Calculating Momentum and Speed: IGCSE Forces and Motion Textbook Example

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The discussion revolves around calculating momentum and speed using the principle of conservation of momentum in a physics problem from an IGCSE textbook. The student is struggling to find the velocity (V) of an object, given its initial and final velocities and the mass relationship between Alpha and a proton. They have set up the momentum equations but are confused about how to proceed without specific mass values. Another participant suggests substituting the momentum equations to derive an expression for V, emphasizing that the mass ratio can be maintained. The conversation highlights the challenge of solving the problem without concrete mass values while encouraging continued exploration of the equations.
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Homework Statement


V of Alpha at T1 = 10^7
V of Alpha at T2 = 0.6 x 10^7
Mass of Alpha = 4x mass of proton

Homework Equations


P=MV
P1 = P2

The Attempt at a Solution


Bear in mind that I am a year 11 IGCSE student. This is from the textbook at the end of the chapter of forces and motion detailing simple momentum and speed equations.
I've tried many solutions that produce varied results for me.
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Can you show us what you have obtained and explain why you think it is incorrect?
 
I could only ever get as far as arranging the equation using the principle that Momentum before = momentum after. But as I have no values for the masses I found I could not rearrange.
p1= 4m x 107
P2= (4m x107x0.6) + (m x V)
P1 = P2

As you can see I'm stumped here.
 
SuchBants said:
I could only ever get as far as arranging the equation using the principle that Momentum before = momentum after. But as I have no values for the masses I found I could not rearrange.
p1= 4m x 107
P2= (4m x107x0.6) + (m x V)
P1 = P2

As you can see I'm stumped here.
You just need to continue. In that last equation, substitute P1 and P2 using the other equalities you have, and try and find and equation for V.
 
But surely it would be impossible to get a value for V ? Given that we don't know the mass of m or 4m.
 
SuchBants said:
But surely it would be impossible to get a value for V ? Given that we don't know the mass of m or 4m.
Write out the equations and see what happens.
 
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Sorry for the late reply.

I reached an answer and my working is attached.
Is it okay to presume M as any number? As long as the ratio of the mass stays 4:1?
 

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