Questions — OCR MEI M1 (268 questions)

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OCR MEI M1 Q4
4 The velocity-time graph shown in Fig. 1 represents the straight line motion of a toy car. All the lines on the graph are straight. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{569e7c0e-7c33-47c9-b986-8587ea239f0a-4_579_1319_381_449} \captionsetup{labelformat=empty} \caption{Fig. 1}
\end{figure} The car starts at the point A at \(t = 0\) and in the next 8 seconds moves to a point B .
  1. Find the distance from A to B .
    \(T\) seconds after leaving A , the car is at a point C which is a distance of 10 m from B .
  2. Find the value of \(T\).
  3. Find the displacement from A to C .
OCR MEI M1 Q5
5 Fig. 3 is a sketch of the velocity-time graph modelling the velocity of a sprinter at the start of a race. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{569e7c0e-7c33-47c9-b986-8587ea239f0a-5_575_1086_482_551} \captionsetup{labelformat=empty} \caption{Fig. 3}
\end{figure}
  1. How can you tell from the sketch that the acceleration is not modelled as being constant for \(0 \leqslant t \leqslant 4\) ? The velocity of the sprinter, \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\), for the time interval \(0 \leqslant t \leqslant 4\) is modelled by the expression $$v = 3 t - \frac { 3 } { 8 } t ^ { 2 } .$$
  2. Find the acceleration that the model predicts for \(t = 4\) and comment on what this suggests about the running of the sprinter.
  3. Calculate the distance run by the sprinter from \(t = 1\) to \(t = 4\).
OCR MEI M1 Q6
6 A car passes a point A travelling at \(10 \mathrm {~m} \mathrm {~s} { } ^ { 1 }\). Its motion over the next 45 seconds is modelled as follows.
  • The car's speed increases uniformly from \(10 \mathrm {~ms} { } ^ { 1 }\) to \(30 \mathrm {~ms} { } ^ { 1 }\) over the first 10 s .
  • Its speed then increases uniformly to \(40 \mathrm {~m} \mathrm {~s} { } ^ { 1 }\) over the next 15 s .
  • The car then maintains this speed for a further 20 s at which time it reaches the point B .
    1. Sketch a speed-time graph to represent this motion.
    2. Calculate the distance from A to B .
    3. When it reaches the point B , the car is brought uniformly to rest in \(T\) seconds. The total distance from A is now 1700 m . Calculate the value of \(T\).
OCR MEI M1 Q1
1 A ring is moving up and down a vertical pole. The displacement, \(s \mathrm {~m}\), of the ring above a mark on the pole is modelled by the displacement-time graph shown in Fig. 1. The three sections of the graph are straight lines. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{bdbebc7f-0cb1-4203-8058-7614ba291508-1_763_1057_439_580} \captionsetup{labelformat=empty} \caption{Fig. 1}
\end{figure}
  1. Calculate the velocity of the ring in the interval \(0 < t < 2\) and in the interval \(2 < t < 3.5\).
  2. Sketch a velocity-time graph for the motion of the ring during the 4 seconds.
  3. State the direction of motion of the ring when
    (A) \(t = 1\),
    (B) \(t = 2.75\),
    (C) \(t = 3.25\).
OCR MEI M1 Q2
2 Fig. 2 shows an acceleration-time graph modelling the motion of a particle. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{bdbebc7f-0cb1-4203-8058-7614ba291508-2_684_1068_408_586} \captionsetup{labelformat=empty} \caption{Fig. 2}
\end{figure} At \(t = 0\) the particle has a velocity of \(6 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) in the positive direction.
  1. Find the velocity of the particle when \(t = 2\).
  2. At what time is the particle travelling in the negative direction with a speed of \(6 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) ?
OCR MEI M1 Q3
3 A cyclist starts from rest and takes 10 seconds to accelerate at a constant rate up to a speed of \(15 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). After travelling at this speed for 20 seconds, the cyclist then decelerates to rest at a constant rate over the next 5 seconds.
  1. Sketch a velocity-time graph for the motion.
  2. Calculate the distance travelled by the cyclist.
OCR MEI M1 Q4
4 Fig. 1 is the velocity-time graph for the motion of a body. The velocity of the body is \(v \mathrm {~m} \mathrm {~s} { } ^ { 1 }\) at time \(t\) seconds. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{bdbebc7f-0cb1-4203-8058-7614ba291508-3_656_1344_401_399} \captionsetup{labelformat=empty} \caption{Fig. 1}
\end{figure} The displacement of the body from \(t = 0\) to \(t = 100\) is 1400 m . Find the value of \(V\).
OCR MEI M1 Q2
2 Fig. 1 is the velocity-time graph for the motion of a body. The velocity of the body is \(v \mathrm {~m} \mathrm {~s} { } ^ { 1 }\) at time \(t\) seconds. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{578555c7-e316-47d3-876a-0b6accce8946-1_662_1354_915_441} \captionsetup{labelformat=empty} \caption{Fig. 1}
\end{figure} The displacement of the body from \(t = 0\) to \(t = 100\) is 1400 m . Find the value of \(V\).
OCR MEI M1 Q3
3 A particle travels in a straight line during the time interval \(0 \leqslant t \leqslant 12\), where \(t\) is the time in seconds. Fig. 1 is the velocity-time graph for the motion. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{578555c7-e316-47d3-876a-0b6accce8946-2_445_854_426_667} \captionsetup{labelformat=empty} \caption{Fig. 1}
\end{figure}
  1. Calculate the acceleration of the particle in the interval \(0 < t < 6\).
  2. Calculate the distance travelled by the particle from \(t = 0\) to \(t = 4\).
  3. When \(t = 0\) the particle is at A . Calculate how close the particle gets to A during the interval \(4 \leqslant t \leqslant 12\). In this question take \(\boldsymbol { g }\) as \(\mathbf { 1 0 } \mathrm { m } \mathrm { s } ^ { \mathbf { 2 } }\).
    A small ball is released from rest. It falls for 2 seconds and is then brought to rest over the next 5 seconds. This motion is modelled in the speed-time graph Fig. 6. \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{578555c7-e316-47d3-876a-0b6accce8946-3_596_1004_517_499} \captionsetup{labelformat=empty} \caption{Fig. 6}
    \end{figure} For this model,
  4. calculate the distance fallen from \(t = 0\) to \(t = 7\),
  5. find the acceleration of the ball from \(t = 2\) to \(t = 6\), specifying the direction,
  6. obtain an expression in terms of \(t\) for the downward speed of the ball from \(t = 2\) to \(t = 6\),
  7. state the assumption that has been made about the resistance to motion from \(t = 0\) to \(t = 2\). The part of the motion from \(t = 2\) to \(t = 7\) is now modelled by \(v = - \frac { 3 } { 2 } t ^ { 2 } + \frac { 19 } { 2 } t + 7\).
  8. Verify that \(v\) agrees with the values given in Fig. 6 at \(t = 2 , t = 6\) and \(t = 7\).
  9. Calculate the distance fallen from \(t = 2\) to \(t = 7\) according to this model.
OCR MEI M1 Q5
5 A box of emergency supplies is dropped to victims of a natural disaster from a stationary helicopter at a height of 1000 metres. The initial velocity of the box is zero. At time \(t \mathrm {~s}\) after being dropped, the acceleration, \(a \mathrm {~ms} ^ { - 2 }\), of the box in the vertically downwards direction is modelled by $$\begin{aligned} & a = 10 - t \text { for } 0 \leqslant t \leqslant 10
& a = 0 \quad \text { for } \quad t > 10 \end{aligned}$$
  1. Find an expression for the velocity, \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\), of the box in the vertically downwards direction in terms of \(t\) for \(0 \leqslant t \leqslant 10\). Show that for \(t > 10 , v = 50\).
  2. Draw a sketch graph of \(v\) against \(t\) for \(0 \leqslant t \leqslant 20\).
  3. Show that the height, \(h \mathrm {~m}\), of the box above the ground at time \(t \mathrm {~s}\) is given, for \(0 \leqslant t \leqslant 10\), by $$h = 1000 - 5 t ^ { 2 } + \frac { 1 } { 6 } t ^ { 3 }$$ Find the height of the box when \(t = 10\).
  4. Find the value of \(t\) when the box hits the ground.
  5. Some of the supplies in the box are damaged when the box hits the ground. So measures are considered to reduce the speed with which the box hits the ground the next time one is dropped. Two different proposals are made. Carry out suitable calculations and then comment on each of them.
    (A) The box should be dropped from a height of 500 m instead of 1000 m .
    (B) The box should be fitted with a parachute so that its acceleration is given by $$\begin{gathered} \quad a = 10 - 2 t \text { for } 0 \leqslant t \leqslant 5 ,
    a = 0 \quad \text { for } \quad t > 5 . \end{gathered}$$ \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{578555c7-e316-47d3-876a-0b6accce8946-5_342_979_319_633} \captionsetup{labelformat=empty} \caption{Fig. 4}
    \end{figure} Particles P and Q move in the same straight line. Particle P starts from rest and has a constant acceleration towards \(Q\) of \(0.5 \mathrm {~m} \mathrm {~s} ^ { - 2 }\). Particle \(Q\) starts 125 m from \(P\) at the same time and has a constant speed of \(10 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) away from \(P\). The initial values are shown in Fig. 4.
  6. Write down expressions for the distances travelled by P and by Q at time \(t\) seconds after the start of the motion.
  7. How much time does it take for P to catch up with Q and how far does P travel in this time?
OCR MEI M1 Q1
1 Fig. 2 shows a 6 kg block on a smooth horizontal table. It is connected to blocks of mass 2 kg and 9 kg by two light strings which pass over smooth pulleys at the edges of the table. The parts of the strings attached to the 6 kg block are horizontal. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{9bff41e0-7be0-4932-ae50-a612abb3fe19-1_345_1141_364_480} \captionsetup{labelformat=empty} \caption{Fig. 2}
\end{figure}
  1. Draw three separate diagrams showing all the forces acting on each of the blocks.
  2. Calculate the acceleration of the system and the tension in each string.
OCR MEI M1 Q2
2 The battery on Carol and Martin's car is flat so the car will not start. They hope to be able to "bump start" the car by letting it run down a hill and engaging the engine when the car is going fast enough. Fig. 6.1 shows the road leading away from their house, which is at A . The road is straight, and at all times the car is steered directly along it.
  • From A to B the road is horizontal.
  • Between B and C , it goes up a hill with a uniform slope of \(1.5 ^ { \circ }\) to the horizontal.
  • Between C and D the road goes down a hill with a uniform slope of \(3 ^ { \circ }\) to the horizontal. CD is 100 m . (This is the part of the road where they hope to get the car started.)
  • From D to E the road is again horizontal.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{9bff41e0-7be0-4932-ae50-a612abb3fe19-2_239_1137_636_484} \captionsetup{labelformat=empty} \caption{Fig. 6.1}
\end{figure} The mass of the car is 750 kg , Carol's mass is 50 kg and Martin's mass is 80 kg .
Throughout the rest of this question, whenever Martin pushes the car, he exerts a force of 300 N along the line of the car.
  1. Between A and B, Martin pushes the car and Carol sits inside to steer it. The car has an acceleration of \(0.25 \mathrm {~m} \mathrm {~s} ^ { - 2 }\). Show that the resistance to the car's motion is 100 N . Throughout the rest of this question you should assume that the resistance to motion is constant at 100 N .
  2. They stop at B and then Martin tries to push the car up the hill BC. Show that Martin cannot push the car up the hill with Carol inside it but can if she gets out.
    Find the acceleration of the car when Martin is pushing it and Carol is standing outside.
  3. While between B and C, Carol opens the window of the car and pushes it from outside while steering with one hand. Carol is able to exert a force of 150 N parallel to the surface of the road but at an angle of \(30 ^ { \circ }\) to the line of the car. This is illustrated in Fig. 6.2. \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{9bff41e0-7be0-4932-ae50-a612abb3fe19-2_216_425_1964_870} \captionsetup{labelformat=empty} \caption{Fig. 6.2}
    \end{figure} Find the acceleration of the car.
  4. At C, both Martin and Carol get in the car and, starting from rest, let it run down the hill under gravity. If the car reaches a speed of \(8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) they can get the engine to start.
OCR MEI M1 Q3
3 Fig. 7 illustrates a train with a locomotive, L, pulling two trucks, A and B. The locomotive has mass 90 tonnes and is subject to a resistance force of 2000 N .
Each of the trucks \(A\) and \(B\) has mass 30 tonnes and is subject to a resistance force of \(500 N\). \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{9bff41e0-7be0-4932-ae50-a612abb3fe19-3_153_1256_457_470} \captionsetup{labelformat=empty} \caption{Fig. 7}
\end{figure} Initially the train is travelling along a straight horizontal track. The locomotive is exerting a driving force of 12000 N .
  1. Find the acceleration of the train.
  2. Find the tension in the coupling between trucks A and B . When the train is travelling at \(10 \mathrm {~ms} ^ { - 1 }\), a fault occurs with truck A and the resistance to its motion changes from 500 N to 5000 N . The driver reduces the driving force to zero and allows the train to slow down under the resistance forces and come to a stop.
  3. Find the distance the train travels while slowing down and coming to a stop. Find also the force in the coupling between trucks A and B while the train is slowing down, and state whether it is a tension or a thrust. The fault in truck A is repaired so that the resistance to its motion is again 500 N . The train continues and comes to a place where the track goes up a uniform slope at an angle of \(\alpha ^ { \circ }\) to the horizontal.
  4. When the train is on the slope, it travels at uniform speed. The driving force remains at 12000 N . Find the value of \(\alpha\).
  5. Show that the force in the coupling between trucks A and B has the same value that it had in part (ii).
OCR MEI M1 Q4
4 Fig. 5 shows blocks of mass 4 kg and 6 kg on a smooth horizontal table. They are connected by a light, inextensible string. As shown, a horizontal force \(F \mathrm {~N}\) acts on the 4 kg block and a horizontal force of 30 N acts on the 6 kg block. The magnitude of the acceleration of the system is \(2 \mathrm {~ms} ^ { - 2 }\). \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{9bff41e0-7be0-4932-ae50-a612abb3fe19-4_119_1108_588_513} \captionsetup{labelformat=empty} \caption{Fig. 5}
\end{figure}
  1. Find the two possible values of \(F\).
  2. Find the tension in the string in each case.
OCR MEI M1 Q5
5 Fig. 8.1 shows a sledge of mass 40 kg . It is being pulled across a horizontal surface of deep snow by a light horizontal rope. There is a constant resistance to its motion. The tension in the rope is 120 N . \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{9bff41e0-7be0-4932-ae50-a612abb3fe19-5_125_852_391_638} \captionsetup{labelformat=empty} \caption{Fig. 8.1}
\end{figure} The sledge is initially at rest. After 10 seconds its speed is \(5 \mathrm {~ms} ^ { - 1 }\).
  1. Show that the resistance to motion is 100 N . When the speed of the sledge is \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), the rope breaks.
    The resistance to motion remains 100 N .
  2. Find the speed of the sledge
    (A) 1.6 seconds after the rope breaks,
    (B) 6 seconds after the rope breaks. The sledge is then pushed to the bottom of a ski slope. This is a plane at an angle of \(15 ^ { \circ }\) to the horizontal. \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{9bff41e0-7be0-4932-ae50-a612abb3fe19-5_263_854_1391_637} \captionsetup{labelformat=empty} \caption{Fig. 8.2}
    \end{figure} The sledge is attached by a light rope to a winch at the top of the slope. The rope is parallel to the slope and has a constant tension of 200 N . Fig. 8.2 shows the situation when the sledge is part of the way up the slope. The ski slope is smooth.
  3. Show that when the sledge has moved from being at rest at the bottom of the slope to the point when its speed is \(8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), it has travelled a distance of 13.0 m (to 3 significant figures). When the speed of the sledge is \(8 \mathrm {~ms} ^ { - 1 }\), this rope also breaks.
  4. Find the time between the rope breaking and the sledge reaching the bottom of the slope.
OCR MEI M1 Q1
1 Fig. 5 shows a block of mass 10 kg at rest on a rough horizontal floor. A light string, at an angle of \(30 ^ { \circ }\) to the vertical, is attached to the block. The tension in the string is 50 N . The block is in equilibrium. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{5a1895e1-abe3-4739-876a-f19458f0f6ed-1_409_585_472_768} \captionsetup{labelformat=empty} \caption{Fig. 5}
\end{figure}
  1. Show all the forces acting on the block.
  2. Show that the frictional force acting on the block is 25 N .
  3. Calculate the normal reaction of the floor on the block.
  4. Calculate the magnitude of the total force the floor is exerting on the block.
OCR MEI M1 Q2
2 In this question, positions are given relative to a fixed origin, O. The \(x\)-direction is east and the \(y\)-direction north; distances are measured in kilometres. Two boats, the Rosemary and the Sage, are having a race between two points A and B.
The position vector of the Rosemary at time \(t\) hours after the start is given by $$\mathbf { r } = \binom { 3 } { 2 } + \binom { 6 } { 8 } t , \text { where } 0 \leqslant t \leqslant 2 .$$ The Rosemary is at point A when \(t = 0\), and at point B when \(t = 2\).
  1. Find the distance AB .
  2. Show that the Rosemary travels at constant velocity. The position vector of the Sage is given by $$\mathbf { r } = \binom { 3 ( 2 t + 1 ) } { 2 \left( 2 t ^ { 2 } + 1 \right) }$$
  3. Plot the points A and B . Draw the paths of the two boats for \(0 \leqslant t \leqslant 2\).
  4. What can you say about the result of the race?
  5. Find the speed of the Sage when \(t = 2\). Find also the direction in which it is travelling, giving your answer as a compass bearing, to the nearest degree.
  6. Find the displacement of the Rosemary from the Sage at time \(t\) and hence calculate the greatest distance between the boats during the race.
OCR MEI M1 Q3
3 Fig. 2 shows a sack of rice of weight 250 N hanging in equilibrium supported by a light rope AB . End A of the rope is attached to the sack. The rope passes over a small smooth fixed pulley. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{5a1895e1-abe3-4739-876a-f19458f0f6ed-3_451_475_426_870} \captionsetup{labelformat=empty} \caption{Fig. 2}
\end{figure} Initially, end B of the rope is attached to a vertical wall as shown in Fig. 2.
  1. Calculate the horizontal and the vertical forces acting on the wall due to the rope. End B of the rope is now detached from the wall and attached instead to the top of the sack. The sack is in equilibrium with both sections of the rope vertical.
  2. Calculate the tension in the rope.
OCR MEI M1 Q4
4 As shown in Fig. 4, boxes P and Q are descending vertically supported by a parachute. Box P has mass 75 kg . Box Q has mass 25 kg and hangs from box P by means of a light vertical wire. Air resistance on the boxes should be neglected. At one stage the boxes are slowing in their descent with the parachute exerting an upward vertical force of 1030 N on box P . The acceleration of the boxes is \(a \mathrm {~m} \mathrm {~s} ^ { - 2 }\) upwards and the tension in the wire is \(T \mathrm {~N}\). \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{5a1895e1-abe3-4739-876a-f19458f0f6ed-3_332_358_1504_1526} \captionsetup{labelformat=empty} \caption{Fig. 4}
\end{figure}
  1. Draw a labelled diagram showing all the forces acting on box P and another diagram showing all the forces acting on box Q .
  2. Write down separate equations of motion for box P and for box Q .
  3. Calculate the tension in the wire.
OCR MEI M1 Q5
5 A cylindrical tub of mass 250 kg is on a horizontal floor. Resistance to its motion other than that due to friction is negligible. The first attempt to move the tub is by pulling it with a force of 150 N in the \(\mathbf { i }\) direction, as shown in Fig. 8.1. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{5a1895e1-abe3-4739-876a-f19458f0f6ed-4_310_1349_451_435} \captionsetup{labelformat=empty} \caption{Fig. 5.1}
\end{figure}
  1. Calculate the acceleration of the tub if friction is ignored. In fact, there is friction and the tub does not move.
  2. Write down the magnitude and direction of the frictional force opposing the pull. Two more forces are now added to the 150 N force in a second attempt to move the tub, as shown in Fig. 8.2. \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{5a1895e1-abe3-4739-876a-f19458f0f6ed-4_497_927_1350_646} \captionsetup{labelformat=empty} \caption{Fig. 5.2}
    \end{figure} Angle \(\theta\) is acute and chosen so that the resultant of the three forces is in the \(\mathbf { i }\) direction.
  3. Determine the value of \(\theta\) and the resultant of the three forces. With this resultant force, the tub moves with constant acceleration and travels 1 metre from rest in 2 seconds.
  4. Show that the magnitude of the friction acting on the tub is 661 N , correct to 3 significant figures. When the speed of the tub is \(1.8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), it comes to a part of the floor where the friction on the tub is 200 N greater. The pulling forces stay the same.
  5. Find the velocity of the tub when it has moved a further 1.65 m .
OCR MEI M1 Q6
6 An empty open box of mass 4 kg is on a plane that is inclined at \(25 ^ { \circ }\) to the horizontal.
In one model the plane is taken to be smooth. The box is held in equilibrium by a string with tension \(T \mathrm {~N}\) parallel to the plane, as shown in Fig. 6.1. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{5a1895e1-abe3-4739-876a-f19458f0f6ed-5_308_561_559_828} \captionsetup{labelformat=empty} \caption{Fig. 6.1}
\end{figure}
  1. Calculate \(T\). A rock of mass \(m \mathrm {~kg}\) is now put in the box. The system is in equilibrium when the tension in the string, still parallel to the plane, is 50 N .
  2. Find \(m\). In a refined model the plane is rough. The empty box, of mass 4 kg , is in equilibrium when a frictional force of 20 N acts down the plane and the string has a tension of \(P \mathrm {~N}\) inclined at \(15 ^ { \circ }\) to the plane, as shown in Fig. 6.2. \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{5a1895e1-abe3-4739-876a-f19458f0f6ed-5_359_559_1599_830} \captionsetup{labelformat=empty} \caption{Fig. 6.2}
    \end{figure}
  3. Draw a diagram showing all the forces acting on the box.
  4. Calculate \(P\).
  5. Calculate the normal reaction of the plane on the box.
OCR MEI M1 Q1
1 Fig. 1.1 shows a circular cylinder of mass 100 kg being raised by a light, inextensible vertical wire AB . There is negligible air resistance. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{bf477f61-9f8f-418a-86d8-392bc30323b1-1_306_256_368_965} \captionsetup{labelformat=empty} \caption{Fig. 1.1}
\end{figure}
  1. Calculate the acceleration of the cylinder when the tension in the wire is 1000 N .
  2. Calculate the tension in the wire when the cylinder has an upward acceleration of \(0.8 \mathrm {~m} \mathrm {~s} ^ { - 2 }\). The cylinder is now raised inside a fixed smooth vertical tube that prevents horizontal motion but provides negligible resistance to the upward motion of the cylinder. When the wire is inclined at \(30 ^ { \circ }\) to the vertical, as shown in Fig. 1.2, the cylinder again has an upward acceleration of \(0.8 \mathrm {~m} \mathrm {~s} ^ { - 2 }\). \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{bf477f61-9f8f-418a-86d8-392bc30323b1-1_308_490_1230_849} \captionsetup{labelformat=empty} \caption{Fig. 1.2}
    \end{figure}
  3. Calculate the new tension in the wire.
OCR MEI M1 Q2
2 Boxes A and B slide on a smooth, horizontal plane. Box A has a mass of 4 kg and box B a mass of 5 kg . They are connected by a light, inextensible, horizontal wire. Horizontal forces of 9 N and 135 N act on A and B in the directions shown in Fig. 5. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{bf477f61-9f8f-418a-86d8-392bc30323b1-1_95_915_2042_650} \captionsetup{labelformat=empty} \caption{Fig. 5}
\end{figure} Calculate the tension in the wire joining the boxes.
OCR MEI M1 Q3
3 Fig. 3 shows a system in equilibrium. The rod is firmly attached to the floor and also to an object, P. The light string is attached to P and passes over a smooth pulley with an object Q hanging freely from its other end. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{bf477f61-9f8f-418a-86d8-392bc30323b1-2_519_629_370_745} \captionsetup{labelformat=empty} \caption{Fig. 3}
\end{figure}
  1. Why is the tension the same throughout the string?
  2. Calculate the force in the rod, stating whether it is a tension or a thrust.
OCR MEI M1 Q4
4 Two trucks, A and B, each of mass 10000 kg , are pulled along a straight, horizontal track by a constant, horizontal force of \(P \mathrm {~N}\). The coupling between the trucks is light and horizontal. This situation and the resistances to motion of the trucks are shown in Fig. 4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{bf477f61-9f8f-418a-86d8-392bc30323b1-2_198_948_1454_592} \captionsetup{labelformat=empty} \caption{Fig. 4}
\end{figure} The acceleration of the system is \(0.2 \mathrm {~ms} ^ { 2 }\) in the direction of the pulling force of magnitude \(P\).
  1. Calculate the value of \(P\). Truck A is now subjected to an extra resistive force of 2000 N while \(P\) does not change.
  2. Calculate the new acceleration of the trucks.
  3. Calculate the force in the coupling between the trucks.