Tension
What is Tension
The tension or tension force is a force experienced by a rope, string, or cable when it is pulled from the opposite end. It acts along the length of the wire and is equal and opposite to the applied force, that is, the force with which it is pulled. In this way, the tension force balances the applied force. It is a contact force and passes through a flexible medium. Tension force is transmitted through a rope only when it is pulled. Otherwise, the action of pushing a rope results in a slack.
Tension Force Examples
Here are a few examples of the tension force from everyday life.
 Suspension of a pendulum bob
 An object suspended by a pully
 Pulling a sleigh by huskies and reindeer
 Plucking a guitar string
 Stretching the muscles
 A swing in a playground
 Elevator suspended by a cable
 Spring in a watch
 Suspension bridge
 Seat belt
Tension Formula
Suppose a force F_{A} is applied to a rope. Then, the tension force T is given by,
T = F_{A}
If a string suspends an object of mass m, then the tension is given by,
T = mg
Where, g is the acceleration due to gravity.
How to Find the Tension Force
Suppose a block of mass m_{1} is lying on a horizontal table. Mass m_{2} pulls m_{1} using a pully as shown in the figure. The two blocks move with an acceleration a. According to Newton’s second law,
For m_{2}: m_{2}a = m_{2}g – T
For m_{1}: m_{1}a = T
Solving for the acceleration,
a = m_{2}g/(m_{1}+m_{2})
By using the expression for a in the second equation above, one can obtain the following.
Tension Force Equation: T = m_{1}m_{2}g/(m_{1}+m_{2})
Unit for Tension: Newton or N
If m_{1 }= m_{2 }= m,
T = mg/2
Tension Problems
Problem 1: An object of mass 12 kg is suspended by light and an inextensible string at one end. If the string is attached firmly to a hook at the other end, calculate the force of tension.
Soln.: Since a string suspends the object, the only force acting on the body is its weight. The string has to bear a tension force equal to the weight to balance it.
T = mg = 12 kg x 9.81 m/s^{2 }= 118 N
Problem 2: An object of mass 8 kg is pulled by a rope over a pulley. It is accelerating upward with an acceleration of 6 m/s^{2}. Calculate the force of tension on the rope.
Soln.: Since the object is pulled upward, the tension force includes its weight and force due to its acceleration.
T = mg + ma = 8 kg x 9.81 m/s^{2}+ 8 kg x 6 m/s^{2 }= 126.5 N
Tension vs. Compression
The following table compares and contrasts tension and compression.
Tension  Compression  
Due to  Extension of an object  Compression of an object 
Direction of force  Away from the object (outward)  Towards the object (inward) 
Applicability  Any solid material, including ropes, cables, and wires  Any solid material that is not flexible 
Examples  Elevator suspended by a cable  Juice maker compressing an orange 

References
Article was last reviewed on Tuesday, December 15, 2020
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