Laws Of Motion-Connected Motion -Physics

What is Connected Motion?

When one body’s motion is directly linked to the motion of another, these bodies are said to be in connected motion. A point mass is attached to one end of a string coiled around a solid body [pulley, disc]. The mass falls vertically downwards when released, and the solid body spins, unwinding the string.

The following method can be used to address a problem involving the motion of two connected bodies:

Drawing a free body diagram is the most basic technique to address the problem. The bodies and connectors are represented on the free-body diagram, which equates the forces using Newton’s second and third laws. The equations on the connector limitations would be required in addition to these equations. If the connector is a rod, then the limitation is that the rod’s length must not change. Similarly, different limits apply to different types of connectors.

 A string over a pulley on separate planes connects the motion of two bodies. Assume a lightweight inextensible string that passes through a smooth pulley with the same tension (T) in both strings. Allow m1 to be greater than m2.  The upward acceleration of mass m2 will be equivalent to the downward acceleration of mass m1 since the string is inextensible.

The acceleration is given by the following:

a= g m1–m2m1+ m2 m/s

And the tension in the string is:

T=(2m1– m2)gm1+ m2 N

When objects are connected by strings and a force F is exerted vertically, horizontally, or along an inclined plane, the string produces tension T, which influences the acceleration to some degree. Let’s have a look at a few examples:

CASE 1: Vertical motion:

Consider two masses, m1 and m2 (m1> m2), which are connected by a light and inextensible string that goes through a pulley.

Let T be the string tension and a be the acceleration. When the system is released, both blocks begin to move with the same acceleration a, m2 vertically upward and m1 downward. The mass m2 is lifted by the gravitational force m1g on mass m1. The y-direction is chosen to be upward.

For mass m2, Newton’s second law is applied.

 The total force acting on m2 is on the left-hand side of the equation, while the product of acceleration and mass of m2 in the y-direction is on the right-hand side.

CASE 2: Horizontal motion:

Mass m2 is placed on a horizontal table, whereas mass m1 is suspended from a tiny pulley. Assume that the surface is free of friction.

Because both blocks are attached to the unstretchable string, if m1 slides, m2 will also move horizontally with the same acceleration.

The forces acting on mass m2 are:

• Gravitational force downward (m2g)
• Surface normal force (N) exerted upwards
• The horizontal tension (T) that the string exerts

The forces that act on mass m1 are as follows:

• The gravitational force acting downward (m1g)
• Tension (T) that acts upwards

When the tension in the string for horizontal motion is compared to the tension in the string for vertical motion, it is evident that the tension in the string for horizontal motion is half of the tension in the string for a vertical motion for the identical set of masses and strings. This finding has significant industrial implications. Conveyor belt ropes (horizontal motion) work for longer periods than crane and lift ropes (vertical motion).

Conclusion:

Connected motion is when a force F is applied vertically or horizontally to two objects connected by a string, the string creates tension, which affects the acceleration to some extent. It can be also referred to as objects that are linked by specific links and travel at the same rate. A point mass is attached to one end of a string coiled around a solid body [pulley, disc]. The mass falls vertically downwards when released, and the solid body spins, unwinding the string.