t4t sr+(L)1.

' tr'igure 1

A particle P of weight ff newtoas is attached to ote end of a light inextensible shing. The

other end of the saing is attached to a fixed point O. Ahorizontal force of magpitude 5 Nis applied to P. The prticle P is itr equilibrium with the string taut and with OP making

an angle of 25" to the downward vertical, as sholvn in Figure 1'

Find

(a) the tension in the string,(3)

(b) the value of W.(3)

[e4:b \^/ .

Two forces (4i-2j)N and (2i+ qilN act on aparticle Pof mass 1.5 kg. The resultant ofthese two forces is parallel to the vector (2i + 1;.

(a) Find the value of g.

(4)

At time t: A, P is moving with veloclty {-2i+ 4j)m st.

(b) Find the speed of P at time f : 2 seconds.

62*3' r [O ra,,r]-l4

(.$, (y.)"(;

({ =rha. t 3-V.vr+a;t V:

o)

b)

3. A car starts from rest and moves with constmt accelerdion along a straight horizontalroad. The carreaches a speed af Vms-l in20 seconds. Itmoves at constant speed I/m s1

for the next 30 seconds, then moves with constcnt deceleration 1 * t' rmtit it has speed2

8 m. 11. It moves at speed 8 m rl for the next 15 seconds and then moves with coastant-t

deceleration I * s-2 until it comes to rest.aJ

(a) Sketch, in the spactr below, a speed-time Saph for this journey.

In the first 20 seconds of this joumey the car travels 140 m.

Find

(b) the value of 4

(c) the total time for this joumeY,

{d) the total distance travelled by the car.

q) Soed

/*

(3)

al

$

(4)

(4)

".. l$vg lttO

V:l$V

eo

€b Ib b.!rt 7- i

I

l\ ?,=L"'cLaEL.N 6*=%dtx- lA ,-l

i

l\ + =t -1 J:L* th.t#$ e ?'* =qb l,

Ir+O +1?O+ 86 r j6 -F rzo rgb - 1*,*250+lz+ts+LY. p\i e&

I

c) IE,*

3e

sbe-lTS

boUat trrta- --

drstrenro,

toh,L tlr,rc, .

IiItiI

I

tttIa

4. At time t: A, a particle is projected vertically upwards with speed rz from a point,4. Theparticle moves freely under gravity. At time I the particle is at its maximum height f1above A.

(a) Find lin terms of u and g.(2)

2

(b) Show that H = u

)o

The point,4 is at a height 3fl above the ground.

(c) Find, in terms of 1} the total time from the instant of projection to &e instant when

the particle hits the ground.(4)

b)

S-HtA=tlv :o^

i -4,8t :-r

,//-LTLro = qL p ,\./I/

,) I Co -TtL

a) V: utaL u

s =(ulv)b = (u9t

= *T >uL ?--

:. H- +Pu\s1f4-E Z3

s--ut+t'ar?'

-3H =]fut *LOV'o)S

(A

va?,

, -3-Hla\U

3 -au -3H.-3 u2

(ru '+bt)

='3Tzorf -

-

'3b2-

LT'O LL:2-AE-3Tt=oi(u - 3-T)1c'+T) =Q

i

':--t =3T i

--i

f,.

a Q*) B {3m)

F'igurc 2

Two particlesl and B have ruxses 2m and3nr respectively. The particles are connectedby a light inexteasible siling whichprr*ses over a smooth light fixed pulley. The systemis held at rest with the string taut. The hanging parts of the string are vertical and A ardB xe above a horizontal plane, as shown in Figure 2. The system is released from rest.

(a) Show that the tension ia the string immediately after the particles are released.12$

Tng.

After descending 1.5 m, B strikes &e plane and is immediately brougfut to rest. Insubsequent motion, r{ does not reach the pulley.

&) find the distance travelled by ,4 between the instant when B strikes the plane and theinstant whenthe string next beccmes taut.

(6)

Given thatm:0.5 kg,

(c) find the magnitude of the impulse on,B due to the impact with the plane.

a)

(6)

the

a":*-g

E)6i'5 ilffitii,.g,_[r r --6 = {-9b --v= .fS --_b

Bxrrs )rou^l,s ;o$ '€ic\ t -!v

,t norJ rnour€a on)'F ;ra'r"\

Srut +*ratl

o --,rsb-ico'

0 = b( - Lt)JA

c) \,r,t,q\ n'ror'^eafurh .rCIa$

{ rr,r.f Mon^e4 tuN\ = o

:' ltrPu\re- -t 3](1jt

6.

<-tm+ +1m---+

Figure 3

A non-uniforxr br;amAD has weight Fnewtons and length 4 m. It is held in equilibrium

in a horizontal position by two vertical ropes attached to the beam. The ropes are attached

to two pcints 3 and C on the beam, where AB = I m and CD:1 m, as shown in Figure 3-

The tension in the rope attached to C is double the tension in drc rope attached to B. The

bea6 is noodetled as a rod and the ropes are modelled as light inextensible strings-

(a) Find the distance of the eentre of mass of the beam &om l.(6)

A small load of weidht kW newtons is attached to the beam at D. The beam remains in

equilibrium in a horizontal position. The load is modelled as a particle.

Find

(b) an expression for the tension in the rope attached to B, $ving your answer in tErms

of k andfi,(3)

(c) the set of possible values of ft for which both ropes remain taut.

4m

(2)

a)r?rr/l'w

Ltl^-Is -Tc & [ruxl+]Lxz sw ra

LTg = LW -k;rAl3Ht-4

3=z5

bi)

Canndh t,tl- aloorrb g

f,ltunS Alaou* L trf^'+ c^J^*,n Lt- tl ^'tnArrrp YaIu€",

lflTs= O

& L(rnax u/.[ = k/[rm.a'v 2

zLj

O/. lL <L-3

7.

X'igure 4

A particle P of mass 2.7 kg lies on a rough plane inclined at 40" to the horizontal- Theparticle is held in equilibrium by a force of magnitude 15 N acting at an angle of 50" to theplane, as shown in Figure 4. The force acts in avertical plane containing a line of greatest

slope of the plane. The particle is in equilibrium and is on the point of sliding down theplane-

Firld

(a) the magaitude of the normal reaction of,&e plane olr P, (4)

(b) th" coefficient of friction between P and the plane.(s)

The force of magnitude 15 N is rernoved.

(c) Detsrmine uihether P moveq justtfyi"g yorn answer.

flnaYry(4)

$e-(e*-19

= 3l'tr4-

JlN:9 -31:-$r-tlsfo&S0.-sS^Sttx== ;i+.3{,6

l,\:ot e,tos,L,f_o_ i -_ ^:frrnusA

-4a-

P qrrtt norac, darrr,* +l--C^r\oz

+-15Srnl5o-

-cTt

6L.

ff-r,srlf onorc:r:

Leave

blank

B:0oFigure I

Figure 1 shCIlvs the curve Cwifh plar equatim

r:2cos20" 0<0<1'4

The line / is parallel to the initial lirc and is a tangent to C-

Find an equation of I, giving your answer in the form r : f(0)"

-{ z- A S,nB -I}S'llQ

f-