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Two trolleys, each of mass m, coupled together are moving with initial velocity v. They collide with three identical stationary trolleys coupled together and continue moving in the same direction. What will be the velocity of the trolleys after the impact?
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Two trolleys, each of mass m, coupled together are moving with initial...
Initial Conditions:
- Two trolleys, each of mass m, are moving with an initial velocity v.
- Three identical stationary trolleys are coupled together.
Collision:
- When the moving trolleys collide with the stationary trolleys, the collision is an example of an elastic collision.
- In an elastic collision, the total kinetic energy of the system is conserved.
Conservation of Momentum:
- According to the law of conservation of momentum, the total momentum of a system before the collision is equal to the total momentum after the collision.
- The momentum (p) of an object is given by the product of its mass (m) and velocity (v): p = m * v.
Calculating Initial Momentum:
- The initial momentum of the two moving trolleys can be calculated as the sum of their individual momenta: p_initial = 2m * v.
- The initial momentum of the three stationary trolleys is zero since they are not moving.
Calculating Final Momentum:
- After the collision, the trolleys continue moving in the same direction.
- Let the final velocity of the trolleys after the collision be V.
- The final momentum of the two moving trolleys is given by: p_final = 2m * V.
- The final momentum of the three stationary trolleys is also zero since they are still stationary.
Applying Conservation of Momentum:
- According to the law of conservation of momentum, the initial momentum of the system is equal to the final momentum of the system.
- Therefore, we can equate the initial momentum to the final momentum and solve for V: 2m * v = 2m * V.
- Simplifying the equation, we find that the velocity of the trolleys after the collision is equal to the initial velocity: V = v.
Conclusion:
- The velocity of the trolleys after the impact is equal to the initial velocity, v.
- This means that the collision did not change the velocity of the trolleys. The trolleys continue moving in the same direction with the same velocity as before the collision.
- Two trolleys, each of mass m, are moving with an initial velocity v.
- Three identical stationary trolleys are coupled together.
Collision:
- When the moving trolleys collide with the stationary trolleys, the collision is an example of an elastic collision.
- In an elastic collision, the total kinetic energy of the system is conserved.
Conservation of Momentum:
- According to the law of conservation of momentum, the total momentum of a system before the collision is equal to the total momentum after the collision.
- The momentum (p) of an object is given by the product of its mass (m) and velocity (v): p = m * v.
Calculating Initial Momentum:
- The initial momentum of the two moving trolleys can be calculated as the sum of their individual momenta: p_initial = 2m * v.
- The initial momentum of the three stationary trolleys is zero since they are not moving.
Calculating Final Momentum:
- After the collision, the trolleys continue moving in the same direction.
- Let the final velocity of the trolleys after the collision be V.
- The final momentum of the two moving trolleys is given by: p_final = 2m * V.
- The final momentum of the three stationary trolleys is also zero since they are still stationary.
Applying Conservation of Momentum:
- According to the law of conservation of momentum, the initial momentum of the system is equal to the final momentum of the system.
- Therefore, we can equate the initial momentum to the final momentum and solve for V: 2m * v = 2m * V.
- Simplifying the equation, we find that the velocity of the trolleys after the collision is equal to the initial velocity: V = v.
Conclusion:
- The velocity of the trolleys after the impact is equal to the initial velocity, v.
- This means that the collision did not change the velocity of the trolleys. The trolleys continue moving in the same direction with the same velocity as before the collision.
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Two trolleys, each of mass m, coupled together are moving with initial velocity v. They collide with three identical stationary trolleys coupled together and continue moving in the same direction. What will be the velocity of the trolleys after the impact?
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Two trolleys, each of mass m, coupled together are moving with initial velocity v. They collide with three identical stationary trolleys coupled together and continue moving in the same direction. What will be the velocity of the trolleys after the impact? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Two trolleys, each of mass m, coupled together are moving with initial velocity v. They collide with three identical stationary trolleys coupled together and continue moving in the same direction. What will be the velocity of the trolleys after the impact? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two trolleys, each of mass m, coupled together are moving with initial velocity v. They collide with three identical stationary trolleys coupled together and continue moving in the same direction. What will be the velocity of the trolleys after the impact?.
Two trolleys, each of mass m, coupled together are moving with initial velocity v. They collide with three identical stationary trolleys coupled together and continue moving in the same direction. What will be the velocity of the trolleys after the impact? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Two trolleys, each of mass m, coupled together are moving with initial velocity v. They collide with three identical stationary trolleys coupled together and continue moving in the same direction. What will be the velocity of the trolleys after the impact? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two trolleys, each of mass m, coupled together are moving with initial velocity v. They collide with three identical stationary trolleys coupled together and continue moving in the same direction. What will be the velocity of the trolleys after the impact?.
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