Moderate -0.3 This is a straightforward momentum conservation problem requiring standard application of impulse-momentum theorem. Students must find the combined velocity after collision using conservation of momentum, then calculate impulse on Q. The setup is clear with no geometric complications, though careful attention to signs/directions is needed. Slightly easier than average due to being a direct application of standard M1 techniques.
Two particles \(P\) and \(Q\) have masses \(4m\) and \(m\) respectively. They are moving in opposite directions towards each other along the same straight line on a smooth horizontal plane and collide directly. Immediately before the collision the speed of \(P\) is \(2u\) and the speed of \(Q\) is \(4u\). In the collision, the particles join together to form a single particle.
Find, in terms of \(m\) and \(u\), the magnitude of the impulse exerted by \(P\) on \(Q\) in the collision.
[6]
First M1 for CLM with correct no. of terms, all dimensionally correct, to give
an equation in m, u and their v only. Condone consistent g’s or cancelled m’s
and sign errors.
(N.B. The CLM equation could be obtained by equating the magnitudes of the
impulses on each particle)
First A1 for a correct equation (they may have - 5mv)
Second A1 for 0.8u or – 0.8u (as appropriate)
Second M1 for using Impulse = Change in Momentum for either P or Q
(M0 if clearly adding momenta or if g is included or if different mass in the
two momentum terms) but condone sign errors.
Third A1 for or
OR for or
Fourth A1 for 4.8mu (must be positive since magnitude)
Question 3:
3 | M1A1
A1
For P: | M1 A1
A1
OR For Q: | M1 A1
A1
6
Notes
3 | First M1 for CLM with correct no. of terms, all dimensionally correct, to give
an equation in m, u and their v only. Condone consistent g’s or cancelled m’s
and sign errors.
(N.B. The CLM equation could be obtained by equating the magnitudes of the
impulses on each particle)
First A1 for a correct equation (they may have - 5mv)
Second A1 for 0.8u or – 0.8u (as appropriate)
Second M1 for using Impulse = Change in Momentum for either P or Q
(M0 if clearly adding momenta or if g is included or if different mass in the
two momentum terms) but condone sign errors.
Third A1 for or
OR for or
Fourth A1 for 4.8mu (must be positive since magnitude)
Two particles $P$ and $Q$ have masses $4m$ and $m$ respectively. They are moving in opposite directions towards each other along the same straight line on a smooth horizontal plane and collide directly. Immediately before the collision the speed of $P$ is $2u$ and the speed of $Q$ is $4u$. In the collision, the particles join together to form a single particle.
Find, in terms of $m$ and $u$, the magnitude of the impulse exerted by $P$ on $Q$ in the collision.
[6]
\hfill \mbox{\textit{Edexcel M1 2017 Q3 [6]}}