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*N35408A0228*
1. A cyclist starts from rest and moves along a straight horizontal road. The combined mass
of the cyclist and his cycle is 120 kg. The resistance to motion is modelled as a constant
force of magnitude 32 N. The rate at which the cyclist works is 384 W. The cyclist
accelerates until he reaches a constant speed ofv m s1.
Find
(a) the value ofv,
(3)
(b) the acceleration of the cyclist at the instant when the speed is 9 m s1.
(3)
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*N35408A0328* Turn over
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(Total 6 marks)
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*N35408A0428*
2. A particle of mass 2 kg is moving with velocity (5i+j) m s1 when it receives an impulse
of (6i+ 8j) N s. Find the kinetic energy of the particle immediately after receiving the
impulse.
(5)
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*N35408A0528* Turn over
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(Total 5 marks)
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*N35408A0628*
3. A particle moves along thex-axis. At time t= 0the particle passes through the origin with
speed 8 m s1 in the positivex-direction. The acceleration of the particle at time tseconds,
t0, is (4t3 12t) m s2 in the positivex-direction.
Find
(a) the velocity of the particle at time tseconds,(3)
(b) the displacement of the particle from the origin at time tseconds,
(2)
(c) the values oftat which the particle is instantaneously at rest.
(3)
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*N35408A0728* Turn over
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*N35408A0828*
Question 3 continued
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*N35408A0928* Turn over
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(Total 8 marks)
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*N35408A01028*
4.
Figure 1
A box of mass 30 kg is held at rest at point A on a rough inclined plane. The plane is
inclined at 20 to the horizontal. PointB is 50 m fromA up a line of greatest slope of the
plane, as shown in Figure 1. The box is dragged fromA toB by a force acting parallel to
AB and then held at rest at B. The coefficient of friction between the box and the plane
is1
4
. Friction is the only non-gravitational resistive force acting on the box. Modelling
the box as a particle,
(a) find the work done in dragging the box fromA toB.
(6)
The box is released from rest at the pointB and slides down the slope. Using the work-
energy principle, or otherwise,
(b) find the speed of the box as it reachesA.
(5)
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*N35408A01128* Turn over
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*N35408A01228*
Question 4 continued
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*N35408A01328* Turn over
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(Total 11 marks)
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*N35408A01428*
5.
Figure 2
The uniform L-shaped laminaABCDEF, shown in Figure 2, has sidesAB andFEparallel,
and sidesBCandED parallel. The pairs of parallel sides are 9 cm apart. The pointsA,F,
D and Clie on a straight line.
AB=BC= 36 cm,FE=ED= 18 cm. ABC=FED= 90, and
BCD=EDF=EFD =BAC=45.
(a) Find the distance of the centre of mass of the lamina from
(i) sideAB,
(ii) sideBC.
(7)
The lamina is freely suspended fromA and hangs in equilibrium.
(b) Find, to the nearest degree, the size of the angle betweenAB and the vertical.
(3)
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A
B C
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F
9 cm
18 cm36 cm
9 cm
36 cm
18 cm
45
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45
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*N35408A01528* Turn over
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*N35408A01628*
Question 5 continued
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*N35408A01728* Turn over
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(Total 10 marks)
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*N35408A01828*
6. [In this question, the unit vectors i andj are in a vertical plane, i being horizontal andj
being vertically upwards.]
Figure 3
At time t = 0, a particle P is projected from the point A which has position vector
10j metres with respect to a fixed origin O at ground level. The ground is horizontal. The
velocity of projection ofP is (3i+ 5j) m s1, as shown in Figure 3. The particle moves
freely under gravity and reaches the ground afterTseconds.
(a) For 0tT, show that, with respect to O, the position vector, r metres, ofPat time
tseconds is given by
r =3ti+(10+5t4.9t2)j
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(b) Find the value ofT.
(3)
(c) Find the velocity ofPat time tseconds (0tT).
(2)
WhenPis at the pointB, the direction of motion ofPis 45below the horizontal.
(d) Find the time taken forPto move fromA toB.
(2)
(e) Find the speed ofPas it passes throughB.
(2)
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10 m
1(3 5 ) m s+i j
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*N35408A01928* Turn over
Question 6 continued
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*N35408A02028*
Question 6 continued
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*N35408A02128* Turn over
Question 6 continued
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(Total 12 marks)
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*N35408A02228*
7.
Figure 4
A uniform plankAB, of weight 100 N and length 4 m, rests in equilibrium with the endA
on rough horizontal ground. The plank rests on a smooth cylindrical drum. The drum is
fixed to the ground and cannot move. The point of contact between the plank and the drum
is C, whereAC= 3 m, as shown in Figure 4. The plank is resting in a vertical plane whichis perpendicular to the axis of the drum, at an angle to the horizontal, where sin =
1
3.
The coefficient of friction between the plank and the ground is . Modelling the plank as
a rod, find the least possible value of.
(10)
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*N35408A02328* Turn over
Question 7 continued
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*N35408A02428*
Question 7 continued
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*N35408A02528* Turn over
Question 7 continued
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(Total 10 marks)
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*N35408A02628*
8. A particle Pof mass m kg is moving with speed 6 m s1 in a straight line on a smooth
horizontal floor. The particle strikes a fixed smooth vertical wall at right angles and
rebounds. The kinetic energy lost in the impact is 64 J. The coefficient of restitution
betweenPand the wall is13
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(a) Show that m = 4. (6)
After rebounding from the wall, Pcollides directly with a particle Q which is moving
towards Pwith speed 3 m s1. The mass ofQ is 2 kg and the coefficient of restitution
betweenPand Q is1
3.
(b) Show that there will be a second collision betweenPand the wall.
(7)
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*N35408A02728* Turn over
Question 8 continued
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TOTAL FOR PAPER: 75 MARKS
Q8
(Total 13 marks)