Conservation of linear momentum problem

In summary: Or if you want to do it your way Vsmall is 5v faster than Vlarge. So you have Vsmall = Vlarge + 5v. At least that's my interpretation.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 a speed 5v relative to the heavier piece. Using the law of conservation of linear momentum, we can set up the equation 5mVi = 2mVsmall + 3mVlarge to solve for the actual speed of the lighter piece. The term "relative" refers to how much faster the
  • #1
risingabove
20
0

Homework Statement


A particle of mass 5m moving with speed v explodes and spilts 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


using law of conservation of linear momentum
initial moment = final moment
mass (m) x Velocity (v) = mass (m) x Velocity (v)


The Attempt at a Solution



using the formula...

5m (v) = 2m(v) - 3m (5v) ...) i used the minus (-) sign because the heavier piece went a different direction

5mv = 2mv -15mv

20mv = 2mv

10v = v

but my answer was wrong...

PLEASE HELP EXPLAIN WHY AND WHAT IS IT IM MISSING TO DO>>>

FIRST CLASS TEST IS TOMORROW!
 
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  • #2
5m (v) = 2m(v) - 3m (5v)

That's not correct. You appear to be assuming that after the explosion the large bit is moving five times faster than the small bit. That's not what the problem states.

i used the minus (-) sign because the heavier piece went a different direction

I wouldn't recommend that. I would just define

Vi is the initial velocity
Vsmall as the new velocity of the small bit
Vlarge as the new velocity of the large bit

So with that in mind it should be something like

5mVi = 2mVsmall + 3mVlarge

I'll let you figure out the other equation to write.

Sorry for the edits to my reply.
 
  • #3
ok soo would i know say

5mVi - 3mVlarge = 2mVsmall

Ok i think I am confusing myself but i do get and understand what you were saying...i think the "relative" word in the problem is what confusing me...

what do they mean when they say "...with a speed 5v relative..."
 
  • #4
Pleas Helppp...i really want to understand this
 
  • #5
Im still stuck on this question can someone give any insights..? PLEASE...
 
  • #6
risingabove said:
ok soo would i know say

5mVi - 3mVlarge = 2mVsmall
Yes
Ok i think I am confusing myself but i do get and understand what you were saying...i think the "relative" word in the problem is what confusing me...

what do they mean when they say "...with a speed 5v relative..."
it's how much faster it's moving. Vsmall = Vlarge + 5v.
 

What is conservation of linear momentum?

Conservation of linear momentum is a fundamental principle in physics that states the total momentum of a system remains constant when there is no external force acting on it. This means that the momentum of the objects within the system may change, but their combined momentum will always remain the same.

How is conservation of linear momentum applied in real-world situations?

Conservation of linear momentum can be applied to many real-world situations, such as collisions between objects, explosions, and rocket propulsion. It helps scientists and engineers understand and predict the motion of objects in these scenarios and design systems that conserve momentum.

What is the equation for calculating linear momentum?

The equation for calculating linear momentum is p = mv, where p is momentum, m is mass, and v is velocity. This equation is based on the principle that the momentum of an object is directly proportional to its mass and velocity.

What happens to the momentum of a system when two objects collide?

When two objects collide, the total momentum of the system remains the same before and after the collision. This means that the momentum of one object may decrease while the other's increases, but the total remains constant. This is known as the law of conservation of momentum.

Can the conservation of linear momentum be violated?

No, the conservation of linear momentum is a fundamental law of physics and cannot be violated. In a closed system where there are no external forces acting, the total momentum will always remain constant. However, in open systems, such as those affected by air resistance, the total momentum may change due to external forces.

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