You must have played this interesting game Tug-Of-War. The main goal of the team is to pull a rope over to their side. When the game starts, both teams try their best to exert huge amounts of pulling force on their end of the rope so that the middle of the rope moves to their side. This pulling force is nothing but tension. You must be a champion in playing this game. Now let’s understand the concept of physics behind this.
Table of Contents
When a string or a rope is being pulled on both ends, then its resistance against any change in its original composition is called tensile force or tension. The tension force is directed over the length of the wire and pulls equally on the bodies at the ends.
Let’s take an example, a string is pulled, if we look at microscopic level, the atoms in the string are pulled away from each other, and this makes them gain some potential energy. Since the equilibrium position of the atoms of the string is disturbed, there is a restoring force experienced by the string that tries to bring back the string to its original position. This restoring force that is experienced throughout the length of the string is known as tension. Take a look below at the atomic level view of a rope under tension.
Without tension, the string or rope will become loose or go slack. So we can say that tension is the opposite of compression.
Since tension is a type of force, it has the same unit and dimension as force.
When a rope is pushed, it will become slack and lose tension, hence we can not push the object by string tension.
Now let’s talk about a string having some mass. Consider, a horizontal force 𝐹 applied on a uniform rod of length 𝐿 and mass 𝑀 is kept on a frictionless surface. Find the tension in the rod shown below at a distance 𝑥?
Let’s divide the rod into two parts to break it at a distance x from the end where force is applied.
Masses of two sections of rod are:
For a section with length x,
m2=(ML)x
For a section with length (L-x),
m1=(ML)(L-x)
Free body diagram of the two bodies is as follows,
For body 1 along x direction,
T=(ML)(L-x)a . . . . . (1)
For body 2 along x direction,
F-T=(ML)xa . . . . . . (2)
Adding equations 1 and 2 we get,
F=Ma
Put a in equation 1 we get,
T=F(1-xL)
At x=0, T=F
At x=L, T=0
Tension varies linearly with the rod.
Video Explanation: Tension in the string
Question 1. How does tension vary in a string having uniform mass if we apply constant force on one end?
Answer: In a string having uniform mass, tension varies linearly with distance from the end where force is applied.
Question 2. Find the tension in the horizontal string connecting 2 Kg and 4 Kg blocks?
Answer:
Consider a system of two blocks and assume tension T in the string,
Net force on the system is F=20-10=10 N
Acceleration of the system= Net ForceTotal mass=106=53
Now only consider 2 Kg block and apply Net Force=massacceleration
T-F2=2a
T-10=253
T=403 N
Question 3. A ball is hanging from the roof of an elevator with the help of a light string. When the elevator starts accelerating up with a uniform acceleration ′ a′ , the tension in the string is T1. When the elevator accelerates downward with same uniform acceleration, the tension in the string is T2. What would be the tension in the string if the elevator is stationary ?
Answer: Applying Newton’s law on ball in each case to get an expression for tension
Case1:
T1-mg=ma
T1=mg+ma……….(1)
Case2:
mg-T2=ma
T2=mg-ma……….(2)
Now, if lift is stationary then tension will be equal to weight of bob, i.e. T=mg
If we add both equations 1 and 2, we get
T1+T2=2mg
mg=T1+T22
T=T1+T22
Question 4. Find the tension in the horizontal string PQ and the string QR shown in the figure?
(g=10 ms-2)
Answer: Let’s assume tension in the string and show all forces, shown in the figure below
From the figure we get,
For equilibrium in y direction, Fy=0
T1 sin(30o)=70
T1=140 N
For equilibrium in x direction, Fx=0
T2=T1 cos(30o)
T2=14032
T2=703 N
Question 1. What is the unit of tension?
Answer: As tension is the type of force it has the same unit as of force, i.e. Newton.
Question 2. What is the direction of the tension force?
Answer: Tension force is always pulling in nature. So it always acts away from the tied ends.
Question 3. What is the tension in the slack (loose) string?
Answer: Slack string does not have any tension, so 0 N.
Question 4. Does the tension throughout the string always remain the same?
Answer: No, not always. Tension in the string having some mass is not the same throughout. Also in some cases where friction is involved in the spring-pulley system, tension is not the same on both sides.