
</figcaption>
</figcaption>
</figure>
</figure>
</center>
</center>
<p>
<p>
Since point $1$ is at rest, the motion is around it. Then the angular velocity of rotation is found through the velocity $v$ of the point $2$
Since point $1$ is at rest, the motion is around it. Then the angular velocity of rotation is found through the velocity $v$ of the point $2$
$$\omega = \frac{v}{l}$$
$$\omega = \frac{v}{l}$$
Now, substitute all of this into the expression for $T_1$
Now, substitute all of this into the expression for $T_1$
According to Newton's third law, since the thread is weightless, the absolute value of tension force of the thread at point $1$ and point $2$ are equal.
According to Newton's third law, since the thread is weightless, the absolute value of tension force of the thread at point $1$ and point $2$ are equal.
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> astrosander01@gmail.com <br></small>
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> astrosander01@gmail.com <br></small>
