Class 12 Exam > Class 12 Questions > a block of mass 10kg is moving in x direction...
Start Learning for Free
a block of mass 10kg is moving in x direction with a constant speed of 10m/s . it is subjected to a retarding force F= -0.1x J/m during its travel from x = 20m to x= 30m . find its final kinetic energy.
Most Upvoted Answer
a block of mass 10kg is moving in x direction with a constant speed o...
Given information:
Mass of the block (m) = 10 kg
Initial velocity (u) = 10 m/s
Retarding force (F) = -0.1x J/m
Initial position (x1) = 20 m
Final position (x2) = 30 m
1. Calculating the work done by the retarding force:
The work done by a force is given by the formula:
Work (W) = Force (F) × Displacement (d) × cosθ
In this case, the force varies with position (F = -0.1x J/m), so we need to calculate the work done in small displacement intervals and then integrate it over the total displacement.
∫W = ∫F dx
∫W = ∫-0.1x dx
∫W = -0.1 ∫x dx
∫W = -0.1 [(1/2)x^2] (from x1 to x2)
Substituting the values of x1 and x2:
∫W = -0.1 [(1/2)(30^2) - (1/2)(20^2)]
∫W = -0.1 [(1/2)(900) - (1/2)(400)]
∫W = -0.1 [(450) - (200)]
∫W = -0.1 [250]
∫W = -25 J
2. Calculating the change in kinetic energy:
The work done by the retarding force is equal to the change in kinetic energy (ΔKE) of the block.
∫W = ΔKE
Therefore, ΔKE = -25 J
3. Calculating the final kinetic energy:
The final kinetic energy (KEf) can be calculated by adding the change in kinetic energy to the initial kinetic energy (KEi).
KEf = KEi + ΔKE
Since the initial velocity is constant, the initial kinetic energy (KEi) can be calculated using the formula:
KEi = 0.5 × mass × velocity^2
Substituting the values:
KEi = 0.5 × 10 kg × (10 m/s)^2
KEi = 0.5 × 10 kg × 100 m^2/s^2
KEi = 500 J
Therefore, the final kinetic energy (KEf) is:
KEf = 500 J + (-25 J)
KEf = 475 J
Final answer:
The final kinetic energy of the block is 475 J.
Mass of the block (m) = 10 kg
Initial velocity (u) = 10 m/s
Retarding force (F) = -0.1x J/m
Initial position (x1) = 20 m
Final position (x2) = 30 m
1. Calculating the work done by the retarding force:
The work done by a force is given by the formula:
Work (W) = Force (F) × Displacement (d) × cosθ
In this case, the force varies with position (F = -0.1x J/m), so we need to calculate the work done in small displacement intervals and then integrate it over the total displacement.
∫W = ∫F dx
∫W = ∫-0.1x dx
∫W = -0.1 ∫x dx
∫W = -0.1 [(1/2)x^2] (from x1 to x2)
Substituting the values of x1 and x2:
∫W = -0.1 [(1/2)(30^2) - (1/2)(20^2)]
∫W = -0.1 [(1/2)(900) - (1/2)(400)]
∫W = -0.1 [(450) - (200)]
∫W = -0.1 [250]
∫W = -25 J
2. Calculating the change in kinetic energy:
The work done by the retarding force is equal to the change in kinetic energy (ΔKE) of the block.
∫W = ΔKE
Therefore, ΔKE = -25 J
3. Calculating the final kinetic energy:
The final kinetic energy (KEf) can be calculated by adding the change in kinetic energy to the initial kinetic energy (KEi).
KEf = KEi + ΔKE
Since the initial velocity is constant, the initial kinetic energy (KEi) can be calculated using the formula:
KEi = 0.5 × mass × velocity^2
Substituting the values:
KEi = 0.5 × 10 kg × (10 m/s)^2
KEi = 0.5 × 10 kg × 100 m^2/s^2
KEi = 500 J
Therefore, the final kinetic energy (KEf) is:
KEf = 500 J + (-25 J)
KEf = 475 J
Final answer:
The final kinetic energy of the block is 475 J.
Community Answer
a block of mass 10kg is moving in x direction with a constant speed o...
Is answer is 475J..
|
Explore Courses for Class 12 exam
|
|
Similar Class 12 Doubts
a block of mass 10kg is moving in x direction with a constant speed of 10m/s . it is subjected to a retarding force F= -0.1x J/m during its travel from x = 20m to x= 30m . find its final kinetic energy.
Question Description
a block of mass 10kg is moving in x direction with a constant speed of 10m/s . it is subjected to a retarding force F= -0.1x J/m during its travel from x = 20m to x= 30m . find its final kinetic energy. for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about a block of mass 10kg is moving in x direction with a constant speed of 10m/s . it is subjected to a retarding force F= -0.1x J/m during its travel from x = 20m to x= 30m . find its final kinetic energy. covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for a block of mass 10kg is moving in x direction with a constant speed of 10m/s . it is subjected to a retarding force F= -0.1x J/m during its travel from x = 20m to x= 30m . find its final kinetic energy..
a block of mass 10kg is moving in x direction with a constant speed of 10m/s . it is subjected to a retarding force F= -0.1x J/m during its travel from x = 20m to x= 30m . find its final kinetic energy. for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about a block of mass 10kg is moving in x direction with a constant speed of 10m/s . it is subjected to a retarding force F= -0.1x J/m during its travel from x = 20m to x= 30m . find its final kinetic energy. covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for a block of mass 10kg is moving in x direction with a constant speed of 10m/s . it is subjected to a retarding force F= -0.1x J/m during its travel from x = 20m to x= 30m . find its final kinetic energy..
Solutions for a block of mass 10kg is moving in x direction with a constant speed of 10m/s . it is subjected to a retarding force F= -0.1x J/m during its travel from x = 20m to x= 30m . find its final kinetic energy. in English & in Hindi are available as part of our courses for Class 12.
Download more important topics, notes, lectures and mock test series for Class 12 Exam by signing up for free.
Here you can find the meaning of a block of mass 10kg is moving in x direction with a constant speed of 10m/s . it is subjected to a retarding force F= -0.1x J/m during its travel from x = 20m to x= 30m . find its final kinetic energy. defined & explained in the simplest way possible. Besides giving the explanation of
a block of mass 10kg is moving in x direction with a constant speed of 10m/s . it is subjected to a retarding force F= -0.1x J/m during its travel from x = 20m to x= 30m . find its final kinetic energy., a detailed solution for a block of mass 10kg is moving in x direction with a constant speed of 10m/s . it is subjected to a retarding force F= -0.1x J/m during its travel from x = 20m to x= 30m . find its final kinetic energy. has been provided alongside types of a block of mass 10kg is moving in x direction with a constant speed of 10m/s . it is subjected to a retarding force F= -0.1x J/m during its travel from x = 20m to x= 30m . find its final kinetic energy. theory, EduRev gives you an
ample number of questions to practice a block of mass 10kg is moving in x direction with a constant speed of 10m/s . it is subjected to a retarding force F= -0.1x J/m during its travel from x = 20m to x= 30m . find its final kinetic energy. tests, examples and also practice Class 12 tests.
|
|
Explore Courses for Class 12 exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup