| Exam Board | OCR MEI |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2007 |
| Session | January |
| Marks | 20 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Coplanar forces in equilibrium |
| Difficulty | Standard +0.8 This is a substantial framework statics problem requiring multiple equilibrium equations, moment calculations, resolution of forces at pin-joints, and method of sections/joints. While the geometry is given (equilateral triangles), students must handle inclined reactions, work through several parts systematically, and distinguish tensions from thrusts. The multi-part structure, surd manipulation, and need for spatial reasoning about force directions make this harder than average, though it follows standard M2 framework methods without requiring exceptional insight. |
| Spec | 3.03m Equilibrium: sum of resolved forces = 03.03n Equilibrium in 2D: particle under forces3.04a Calculate moments: about a point3.04b Equilibrium: zero resultant moment and force |
Question 2:
2
1 Asledge and a child sitting on it have a combined mass of 29.5kg. The sledge slides on horizontal
ice with negligible resistance to its movement.
(i) While at rest, the sledge is hit directly from behind by a ball of mass 0.5 kg travelling
horizontally at 10ms–1. The coefficient of restitution in the collision is 0.8. After the impact
(cid:1)1 (cid:1)1
the speeds of the sledge and the ball are V m s and V m s respectively.
1 2
Calculate V and V and state the direction in which the ball is travelling after the impact. [7]
1 2
(ii) While at rest, the sledge is hit directly from behind by a snowball of mass 0.5kg travelling
horizontally at 10ms–1. The snowball sticks to the sledge.
(A) Calculate the velocity with which the combined sledge and snowball start to move. [3]
(B) The child scoops up the 0.5kg of snow and drops it over the back of the sledge. What
happens to the velocity of the sledge? Give a reason for your answer. [2]
(iii) In another situation, the sledge is travelling over the ice at 2ms–1 with 10.5kg of snow on it
(giving a total mass of 40kg). The child throws a snowball of mass 0.5kg from the sledge,
parallel to the ground and in the positive direction of the motion of the sledge. Immediately
(cid:1)1
after the snowball is thrown, the sledge has a speed of V m s and the snowball and sledge
are separating at a speed of 10ms–1.
Draw a diagram showing the velocities of the sledge and snowball before and after the
snowball is thrown.
Calculate V. [5]
© OCR 2007 4762/01 Jan 07\includegraphics{figure_2}
Fig. 2 shows a framework in a vertical plane made from the equal, light, rigid rods AB, BC, AD, BD, BE, CE and DE. [The triangles ABD, BDE and BCE are all equilateral.]
The rods AB, BC and DE are horizontal.
The rods are freely pin-jointed to each other at A, B, C, D and E.
The pin-joint at A is also fixed to an inclined plane. The plane is smooth and parallel to the rod AD. The pin-joint at D rests on this plane.
The following external forces act on the framework: a vertical load of $LN$ at C; the normal reaction force $RN$ of the plane on the framework at D; the horizontal and vertical forces $XN$ and $YN$, respectively, acting at A.
\begin{enumerate}[label=(\roman*)]
\item Write down equations for the horizontal and vertical equilibrium of the framework. [3]
\item By considering moments, find the relationship between $R$ and $L$. Hence show that $X = \sqrt{3}L$ and $Y = 0$. [4]
\item Draw a diagram showing all the forces acting on the pin-joints, including the forces internal to the rods. [2]
\item Show that the internal force in the rod AD is zero. [2]
\item Find the forces internal to AB, CE and BC in terms of $L$ and state whether each is a tension or a thrust (compression). [You may leave your answers in surd form.] [7]
\item Without calculating their values in terms of $L$, show that the forces internal to the rods BD and BE have equal magnitude but one is a tension and the other a thrust. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI M2 2007 Q2 [20]}}