Standard +0.8 This is an oblique collision problem requiring conservation of momentum in two perpendicular directions, Newton's experimental law along the line of centres, and solving simultaneous equations with the given angle constraint. It requires careful decomposition of velocities and systematic application of multiple principles, going beyond standard direct impact questions but using established Further Mechanics techniques.
5 Two small uniform smooth spheres A and B , of equal radius, have masses 2 kg and 4 kg respectively. They are moving on a horizontal surface when they collide. Immediately before the collision, A has speed \(6 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and is moving along the line of centres, and B has speed \(2.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and is moving along a line which is perpendicular to the line of centres (see diagram).
\includegraphics[max width=\textwidth, alt={}, center]{17e92314-d7df-49b8-a441-8d18c91dbbb0-03_389_764_1592_244}
The direction of motion of B after the collision makes an angle of \(45 ^ { \circ }\) with the line of centres.
Determine the coefficient of restitution between A and B .
Question 5:
5 | Let w and w be the horizontal components of the
A B
velocity of A and B after collision
w = 2.5
B
2(6) + 4(0) = 2w + 4(2.5)
A
w − 2.5 = −e(6 − 0)
A
e = 0.25 | B1
M1
A1
M1
A1
A1
[6] | 1.2
3.3
1.1
3.3
1.1
1.1 | Use of conservation of linear momentum
(parallel to the line of centres) – correct
number of terms
Allow with w instead of 2.5
B
Use of Newton’s experimental law
(parallel to the line of centres) – correct
number of terms
Use of NEL must be consistent with
CLM – allow with w instead of 2.5 and
B
possibly their w
A | For reference: w = 1
A
5 Two small uniform smooth spheres A and B , of equal radius, have masses 2 kg and 4 kg respectively. They are moving on a horizontal surface when they collide. Immediately before the collision, A has speed $6 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and is moving along the line of centres, and B has speed $2.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and is moving along a line which is perpendicular to the line of centres (see diagram).\\
\includegraphics[max width=\textwidth, alt={}, center]{17e92314-d7df-49b8-a441-8d18c91dbbb0-03_389_764_1592_244}
The direction of motion of B after the collision makes an angle of $45 ^ { \circ }$ with the line of centres.
Determine the coefficient of restitution between A and B .
\hfill \mbox{\textit{OCR MEI Further Mechanics Major 2021 Q5 [6]}}