Two masses coalesce into one body during collision

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SUMMARY

The discussion centers on a physics problem involving two masses, each of mass m, colliding at equal velocities v in perpendicular directions. The key equations discussed include the conservation of momentum and the calculation of kinetic energy. Participants clarified that momentum is a vector quantity, requiring both magnitude and direction, and emphasized the importance of using correct formulas, specifically P=mv for momentum and K.E=1/2 mv² for kinetic energy. The conversation highlights the need for understanding vector components in rectangular coordinates to solve the problem accurately.

PREREQUISITES
  • Understanding of vector quantities in physics
  • Familiarity with momentum and its conservation principles
  • Knowledge of kinetic energy formulas, specifically K.E=1/2 mv²
  • Basic skills in resolving vectors into components
NEXT STEPS
  • Study vector addition and subtraction in rectangular coordinates
  • Learn about the conservation of momentum in two-dimensional collisions
  • Explore the concept of kinetic energy transformation during collisions
  • Review resources on basic vector operations, such as those available on Hyperphysics
USEFUL FOR

Students preparing for physics examinations, particularly those following the CBSE syllabus for JEE, as well as educators and tutors assisting learners in understanding collision dynamics and vector analysis.

Yaseen

Homework Statement


Question: A body of mass M1=m moving with a velocity V1=v in the x-direction collides with another body of the same mass m2=m moving in the y-direction with the same speed V2=v The coalesce into one body during collision

Homework Equations


(a) Find the magnitude of the momentum of the composite body
(b)The angle which the direction of the momentum vector of the composite body makes with the x-axis
(c) The fraction of the kinetic energy transformed into heat during collision

The Attempt at a Solution


For finding the momentum is it Just P=mv ?
I don't know the formula for finding the direction of momentum
and, Do we use the formula K.E=1/2 mv^2 or K.E=1/2 Iw^2

I Have high expectations and Hopes from this website :)
 
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Yaseen said:

Homework Statement


Question: A body of mass M1=m moving with a velocity V1=v in the x-direction collides with another body of the same mass m2=m moving in the y-direction with the same speed V2=v The coalesce into one body during collision

Homework Equations


(a) Find the magnitude of the momentum of the composite body
(b)The angle which the direction of the momentum vector of the composite body makes with the x-axis
(c) The fraction of the kinetic energy transformed into heat during collision

The Attempt at a Solution


For finding the momentum is it Just P=mv ?
I don't know the formula for finding the direction of momentum
and, Do we use the formula K.E=1/2 mv^2 or K.E=1/2 Iw^2

I Have high expectations and Hopes from this website :)

Momentum is a vector, and total momentum (the vector) is preserved in the collision.
 
Ray Vickson said:
Momentum is a vector, and total momentum (the vector) is preserved in the collision.
So this means that the (vector) momentum has no magnitude ?
I'm really a noob at doing vectors its a very hard concept for me !
 
Yaseen said:
So this means that the (vector) momentum has no magnitude ?
I'm really a noob at doing vectors its a very hard concept for me !
Vectors have a magnitude and a direction. In this problem, it is probably easiest to use rectangular coordinates. Can you write the equations for the initial momentum vectors of each of the masses before the collision? Then what should you write next? :smile:
 
berkeman said:
Vectors have a magnitude and a direction. In this problem, it is probably easiest to use rectangular coordinates. Can you write the equations for the initial momentum vectors of each of the masses before the collision? Then what should you write next? :smile:
Momentum=Mass * velocity
P=mv
(m1+v1)+(m2+v2)=(m1+v1)+(m2+v2) (LHS)--Intial=final--(RHS) Conservation of momentum
Initial momentum equ. (m1+v1)+(m2+v2)initial
Ok so is this the equation ? I really hope so !
And Is this the equation to find the magnitude of momentum ?
 
Yaseen said:
Momentum=Mass * velocity
P=mv
(m1+v1)+(m2+v2)=(m1+v1)+(m2+v2) (LHS)--Intial=final--(RHS) Conservation of momentum
Initial momentum equ. (m1+v1)+(m2+v2)initial
Ok so is this the equation ? I really hope so !
And Is this the equation to find the magnitude of momentum ?

Your equations are all wrong. You start by saying P = mV (and that is OK)l but then you take (m1+v1) and (m2+v2), which makes no sense (and is "dimensionally" wrong: you cannot add "kg" to "m/sec" for example).
 
Ray Vickson said:
Your equations are all wrong. You start by saying P = mV (and that is OK)l but then you take (m1+v1) and (m2+v2), which makes no sense (and is "dimensionally" wrong: you cannot add "kg" to "m/sec" for example).
I equated P(initial)=P(final) that's conservation of momentum right?
m1=mass of body one v1=velocity of body one
m2=mass of body 2 v2=velocity of body 2
 
Last edited by a moderator:
Yaseen said:
I equated P(initial)=P(final) that's conservation of momentum right?
m1=mass of body one v1=velocity of body one
m2=mass of body 2 v2=velocity of body 2

No, you did NOT do that: m1+v1 is not the momentum of body 1 and m2+v2 is not the momentum of body 2. You need to be careful about what you write down. You will get correct answers if you use correct formulas, but will get nonsense if you write formulas that make no sense and have no basis in physics.
 
Ray Vickson said:
No, you did NOT do that: m1+v1 is not the momentum of body 1 and m2+v2 is not the momentum of body 2. You need to be careful about what you write down. You will get correct answers if you use correct formulas, but will get nonsense if you write formulas that make no sense and have no basis in physics.
Ok now I feel hopeless can you please guide me before atleast I had some confidience that I can do it but now I feel really disappointed that I can't do anything please can you guide me
 
  • #10
Remember that momentum is a vector, and in rectangular coordinates it has an x and a y component. One way to write that is like this:

P1 = [P1x, P1y] = [M1V1x, M1V1y]

Now can you write the equations for the momenta of the individual particles as 2-D vectors (like I did above) before and after the collision? It's important that the particles are moving in different directions before the collision, and in the same direction after the collision...
 
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  • #11
berkeman said:
Remember that momentum is a vector, and in rectangular coordinates it has an x and a y component. One way to write that is like this:

P1 = [P1x, P1y] = [M1V1x, M1V1y]

Now can you write the equations for the momenta of the individual particles as 2-D vectors (like I did above) before and after the collision? It's important that the particles are moving in different directions before the collision, and in the same direction after the collision...
Ok yeah that was my mistake insted of taking it like Mx and My I took it as M1 and M2 ok so this is the initial step then after equating momentum before collision and after collision what do I do ?
 
  • #12
Yaseen said:

Homework Statement


Question: A body of mass M1=m moving with a velocity V1=v in the x-direction collides with another body of the same mass m2=m moving in the y-direction with the same speed V2=v The coalesce into one body during collision

Homework Equations


(a) Find the magnitude of the momentum of the composite body
(b)The angle which the direction of the momentum vector of the composite body makes with the x-axis
(c) The fraction of the kinetic energy transformed into heat during collision
You work through the questions. Do you know how to find the magnitude and direction of a vector in rectangular coordinates?
 
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  • #13
berkeman said:
You work through the questions. Do you know how to find the magnitude and direction of a vector in rectangular coordinates?
No I don't know how to find the magnitude as I'm stated above I really a noob at vectors
 
  • #14
berkeman said:
You work through the questions. Do you know how to find the magnitude and direction of a vector in rectangular coordinates?
Is it the same formula used to find the magnitude of unit vectors ?
 
  • #16
Yaseen said:
No I don't know how to find the magnitude as I stated above I really a noob at vectors
What class is this for? What textbook are you using, or what learning resources do you have as part of this class?
 
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  • #17
berkeman said:
What class is this for? What textbook are you using, or what learning resources do you have as part of this class?
This for the cbse syllabus from the JEE questions for class XI India (I'm from india)
 
  • #18
Yaseen said:
This for the cbse syllabus from the JEE questions for class XI India (I'm from india)
Actually this is the homework given to me and our teacher selects the hardest questions of all for us !
 
  • #20
berkeman said:
What class is this for? What textbook are you using, or what learning resources do you have as part of this class?
This is for class XI JEE paper CBSE, I use the NCERT books as a resource
 
  • #21
Special thanks to @berkeman for helping out I got it its 1/2mv*2
 
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