In our daily lives, we rely on machines to do our work for us. One of these simple machines is a fixed pulley. So we’ll look at how does a fixed pulley make work easier in this post. Let us continue to read!!
A fixed pulley is used to help raise large objects. Fixed pulleys make it easier to lift objects with the same effort but in a more convenient or correct direction.
Before seeing how does a fixed pulley make work easier, first, let’s see what a fixed pulley is.
A fixed pulley:
A fixed pulley is one of the simplest kinds of the pulley. It is just a metallic or wooden disc whose rim is grooved. Around this groomed rim, a rope or string is made to be passed. The disc with a grooved rim keeps on rotating about the axis, which is fixed, passing through its center. Thus, a fixed pulley is one in which the axis of rotation on which the pulley rotates is not changing.
You may have seen a flag being hoisted. Fixed pulleys are used in flagpoles for flag hoisting. The pulley is fixed, but the flag can simply be hoisted by pulling one end of the rope.
How does a fixed pulley make work easier: Working, M.A., V.R. & Efficiency
➤ Working of a fixed pulley:
The load is attached to a fixed pulley through a string or rope. The heavy object we aim to lift with the pulley is referred to as the load. Now, whenever a rope or string is stretched or compressed, tension is created in that rope.
As you suspend the object from the rope, the rope will stretch, causing stress in the rope. You are applying a downward force by hanging an object. As a result, tension force will be developed in the opposite direction to counter the object’s weight. The imposed load will have the same magnitude as the tension force created in the rope. However, the tension force and load will be in opposite directions. Thus,
Imposed Load = Created Tension in string
If we use the letters L and T to represent the load and the tension created in the string, we can write:
∴ L = T …..(１)
Let’s look at the opposite side of the rope now.
You are pulling the rope on the opposite side as you try to lift the object. The rope is pulled downwards by applying downward efforts. By pulling on the rope, you are essentially stretching it. As a result, tension is created on this side as well. The tension that is created in the rope will be proportional to the amount of effort applied.
Applied effort = Created tension in string
If we use the letter E to represent effort, we may write:
∴ E = T …..(２)
We can deduce the following from equations (1) and (2):
∴ L = E …..(3)
According to the above equation, in the ideal case of a single fixed pulley, the effort required to lift the weight is equal to the load. It means that the applied effort is not lowered while using a fixed pulley. It provides you a better pulling angle and direction to lift heavy objects with the same force with all your weight.
If we go into further depth, we may state that when we apply effort E to the rope, it moves distance d in the downward direction, and subsequently, load L moves distance d in the upward direction.
➤ Mechanical advantage of a fixed pulley:
The mechanical advantage of any machine is the measurement of the force amplification that the machine achieves. In other words, it displays how much output is amplified when input is applied to the machine. The upward movement of the object is the output, while the effort you apply by pulling the rope is the input.
Mathematically, the mechanical advantage is the ratio of the output force to the input force. Thus, for a fixed pulley, the mechanical advantage is:
But as L = E,
∴ M.A. = 1
As a result of this equation, we can conclude that in the case of a fixed pulley, there is no mechanical gain. Thus, it is a direction provider, not a force multiplier.
➤ Velocity ratio of a fixed pulley:
As the name suggests, velocity ratio is the ratio of input velocity to the output velocity in the unit time. The velocity ratio can be represented as the distance traveled by the effort divided by the distance traveled by the load applied because time is constant. As it is the ratio of distances, it is a unitless quantity.
If the distance traveled by the load L is Ld, the distance traveled by the effort E is Ed, and the time spent by both is T, we can write:
However, with a fixed pulley, the distance traveled by load L in the upward direction is the same as the distance traveled by effort E in the downward direction. Thus, for a fixed pulley Ed = Ld, we can write:
∴ V.R. = 1
➤ The efficiency of a fixed pulley:
If the load lifted by the machine is L and Ld is the distance traveled by the load L, then the work done on the load by the machine is output work, which can be expressed as:
Work done on Load = L x Ld
If the effort that the machine applies is E and Ed is the distance traveled by the effort applied E, then the work done by the effort on the machine is input work, which can be expressed as:
Work done by Effort = E x Ed
The work done on load L (output work) divided by the work done through effort E is the efficiency of a fixed pulley (input work).
Thus, for fixed pulley efficiency is:
∴ ???? = 100%
We get efficiency 100% because we have assumed a fixed pulley with no friction and negligible mass of rope. But in reality, it is not possible not to have friction between the rope and grooved rim of the disc.
As a result of friction, E > L, i.e., M.A. = 1 but V.R. = 1 in actuality. Thus, efficiency ???? < 100%.
With this post, we hope to have adequately answered your question on how does a fixed pulley make work easier.
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I am Alpa Rajai, Completed my Masters in science with specialization in Physics. I am very enthusiastic about Writing about my understanding towards Advanced science. I assure that my words and methods will help readers to understand their doubts and clear what they are looking for. Apart from Physics, I am a trained Kathak Dancer and also I write my feeling in the form of poetry sometimes. I keep on updating myself in Physics and whatever I understand I simplify the same and keep it straight to the point so that it deliver clearly to the readers.