All physical objects that are in contact exert force on each other. We give these forces different names based on the type of objects in contact. If one of the objects happen to be a rope, string, chain, or cable we call the force tension. Ropes and cables are useful for exerting forces since they can efficiently transfer a force over a significant distance.
It is important to remember that tension is only a pulling force. Trying to push with a rope causes it to lose the tension. This might sound obvious to you, but quite often people draw the force of tension going in the wrong direction
What is Tension?
Tension can be defined as an action-reaction pair of forces acting at each end of the said elements. While considering a rope, the tension force is felt by every section of the rope in both the directions, apart from the endpoints. The endpoints experience tension on one side and the force from the weight attached. Throughout the string, the tension varies in some circumstances.
Tension can be defined as a pulling force applied by a string or chain on another body
Watch the video below for a concise explanation of tension
How do we calculate the force of tension?
The tension on an object is equal to the product of the mass of the object and gravitational force added to the product of the mass and acceleration.
Mathematically, it is represented as follows:
T = mg + ma
Let us look at the solved example to better understand.
- There is a 10 kg mass hanging from a rope. What is the tension in the rope if the acceleration of the mass is zero?
We know that the force of tension is calculated using the formula T = mg + ma.
Substituting the values in the equation, we get
T= (10 kg) (9.8 m/s2) + (10 kg) (0)
T = 108 N
(i)Now, assume that there is an acceleration +5 m/s2 upwards.
Substituting, we get
T= (10 kg) (9.8 m/s2) + (10 kg) (5 m/s2)
(ii) Assume a downwards acceleration of a = -5m/s2
Substituting, we get
T= (10 kg) (9.8 m/s2) + (10 kg) (-5)
T= 48 N
Law of Tension
The frequency of transverse vibration of a strained string is proportional to the square root of the tension (T) exerted on the string provided the vibrating length ll and mass per unit length m are kept constant.
That is if l and m are constant, ν ∝ √T, Newton (N) is the unit for tension.
Frequently Asked Questions
- Why is the work done by tension always zero?
Work done depends on both force and displacement. Tension is a force but it doesn’t cause any displacement. If the work done is given by the following equation:
W = FS
where F is the force and S is the displacement
then, in the case of tension
W = F × 0 = 0
Therefore, the work done by tension is zero.
- How can we find the direction of tension force?
The direction of tension is the pull which is given the name tension. Thus, the tension will point away from the mass in the direction of the string/rope. In case of the hanging mass, the string pulls it upwards, so the string/rope exerts an upper force on the mass and the tension will be in the upper side.
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