Conservation of Linear Momentum

In summary, a particle of mass 5m moving with speed v explodes and splits into two pieces with masses of 2m and 3m. The lighter piece continues to move in the original direction with speed 5v relative to the heavier piece. By applying the conservation of linear momentum equation and determining speeds with respect to the ground, the actual speed of the lighter piece is 4v. The problem with determining the speed lies with the term "relative speed" and can be solved by considering the speed of the heavier piece with respect to the ground, v2.
  • #1
skunk
2
0

Homework Statement


A particle of mass 5m moving with speed v explodes and splits into two pieces with masses of 2m and 3m. The lighter piece continues to move in the original direction with speed 5v relative to the heavier piece. What is the actual speed of the lighter piece?


Homework Equations


Momentum = Mass x Velocity


The Attempt at a Solution


The answer is 4v, as stated in the answer sheet, but I've no idea how to get it. Appreciate any help here, thanks!
 
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  • #2
Start by writing the conservation of linear momentum equation.
 
  • #3
I've only got: 5m x v = (2m x 5v) + (3m x -1 2/3 v)

Does the problem lie with the term "relative speed"?
 
  • #4
skunk said:
I've only got: 5m x v = (2m x 5v) + (3m x -1 2/3 v)

Does the problem lie with the term "relative speed"?

Certainly does!
 
  • #5
skunk said:
I've only got: 5m x v = (2m x 5v) + (3m x -1 2/3 v)

Does the problem lie with the term "relative speed"?
Yes. You should always determine speeds with respect to the ground when using this equation. If the lighter piece is moving at 5v with respect to the heavier piece, and the heavier piece is moving at a speed v2 with respect to the ground, then what is the speed of the lighter piece with respect to the ground, in terms of v and v2?
 

1. What is the law of conservation of linear momentum?

The law of conservation of linear momentum states that the total momentum of a closed system remains constant, unless acted upon by an external force.

2. How is momentum defined?

Momentum is defined as the product of an object's mass and its velocity. It is a measure of an object's motion.

3. What is an example of conservation of linear momentum in action?

An example of conservation of linear momentum is when two objects collide and their total momentum before the collision is equal to their total momentum after the collision, as long as there are no external forces acting on the system.

4. How does conservation of linear momentum relate to Newton's third law of motion?

Conservation of linear momentum is related to Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. In other words, when two objects collide, the forces they exert on each other are equal and opposite, resulting in a conservation of momentum.

5. Why is conservation of linear momentum important in physics?

Conservation of linear momentum is important in physics because it is a fundamental law that governs the motion of objects. It allows us to predict and understand the behavior of objects in motion, and it is a key principle in many areas of physics, including mechanics, thermodynamics, and electromagnetism.

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