UPSC Exam > UPSC Questions > A ball of mass m moving at a speed v makes a ...
Start Learning for Free
A ball of mass m moving at a speed v makes a head on collision with an identical ball at rest.The kinetic energy of the ball after the collision is 4% of the original.Find the coefficient of restitution.?
Most Upvoted Answer
A ball of mass m moving at a speed v makes a head on collision with an...
Given data:
- Mass of each ball, m
- Initial speed of the moving ball, v
- Final kinetic energy of the moving ball after collision = 4% of initial kinetic energy
Coefficient of restitution:
- The coefficient of restitution (e) is a measure of how much kinetic energy is retained after a collision between two objects.
- It is defined as the ratio of the relative velocity of separation after the collision to the relative velocity of approach before the collision.
Initial momentum:
- Before the collision, the total momentum of the system is given by:
Initial momentum = m*v + 0 (since the second ball is at rest)
Final momentum:
- After the collision, the total momentum of the system is given by:
Final momentum = m*v1 + m*v2 (where v1 and v2 are the velocities of the two balls after the collision)
Initial kinetic energy:
- The initial kinetic energy of the system is given by:
Initial KE = 0.5*m*v^2
Final kinetic energy:
- The final kinetic energy of the system is given by:
Final KE = 0.5*m*v1^2 + 0.5*m*v2^2
Using the given information:
- Final KE = 0.04 * Initial KE
- Final KE = 0.5*m*v1^2 + 0.5*m*v2^2
Coefficient of restitution calculation:
- Using the formula for coefficient of restitution:
e = (v2 - v1) / (v - 0)
Solving the equations:
- Substitute the values of final KE and initial KE into the equation for final KE.
- Determine v2 in terms of v1.
- Substitute the expressions for v1 and v2 into the equation for coefficient of restitution.
- Solve for e.
Conclusion:
- The coefficient of restitution can be calculated using the above steps based on the given information. The final value of e will indicate how much kinetic energy is retained after the collision between the two identical balls.
- Mass of each ball, m
- Initial speed of the moving ball, v
- Final kinetic energy of the moving ball after collision = 4% of initial kinetic energy
Coefficient of restitution:
- The coefficient of restitution (e) is a measure of how much kinetic energy is retained after a collision between two objects.
- It is defined as the ratio of the relative velocity of separation after the collision to the relative velocity of approach before the collision.
Initial momentum:
- Before the collision, the total momentum of the system is given by:
Initial momentum = m*v + 0 (since the second ball is at rest)
Final momentum:
- After the collision, the total momentum of the system is given by:
Final momentum = m*v1 + m*v2 (where v1 and v2 are the velocities of the two balls after the collision)
Initial kinetic energy:
- The initial kinetic energy of the system is given by:
Initial KE = 0.5*m*v^2
Final kinetic energy:
- The final kinetic energy of the system is given by:
Final KE = 0.5*m*v1^2 + 0.5*m*v2^2
Using the given information:
- Final KE = 0.04 * Initial KE
- Final KE = 0.5*m*v1^2 + 0.5*m*v2^2
Coefficient of restitution calculation:
- Using the formula for coefficient of restitution:
e = (v2 - v1) / (v - 0)
Solving the equations:
- Substitute the values of final KE and initial KE into the equation for final KE.
- Determine v2 in terms of v1.
- Substitute the expressions for v1 and v2 into the equation for coefficient of restitution.
- Solve for e.
Conclusion:
- The coefficient of restitution can be calculated using the above steps based on the given information. The final value of e will indicate how much kinetic energy is retained after the collision between the two identical balls.
Attention UPSC Students!
To make sure you are not studying endlessly, EduRev has designed UPSC study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in UPSC.
|
Explore Courses for UPSC exam
|
|
Similar UPSC Doubts
Top Courses for UPSCView all
A ball of mass m moving at a speed v makes a head on collision with an identical ball at rest.The kinetic energy of the ball after the collision is 4% of the original.Find the coefficient of restitution.?
Question Description
A ball of mass m moving at a speed v makes a head on collision with an identical ball at rest.The kinetic energy of the ball after the collision is 4% of the original.Find the coefficient of restitution.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A ball of mass m moving at a speed v makes a head on collision with an identical ball at rest.The kinetic energy of the ball after the collision is 4% of the original.Find the coefficient of restitution.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A ball of mass m moving at a speed v makes a head on collision with an identical ball at rest.The kinetic energy of the ball after the collision is 4% of the original.Find the coefficient of restitution.?.
A ball of mass m moving at a speed v makes a head on collision with an identical ball at rest.The kinetic energy of the ball after the collision is 4% of the original.Find the coefficient of restitution.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A ball of mass m moving at a speed v makes a head on collision with an identical ball at rest.The kinetic energy of the ball after the collision is 4% of the original.Find the coefficient of restitution.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A ball of mass m moving at a speed v makes a head on collision with an identical ball at rest.The kinetic energy of the ball after the collision is 4% of the original.Find the coefficient of restitution.?.
Solutions for A ball of mass m moving at a speed v makes a head on collision with an identical ball at rest.The kinetic energy of the ball after the collision is 4% of the original.Find the coefficient of restitution.? in English & in Hindi are available as part of our courses for UPSC.
Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of A ball of mass m moving at a speed v makes a head on collision with an identical ball at rest.The kinetic energy of the ball after the collision is 4% of the original.Find the coefficient of restitution.? defined & explained in the simplest way possible. Besides giving the explanation of
A ball of mass m moving at a speed v makes a head on collision with an identical ball at rest.The kinetic energy of the ball after the collision is 4% of the original.Find the coefficient of restitution.?, a detailed solution for A ball of mass m moving at a speed v makes a head on collision with an identical ball at rest.The kinetic energy of the ball after the collision is 4% of the original.Find the coefficient of restitution.? has been provided alongside types of A ball of mass m moving at a speed v makes a head on collision with an identical ball at rest.The kinetic energy of the ball after the collision is 4% of the original.Find the coefficient of restitution.? theory, EduRev gives you an
ample number of questions to practice A ball of mass m moving at a speed v makes a head on collision with an identical ball at rest.The kinetic energy of the ball after the collision is 4% of the original.Find the coefficient of restitution.? tests, examples and also practice UPSC tests.
|
|
Explore Courses for UPSC 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