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An object of mass m slides down a hill of height h of arbitary shape and after travelling a certain horizontal path stops because of friction.The friction coefficient is different for different segments for the entire path but is independent of the velocity and direction of motion .the work that a force must perform to return the object to its initial position along the same path is:?
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An object of mass m slides down a hill of height h of arbitary shape a...
Introduction:
When an object slides down a hill and comes to a stop due to friction, the work required to return the object to its initial position along the same path can be determined. In this scenario, the friction coefficient may vary for different segments of the path, but it remains independent of the velocity and direction of motion.
Understanding the Problem:
To calculate the work required to return the object, we need to consider the potential energy lost while sliding down the hill, as well as the work done against friction while returning to the initial position. The height of the hill (h) and the mass of the object (m) are given.
Determining the Potential Energy:
The potential energy (PE) of an object at a certain height (h) can be calculated using the formula PE = mgh, where g is the acceleration due to gravity (approximately 9.8 m/s²). As the object slides down the hill, it loses potential energy and gains kinetic energy.
Work Done by Friction:
Friction, being an opposing force, does negative work on the object as it moves along the path. The work done by friction can be calculated using the formula W = μNds, where μ is the friction coefficient, N is the normal force, and ds is the displacement along the path.
Returning the Object:
To return the object to its initial position, we need to apply a force equal in magnitude but opposite in direction to the force of friction. The work done by this force will be equal to the work done against friction during the object's initial slide down the hill.
Calculating the Work:
To calculate the total work done, we need to sum up the work done by friction for each segment of the path. Since the friction coefficient may vary for different segments, we will integrate the work done over the entire path. The integral of μNds will give us the total work done against friction.
Conclusion:
By calculating the potential energy lost while sliding down the hill and the work done against friction while returning the object to its initial position, we can determine the total work required. The varying friction coefficients for different segments of the path are taken into account through integration.
When an object slides down a hill and comes to a stop due to friction, the work required to return the object to its initial position along the same path can be determined. In this scenario, the friction coefficient may vary for different segments of the path, but it remains independent of the velocity and direction of motion.
Understanding the Problem:
To calculate the work required to return the object, we need to consider the potential energy lost while sliding down the hill, as well as the work done against friction while returning to the initial position. The height of the hill (h) and the mass of the object (m) are given.
Determining the Potential Energy:
The potential energy (PE) of an object at a certain height (h) can be calculated using the formula PE = mgh, where g is the acceleration due to gravity (approximately 9.8 m/s²). As the object slides down the hill, it loses potential energy and gains kinetic energy.
Work Done by Friction:
Friction, being an opposing force, does negative work on the object as it moves along the path. The work done by friction can be calculated using the formula W = μNds, where μ is the friction coefficient, N is the normal force, and ds is the displacement along the path.
Returning the Object:
To return the object to its initial position, we need to apply a force equal in magnitude but opposite in direction to the force of friction. The work done by this force will be equal to the work done against friction during the object's initial slide down the hill.
Calculating the Work:
To calculate the total work done, we need to sum up the work done by friction for each segment of the path. Since the friction coefficient may vary for different segments, we will integrate the work done over the entire path. The integral of μNds will give us the total work done against friction.
Conclusion:
By calculating the potential energy lost while sliding down the hill and the work done against friction while returning the object to its initial position, we can determine the total work required. The varying friction coefficients for different segments of the path are taken into account through integration.
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An object of mass m slides down a hill of height h of arbitary shape and after travelling a certain horizontal path stops because of friction.The friction coefficient is different for different segments for the entire path but is independent of the velocity and direction of motion .the work that a force must perform to return the object to its initial position along the same path is:?
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An object of mass m slides down a hill of height h of arbitary shape and after travelling a certain horizontal path stops because of friction.The friction coefficient is different for different segments for the entire path but is independent of the velocity and direction of motion .the work that a force must perform to return the object to its initial position along the same path is:? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about An object of mass m slides down a hill of height h of arbitary shape and after travelling a certain horizontal path stops because of friction.The friction coefficient is different for different segments for the entire path but is independent of the velocity and direction of motion .the work that a force must perform to return the object to its initial position along the same path is:? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An object of mass m slides down a hill of height h of arbitary shape and after travelling a certain horizontal path stops because of friction.The friction coefficient is different for different segments for the entire path but is independent of the velocity and direction of motion .the work that a force must perform to return the object to its initial position along the same path is:?.
An object of mass m slides down a hill of height h of arbitary shape and after travelling a certain horizontal path stops because of friction.The friction coefficient is different for different segments for the entire path but is independent of the velocity and direction of motion .the work that a force must perform to return the object to its initial position along the same path is:? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about An object of mass m slides down a hill of height h of arbitary shape and after travelling a certain horizontal path stops because of friction.The friction coefficient is different for different segments for the entire path but is independent of the velocity and direction of motion .the work that a force must perform to return the object to its initial position along the same path is:? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An object of mass m slides down a hill of height h of arbitary shape and after travelling a certain horizontal path stops because of friction.The friction coefficient is different for different segments for the entire path but is independent of the velocity and direction of motion .the work that a force must perform to return the object to its initial position along the same path is:?.
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An object of mass m slides down a hill of height h of arbitary shape and after travelling a certain horizontal path stops because of friction.The friction coefficient is different for different segments for the entire path but is independent of the velocity and direction of motion .the work that a force must perform to return the object to its initial position along the same path is:?, a detailed solution for An object of mass m slides down a hill of height h of arbitary shape and after travelling a certain horizontal path stops because of friction.The friction coefficient is different for different segments for the entire path but is independent of the velocity and direction of motion .the work that a force must perform to return the object to its initial position along the same path is:? has been provided alongside types of An object of mass m slides down a hill of height h of arbitary shape and after travelling a certain horizontal path stops because of friction.The friction coefficient is different for different segments for the entire path but is independent of the velocity and direction of motion .the work that a force must perform to return the object to its initial position along the same path is:? theory, EduRev gives you an
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