# Mechanics- connected particles

• MHB
• Shah 72
In summary, the conversation discussed the setup of a pulley system with two smooth pulleys 8m apart at the same horizontal level. A light inextensible rope passes over the pulleys and has a total length of 16m. Three boxes, one with a mass of 5kg and the other with an unknown mass m kg, hang from the rope at equal horizontal levels. The conversation then moved on to solving for the value of m, with the correct answer being 6kg. The method used involved solving a radical equation and the conversation concluded with a recommendation to review this concept for future problems.
Shah 72
MHB
Two smooth pulleys are 8m apart at the same horizontal level. A light inextensible rope passes over the pulleys and a box of mass 5kg hangs at each end of the rope. A third box of mass m kg is attached to the midpoint of the rope and hangs between the pulleys so that all the three boxes are at the same horizontal
level. The total length of the box is 16m. Find the value of m

total length of the box? … maybe the string length is 16 m ?

if so, I get m = 7.5 kg

Last edited by a moderator:
skeeter said:
total length of the box? … maybe the string length is 16 m ?

if so, I get m = 7.5 kg
Iam so so sorry again typo error. Its the total length of the rope = 16m

skeeter said:
total length of the box? … maybe the string length is 16 m ?

if so, I get m = 7.5 kg
The ans in the textbook says 6 kg.

skeeter said:
total length of the box? … maybe the string length is 16 m ?

if so, I get m = 7.5 kg
Can you pls pls tell me how to work it out?

Shah 72 said:
The ans in the textbook says 6 kg.

6 kg is correct … I used the wrong value for a trig ratio.

skeeter said:
6 kg is correct … I used the wrong value for a trig ratio.
Can you pls pls tell me the method you worked it out? I have no clue how to solve it.

skeeter said:
I have no clue how to do it. Sin theta= h/ sq root(h^2+16).

$h + \sqrt{h^2+16} = 8$

skeeter said:
$h + \sqrt{h^2+16} = 8$

By squaring both sides I will get 2h^2=-8 .

$h + \sqrt{h^2+16} = 8$

$\sqrt{h^2+16} = 8-h$

square both sides …

$h^2+16 = 64 - 16h + h^2$

$16h = 48$

$h =3$

check solution …

$3 + \sqrt{3^2+16} = 3 + 5 = 8$

checks good.

recommend you review solving radical equations …

skeeter said:
$h + \sqrt{h^2+16} = 8$

$\sqrt{h^2+16} = 8-h$

square both sides …

$h^2+16 = 64 - 16h + h^2$

$16h = 48$

$h =3$

check solution …

$3 + \sqrt{3^2+16} = 3 + 5 = 8$

checks good.

recommend you review solving radical equations …
Thank you so so much! None of these things are explained in the textbook. Iam really struggling with the pulley and string questions. I will surely look into solving radical equations.

## 1. What is the definition of connected particles in mechanics?

Connected particles in mechanics refers to two or more particles that are linked together by a physical connection, such as a string, rod, or spring. They are often used in physics problems to study the motion and forces between multiple objects.

## 2. How do you determine the acceleration of connected particles?

The acceleration of connected particles can be found by analyzing the forces acting on each particle and using Newton's second law, F=ma. The net force on the system of particles will determine the acceleration of the center of mass of the system.

## 3. Can connected particles have different masses?

Yes, connected particles can have different masses. In fact, systems of connected particles with different masses are commonly used in physics problems to demonstrate the principles of mechanics.

## 4. What are the different types of connections between particles?

The different types of connections between particles include rigid connections, where the particles are connected by a rigid rod or bar, and non-rigid connections, such as strings or springs. These connections can also be classified as fixed, where the particles cannot move relative to each other, or movable, where the particles can move relative to each other.

## 5. How does the motion of one particle affect the motion of the other connected particles?

The motion of one particle in a system of connected particles can affect the motion of the other particles through the physical connection between them. For example, if one particle accelerates, it can cause the other particles to accelerate or change direction as well, depending on the type of connection and the forces involved.

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