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Further Mechancis Impulse question

A particle P, of mass 0.5 kg, is moving with velocity (4i + 4j) ms-1 when it receives an impulse I of magnitude 2.5 Ns. As a result of the impulse, the direction of motion of P is deflected through an angle of 45°.
Given that I = (λi + μj) Ns, find all the possible pairs of values of λ and μ.

How do I start with this question. The mark scheme uses a diagram with vector 2i + 2j, but I dont' get why that's used instead of 4i +4j
Reply 1
Original post by Amy.fallowfield
A particle P, of mass 0.5 kg, is moving with velocity (4i + 4j) ms-1 when it receives an impulse I of magnitude 2.5 Ns. As a result of the impulse, the direction of motion of P is deflected through an angle of 45°.
Given that I = (λi + μj) Ns, find all the possible pairs of values of λ and μ.

How do I start with this question. The mark scheme uses a diagram with vector 2i + 2j, but I dont' get why that's used instead of 4i +4j


An impulse is (constant) force times time and it equals the change in momentum as
v-u = at
or
mv - mu = mat
and f=ma.
Original post by mqb2766
An impulse is (constant) force times time and it equals the change in momentum as
v-u = at
or
mv - mu = mat
and f=ma.


I have the formula, I'm just not sure where to go with it
Reply 3
Original post by Amy.fallowfield
I have the formula, I'm just not sure where to go with it


A sketch helps so mark on either the initial momentum or the initial velocity and how might the impulse (force) be appllied to turn it through 45 degrees? You say youve got the mark scheme, so which part of that do/dont you understand.
Original post by mqb2766
A sketch helps so mark on either the initial momentum or the initial velocity and how might the impulse (force) be appllied to turn it through 45 degrees? You say youve got the mark scheme, so which part of that do/dont you understand.

My diagram looks like the mark scheme, only with 4i + 4j instead of 2i + 2j, It's where the 2i + 2j came from that I don't get
The MS is page 6 of this: https://www.physicsandmathstutor.com/pdf-pages/?pdf=https%3A%2F%2Fpmt.physicsandmathstutor.com%2Fdownload%2FMaths%2FA-level%2FFurther%2FMechanics%2FEdexcel%2FFM1%2FTopic-Qs%2FSet-A%2FCh.1%2520Momentum%2520and%2520Impulse.pdf
(edited 6 months ago)
Reply 5
Original post by Amy.fallowfield
My diagram looks like the mark scheme, only with 4i + 4j instead of 2i + 2j, It's where the 2i + 2j came from that I don't get

thats the initial momentum, so mu. You could mark on the initial velocity instead of the momentum as its similar, though as the question is about impulses/momentum its natural to do that.
(edited 6 months ago)
Reply 6
Original post by Amy.fallowfield
My diagram looks like the mark scheme, only with 4i + 4j instead of 2i + 2j, It's where the 2i + 2j came from that I don't get
The MS is page 6 of this: https://www.physicsandmathstutor.com/pdf-pages/?pdf=https%3A%2F%2Fpmt.physicsandmathstutor.com%2Fdownload%2FMaths%2FA-level%2FFurther%2FMechanics%2FEdexcel%2FFM1%2FTopic-Qs%2FSet-A%2FCh.1%2520Momentum%2520and%2520Impulse.pdf

Do you get it now? Plotting the initial momentum means you can use the impulse as the second side in the triangle (add vectors) and get the third side (final momentum) which is in the direction of the positive i or positive j axes. Its fairly easy to see that as the impulse is just a bit shorter than the initial momentum, there will be two solutions for each case, so there will be 4 impulse vectors in total. By thinking about it in cartesian coordinates, its obv related to 3:4:5 triangle and you can pretty much just write down the solution.
(edited 6 months ago)

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