# Mechanics- connected particles

• MHB
• Shah 72
In summary, a 1kg horizontal bar is connected to two vertical rods and a third vertical rod with a 4kg mass hanging below it. The tension in the third rod is 40N, but the tensions in the other two rods are unknown. By analyzing the forces acting on the bar, we can determine that the tensions in the first two rods are equal and both 25N. This is due to the principles of translational and rotational equilibrium. It is recommended to research these terms for a better understanding.
Shah 72
MHB
A horizontal bar of mass 1kg hangs from a pair of parallel vertical rods of negligible mass, attached to either end of the bar. A third vertical rod is connected to the middle of the bar and a 4kg mass hangs from this below the rod. Work out the tension in each of the rods.
I got the tension in the third vertical rod= 40N. I don't know how to find the tension of the other two rods.

did you sketch a FBD?

forces acting on the 1 kg bar …

$T_1+T_2$ up, $1g + T_3$ down

skeeter said:
did you sketch a FBD?

forces acting on the 1 kg bar …

$T_1+T_2$ up, $1g + T_3$ down
T1+T2=50N, T3=40N

Shah 72 said:
T1+T2=50N, T3=40N

so …

$T_1 =$ ?

$T_2 =$ ?

… and why?

skeeter said:
so …

$T_1 =$ ?

$T_2 =$ ?

… and why?
T1=T2 = 25 as T3 is at the midpoint of the horizontal bar

yes, but that’s not the “physics” reason … what do you know about translational and rotational equilibrium?

recommend you look them up if you haven’t heard those terms before

skeeter said:
yes, but that’s not the “physics” reason … what do you know about translational and rotational equilibrium?

recommend you look them up if you haven’t heard those terms before
Sure. Thanks!

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

Connected particles in mechanics refer to a system of two or more particles that are linked together by a constraint, such as a rigid rod or a string. These particles are considered to be connected because their positions and movements are interdependent.

## 2. How are the movements of connected particles related?

The movements of connected particles are related by the constraints that connect them. This means that the position, velocity, and acceleration of one particle will affect the position, velocity, and acceleration of the other particles in the system.

## 3. What are the equations used to analyze connected particle systems?

The equations used to analyze connected particle systems include Newton's laws of motion, conservation of momentum, and conservation of energy. These equations can be applied to determine the forces acting on each particle and the resulting motion of the system.

## 4. How do you determine the degrees of freedom in a connected particle system?

The degrees of freedom in a connected particle system can be determined by counting the number of independent coordinates needed to describe the positions of each particle. For example, a system of two particles connected by a string will have two degrees of freedom, as the position of one particle can be described by the position of the other and the length of the string.

## 5. What are some real-world examples of connected particle systems?

Real-world examples of connected particle systems include pendulums, pulley systems, and double pendulums. These systems can be found in everyday objects such as clocks, elevators, and amusement park rides. They are also commonly used in engineering and physics experiments to study the principles of mechanics.

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