# How to Calculate Tension Between Two Objects Horizontally

Understanding the tension between two objects horizontally is a vital concept in physics, particularly when dealing with situations where forces are acting on objects lying on a horizontal plane. In this article, we will explore the methods used to calculate tension between two objects horizontally.

**Step 1: Identify the Forces:**

The first step in calculating tension between two objects horizontally is identifying the forces acting upon the objects. These may include gravitational force, frictional force, normal force, and any external forces applied.

**Step 2: Determine the Net Force:**

The net force is the vector sum of all forces acting on an object. In most cases, this involves adding up each force vector’s components. For example, for two horizontal forces F1 and F2 acting on an object, the net force Fnet can be calculated as follows:

Fnet = F1 + F2

**Step 3: Calculate Tension:**

To calculate tension, consider one of the objects on the horizontal plane and identify all forces acting upon it. Then, set up equations using Newton’s Second Law of Motion (F = ma). For horizontal motion where no vertical acceleration takes place:

∑Fx = m * ax

∑Fy = m * ay

In these equations, ∑Fx and ∑Fy represent the sum of the forces in the x (horizontal) and y (vertical) directions, respectively; m is the mass of the object; and ax and ay are the accelerations in x (horizontal) and y (vertical) directions.

Assuming all forces are in equilibrium (no acceleration), we can then write:

Tension (T) – Force Due to Other Object’s movement = 0

T = Force Due to Other Object’s movement

In some cases, friction may also come into play. If friction exists between surfaces:

T = Force Due to Other Object’s movement + Frictional Force

**Step 4: Solve the Equations:**

Solve the equations obtained in Step 3 to find the horizontal tension between the two objects.

Example:

Consider two objects A and B connected by a rope on a horizontal surface. The weight of A is 30 kg, and B is 40 kg. A force of 100 N is applied horizontally to B. There is no friction between the objects and the surface. Find the tension between objects A and B.

1. Identify the forces acting on object B: an external force (100 N) towards right, tension (T) towards left, normal force (Fn), and gravitational force (downwards).

2. Determine net force sum in horizontal direction (∑Fx = m * ax)

∑Fx = Tension (T) – 100 N

Since there is no acceleration, net force is 0.

T = 100 N

Thus, tension between objects A and B is 100 N.

In summary, calculating tension between two objects horizontally involves identifying forces, determining net force, setting up equations using Newton’s Laws of Motion, and solving these equations to find tension. With a clear understanding of these concepts, you’ll be well-equipped to handle various physics problems involving horizontal forces.