Edexcel M2 (Mechanics 2)

Question 1
View details
  1. Particles of mass \(2 m , 3 m\) and \(5 m\) are placed at the points in the \(x - y\) plane with coordinates \(( - 1,5 ) , ( 0,6 )\) and \(( 3 , - 2 )\) respectively.
    Find the coordinates of the centre of mass of this system of particles.
  2. A lorry of mass 3800 kg is pulling a trailer of mass 1200 kg along a straight horizontal road. At a particular moment, the lorry and trailer are moving at a speed of \(10 \mathrm {~ms} ^ { - 1 }\) and accelerating at \(0.8 \mathrm {~ms} ^ { - 2 }\). The resistances to the motion of the lorry and the trailer are constant and of magnitude 1600 N and 600 N respectively.
    Find the rate, in kW , at which the engine of the lorry is working.
  3. A bullet of mass 0.05 kg is fired with speed \(u \mathrm {~ms} ^ { - 1 }\) from a gun, which recoils at a speed of \(0.008 u \mathrm {~ms} ^ { - 1 }\) in the opposite direction to that in which the bullet is fired.
    1. Find the mass of the gun.
    2. Find, in terms of \(u\), the kinetic energy given to the bullet and to the gun at the instant of firing.
    3. If the total kinetic energy created in firing the gun is 5100 J , find the value of \(u\).
    4. The acceleration of a particle \(P\) at time \(t \mathrm {~s}\) is \(\mathbf { a } \mathrm { ms } ^ { - 2 }\), where \(\mathbf { a } = 4 \mathrm { e } ^ { t } \mathbf { i } - \mathrm { e } ^ { t } \mathbf { j }\). When \(t = 0 , P\) has velocity \(4 \mathrm { i } \mathrm { ms } ^ { - 1 }\).
    5. Find the speed of \(P\) when \(t = 2\).
    6. Find the time at which the direction of motion of \(P\) is parallel to the vector \(5 \mathbf { i } - \mathbf { j }\).
    \includegraphics[max width=\textwidth, alt={}]{63133ab4-9381-4777-a575-1207219948b7-1_323_383_1992_429}
    A uniform plank \(A B\), of mass 3 kg and length 2 m , rests in equilibrium with the point \(P\) in contact with a smooth cylinder. The end \(B\) rests on a rough horizontal surface and the coefficient of friction between the plank and the surface is \(\frac { 1 } { 3 } . A B\) makes an angle of \(60 ^ { \circ }\) with the horizontal.
    If the plank is in limiting equilibrium in this position, find
  4. the magnitude of the force exerted by the cylinder on the plank at \(P\),
  5. the distance \(A P\). \section*{MECHANICS 2 (A) TEST PAPER 10 Page 2}
Question 6
View details
  1. Two smooth spheres \(A\) and \(B\) have equal radii and masses 0.4 kg and 0.8 kg respectively. They are moving in opposite directions along the same straight line, with speeds \(3 \mathrm {~ms} ^ { - 1 }\) and 2 \(\mathrm { ms } ^ { - 1 }\) respectively, and collide directly. The coefficient of restitution between \(A\) and \(B\) is 0.8 .
    1. Calculate the speeds of \(A\) and \(B\) after the impact, stating in each case whether the direction of motion has been reversed.
    2. Find the kinetic energy, in J, lost in the impact.
    3. A point of light, \(P\), is moving along a straight line in such a way that, \(t\) seconds after passing through a fixed point \(O\) on the line, its velocity is \(v \mathrm {~ms} ^ { - 1 }\), where \(v = \frac { 1 } { 2 } t ^ { 2 } - 4 t + 10\). Calculate
    4. the velocity of \(P 6\) seconds after it passes \(O\),
    5. the magnitude of the acceleration of \(P\) when \(t = 1\),
    6. the minimum speed of \(P\),
    7. the distance travelled by \(P\) in the fourth second after it passes \(O\).
    8. A bullet is fired out of a window at a height of 5.2 m above horizontal ground. The initial velocity of the bullet is \(392 \mathrm {~ms} ^ { - 1 }\) at an angle \(\alpha\) above the vertical, where \(\sin \alpha = \frac { 1 } { 20 }\), as shown.
      Find
      \includegraphics[max width=\textwidth, alt={}, center]{63133ab4-9381-4777-a575-1207219948b7-2_335_490_1343_1419}
    9. the range of times after firing during which the bullet is 15 m or more above ground level,
    10. the greatest height above the ground reached by the bullet,
    11. the horizontal distance travelled by the bullet before it reaches its highest point.
    Certain modelling assumptions have been made about the bullet.
  2. State these assumptions and suggest a way in which the model could be refined.
  3. State, with a reason, whether you think this refinement would make a significant difference to the answers.
    (2 marks)