Two masses coalesce into one body during collision

In summary, the question asks about a collision between two bodies with the same mass and velocity in different directions. The homework equations involve finding the magnitude and direction of the momentum of the composite body, as well as the fraction of kinetic energy transformed into heat during the collision. The attempt at a solution involved incorrectly equating the momentum of each body as (mass + velocity) and not considering the vector nature of momentum. The next step would be to correctly write out the equations for the momenta of each body as 2-D vectors and equate the initial and final momenta to solve for the unknown quantities.
  • #1
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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  • #2
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.
 
  • #3
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 !
 
  • #4
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:
 
  • #5
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 ?
 
  • #6
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).
 
  • #7
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
 
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  • #8
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.
 
  • #9
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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What is a collision between two masses?

A collision between two masses occurs when two objects come into contact with each other and exchange energy and momentum. This can happen in various scenarios, such as a car crash or two billiard balls colliding.

What causes two masses to coalesce into one body during a collision?

The main factor that causes two masses to coalesce into one body during a collision is the conservation of momentum. When two objects collide, their momentum must remain the same before and after the collision. This means that if the two objects stick together after the collision, their combined mass will have a lower velocity than the individual objects had before the collision.

What are the factors that affect the outcome of a collision between two masses?

The outcome of a collision between two masses is affected by several factors, including the masses of the objects, their velocities, the angle at which they collide, and the type of collision (e.g. elastic or inelastic). The shape and composition of the objects can also play a role in the outcome of the collision.

How does the conservation of energy apply to a collision between two masses?

The conservation of energy also plays a role in a collision between two masses. In an ideal scenario, the total kinetic energy of the objects before the collision will be equal to the total kinetic energy after the collision. However, in real-world situations, some energy may be lost due to factors such as friction and deformation of the objects.

What are some real-world applications of studying collisions between two masses?

The study of collisions between two masses has many real-world applications, including car safety design, sports equipment design, and forensic investigations. It is also essential in understanding the formation of celestial bodies, such as planets and stars, and in predicting the behavior of particles in particle accelerators.

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