Physics question help please

Hi, please could I have help on question 3b iii part 2? Surely A would have larger kinetic energy because it has a greater mass so it will have a greater momentum?
This is the paper: https://pmt.physicsandmathstutor.com/download/Physics/A-level/Past-Papers/CAIE/Paper-2/QP/June%202010%20(v1)%20QP.pdf
It’s page 10.
Thank you!

Hi, please could I have help on question 3b iii part 2? Surely A would have larger kinetic energy because it has a greater mass so it will have a greater momentum?
This is the paper: https://pmt.physicsandmathstutor.com/download/Physics/A-level/Past-Papers/CAIE/Paper-2/QP/June%202010%20(v1)%20QP.pdf
It’s page 10.
Thank you!

Similar to the previous reply. The total momentum is constant, so when the springs extension is zero, the momentum of each body is equal but opposite (zero momentum to begin with). So p^2 for each body is the same. Then as per previous reply for the KE.
The basic suvat/momentum equation is
mv - mu = ft
here u = 0 and while this assumes constant force f, really we integrate the springs force/tension over time (impulse) which doesnt change the interpretation. So both bodies experience the same force (spring tension, opposing directions) over the same time duration so p_A = -p_B.

thank you just to confirm, is the momentum of trolley A and trolley B both zero but just in the opposite directions because the extension is zero? So does that mean v1 and v2=0?

No.
Initially the velocity of A and B is zero, hence their momentum is zero, hence the total momentum is zero.
An equal but opposite force (tension) acts on both bodies to accelerate them, but the total momentum is zero as mv = -MV. This is true for all time, including when the extension (tension) is zero. So, if M=2m say (one body is twice the mass), then V = -v/2.
Just consider a thought experiment when one body has a large mass and the other is small. The acceleration, and hence the velocity, of the smaller mass will be larger but the total momentum at any time is zero. Both masses will accelerate, but it will be inversely proportional to mass.

But in the equation Ek= p^2/2m are we not considering the momentum of the individual objects rather than the total momentum so surely the momentum of the individual objects will change?

That applies to both objects individually and the total. For this question part though, its the individual objects momentum and energy you want to consider. The squaring means youre really just consdering the magnitude of individual momentums (which is the same), so the individual energy is inversely proportional to its individual mass.

but for the individual objects, the velocity is changing and momentum=mass*velocity so surely the momentum for individual objects will change?

Youre really not understanding momentum (velocity) and force (impulse). For one object you have
ma = f
here we have two objects with masses m and M and instantaneous acceleration a and A and the force applied to them is f and -f (tension, equal and opposite). So for the two objects at any time
ma = MA
consider integrating from 0 to t (where t.>0 ) and the acceleration causes a velocity change from 0->v and 0->V so
mv = MV
so the individual momentums, at any time, are equal and opposite. The total momentum at any time will be zero. This includes the time when the extension is zero. Note that A and a will have opposing signs as will v and V.
So in this question part, the momentum of each object is equal and opposite (and nonzero, theyve had an accelerating force acting on them as the extension decreases to zero). So p^2 for each object at any time is the same, and the energy of each object is inversely proportional to mass.