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Work Done in Pulling the Chain Against Gravity

To calculate the work done in pulling the chain against gravity, you can use the formula for work done against a gravitational force. When an object is subjected to a force and is propelled over a distance in the direction of the force
authorImageMurtaza Mushtaq23 Sept, 2023
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Work Done in Pulling the Chain

Work done in pulling the chain against gravity: In physics, three fundamental concepts play a crucial role in understanding and describing the motion and interactions of objects: Work, Energy, and Power. These concepts are interrelated and form the foundation of the study of mechanics and other branches of science and engineering.

What is Work?

When an object is subjected to a force and is propelled over a distance in the direction of the force, work is defined in the context of physics as the transfer of energy from one system to another. In simpler terms, work is done when a force causes a displacement. Work is a scalar quantity and is measured in joules (J) in the International System of Units (SI). The formula for calculating work is: : Work (W) = Force (F) × Displacement (d) × cos(θ) Where:
  • W is the work done,
  • F is the magnitude of the force applied,
  • d is the displacement of the object, and
  • θ is the angle between the force and the displacement vectors.

Also Check - Transfer of Heat Formula

Example: Lifting a box from the ground to a shelf. When you apply a force to lift the box, you do work on it by transferring energy, increasing its potential energy as it moves upward. To calculate the work done in pulling a chain against gravity, you can use the formula for work done against a gravitational force. The formula is: W = F*cos(θ) Where: - W is the work done (measured in joules, J). - F is the force applied (measured in newtons, N). - d is the displacement (measured in meters, m). - θ is the angle between the force applied and the direction of displacement (measured in degrees).

Also Check - Thermodynamics Formula

In the context of pulling a chain against gravity, you would consider the following:
  1. The force (\(F\)): This is the force required to lift or pull the chain against gravity. It is equal to the weight of the chain, which can be calculated using the formula:
F = m * g Where: - m is the mass of the chain (measured in kilograms, kg). - g is the acceleration due to gravity (approximately 9.81 m/s² on the surface of the Earth).
  1. The displacement (\(d\)): This is the vertical distance over which you are pulling the chain.
  2. The angle (\(\theta\)): In this case, \(\theta\) is the angle between the force applied and the direction of vertical displacement, which is usually 0 degrees because you are pulling the chain vertically upward.
So, in most cases, \(\cos(\theta)\) will be 1 because \(\cos(0^\circ) = 1\), and the force and displacement are in the same direction. Therefore, the formula for work done against gravity when pulling a chain vertically upward simplifies to: W = F * d You can calculate the work done by substituting the force (\(F\)) and displacement (\(d\)) into this formula.

Also Check - Gravitation Force Formula

Examples Of Work Done in Pulling the Chain

Example 1: Suppose you have a chain with a mass of 5 kilograms, and you need to lift it vertically upward by 10 meters. Calculate the work done in lifting the chain against gravity. First, calculate the force (\(F\)) required to lift the chain: F = m * g = 5 *9.81  = 49.05 N Now, use the formula for work done: W = F * d = 49.05 *10 \, = 490.5 \,Joules (J) So, the work done in lifting the 5 kg chain vertically upward by 10 meters against gravity is approximately 490.5 Joules. Example 2: Let's consider a more complex scenario. Suppose you have a chain that is initially lying on the ground, and you need to pull it up a rough incline that makes an angle of 30 degrees with the horizontal. The chain has a mass of 8 kilograms, and you need to pull it up the incline for a horizontal distance of 5 meters. Calculate the work done.

Also Check - Ohm's Law Formula

First, calculate the vertical component of the force (\(F_v\)) required to lift the chain: F = m * g  = 8* 9.81= 78.48 N Now, calculate the force applied along the incline (\(F_{\text{pull}}\)) using trigonometry. Since the incline makes a 30-degree angle with the horizontal, we have: F= F cos(30) = 78.48*cos(30) = 68.02 \,N Now, use the formula for work done: W = F_*d = 68.02* 5 = 340.1 (J) So, the work done in pulling the 8 kg chain up the 30-degree incline for a horizontal distance of 5 meters against gravity is approximately 340.1 Joules.

Work Done in Pulling the Chain FAQs

What is work done against gravity?

Work done against gravity is the energy expended when lifting or pulling an object against the force of gravity. It depends on the force applied, the distance over which the force is applied, and the angle between the force and the direction of motion.

How is work done calculated when lifting an object vertically?

When lifting an object vertically, you can calculate work done using the formula: \(W = F \cdot d\), where \(F\) is the force required to lift the object (equal to its weight), and \(d\) is the vertical distance over which the object is lifted.

Does the angle between the force and displacement affect work done against gravity?

Yes, the angle between the force applied and the direction of displacement affects the work done. When the force and displacement are in the same direction, as in lifting an object vertically, the angle is 0 degrees, and the work done is maximized. If the force is applied at an angle, you need to consider the cosine of that angle in the calculation.

How is work done affected by the mass of the object being lifted?

The mass of the object being lifted affects the force required (weight = mass × gravity), which in turn affects the work done. Heavier objects require more force and, therefore, more work to lift against gravity.

What are the units of work done against gravity?

The units of work done are joules (J). A joule is the energy transferred when a force of one newton is applied over a distance of one meter. In the context of work done against gravity, it represents the energy expended in lifting or pulling an object against the Earth's gravitational force.
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