cambridge international as & a level...cambridge international as & a level mathematics...
TRANSCRIPT
Cambridge International AS & A Level
MATHEMATICS 9709/04
Paper 4 Mechanics For examination from 2020
SPECIMEN PAPER 1 hour 15 minutes
You must answer on the question paper.
You will need: List of formulae (MF19)
INSTRUCTIONS ● Answer all questions. ● Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs. ● Write your name, centre number and candidate number in the boxes at the top of the page. ● Write your answer to each question in the space provided. ● Do not use an erasable pen or correction fluid. ● Do not write on any bar codes. ● If additional space is needed, you should use the lined page at the end of this booklet; the question
number or numbers must be clearly shown. ● You should use a calculator where appropriate. ● You must show all necessary working clearly; no marks will be given for unsupported answers from a
calculator. ● Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in
degrees, unless a different level of accuracy is specified in the question. ● Where a numerical value for the acceleration due to gravity (g) is needed, use 10 m s–2.
INFORMATION ● The total mark for this paper is 50. ● The number of marks for each question or part question is shown in brackets [ ].
*0123456789*
© UCLES 2017 [Turn over
This document has 14 pages. Blank pages are indicated.
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1 A pa r t i c l e P i s pr oj e c t e d ve r t i c a l l y upw a r ds w i t h s pe e d 20 m s – 1 f r om a poi nt on t he gr ound.
(a) F i nd t he gr e a t e s t he i ght a bove t he gr ound r e a c he d by P . [ 2]
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(b) F i nd t he t ot a l t i m e f r om pr oj e c t i on unt i l P r e t ur ns t o t he gr ound. [ 2]
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2 A c ons t a nt r e s i s t a nc e o f m a gn i t ude 1350 N a c t s on a c a r of m a s s 1200 kg.
(a) T he c a r i s m ovi ng a l ong a s t r a i ght l e ve l r oa d a t a c ons t a nt s pe e d of 32 m s – 1 .
F i nd, i n kW , t he r a t e a t w hi c h t he e ngi ne of t h e c a r i s w o r ki ng. [ 2]
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(b) T he c a r t r a ve l s a t a c ons t a nt s pe e d dow n a hi l l i nc l i ne d a t a n a ngl e of θ ° t o t he hor i z ont a l , w he r e s i n θ ° = 20
1 , w i t h t he e ngi ne w or ki ng a t 31.5 kW .
F i nd t he s pe e d of t he c a r . [ 3]
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3 T hr e e s m a l l s m oot h s phe r e s A , B a nd C of e qua l r a di i a nd of m a s s e s 4 kg, 2 kg a nd 3 kg r e s pe c t i ve l y , l i e i n t ha t or de r i n a s t r a i ght l i ne on a s m oot h hor i z ont a l pl a ne . I ni t i a l l y , B a nd C a r e a t r e s t a nd A i s m ovi ng t ow a r ds B w i t h s pe e d 6 m s – 1 . A f t e r t he c ol l i s on w i t h B , s phe r e A c ont i nue s t o m ove i n t he s a m e di r e c t i on but w i t h s pe e d 2 m s – 1 .
(a) F i nd t he s pe e d of B a f t e r t hi s c ol l i s on. [ 2]
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S phe r e B c ol l i de s w i t h C . I n t hi s c ol l i s on t he s e t w o s phe r e s c oa l e s c e t o f or m a n o bj e c t D .
(b) F i nd t he s pe e d of D a f t e r t hi s c ol l i s i on. [ 2]
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(c) S how t ha t t he t ot a l l os s of ki ne t i c e ne r gy i n t he s ys t e m due t o t he t w o c ol l i s i ons i s 38.4 J . [ 2]
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4 A pa r t i c l e o f m a s s 20 kg i s on a r ough pl a ne i nc l i ne d a t a n a ngl e of 30 ° t o t he hor i z on t a l . A f or c e of m a gni t ude 25 N , a c t i ng a t a n a ngl e of 20 ° a bove a l i ne of gr e a t e s t s l ope of t he pl a ne , i s us e d t o pr e ve nt t he pa r t i c l e f r om s l i di ng dow n t he pl a ne . T he c oe f f i c i e n t of f r i c t i on be t w e e n t he pa r t i c l e a nd t h e pl a ne i s μ.
(a) C om pl e t e t he di a gr a m be l ow t o s how a l l t he f o r c e s a c t i n g on t he pa r t i c l e . [ 1]
30°
25 N
20°
(b) F i nd t he l e a s t pos s i bl e va l ue of μ. [ 5]
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5 A c a r of m a s s 1200 kg i s pul l i ng a t r a i l e r of m a s s 800 kg up a hi l l i nc l i ne d a t a n a ngl e of s i n – 1 ( 0.1 ) t o t he hor i z ont a l . T he c a r a n d t he t r a i l e r a r e c onne c t e d by a l i ght r i gi d t ow - ba r w hi c h i s pa r a l l e l t o t he r oa d. T he dr i vi ng f or c e of t he c a r ’ s e ngi ne i s 2500 N a nd t he r e s i s t a nc e s t o t he c a r a nd t r a i l e r a r e 300 N a nd 100 N r e s pe c t i ve l y .
(a) F i nd t he a c c e l e r a t i on of t he s ys t e m a nd t he t e n s i on i n t he t ow - ba r . [ 4]
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(b) W he n t he c a r a nd t r a i l e r a r e t r a ve l l i ng a t a s pe e d of 30 m s – 1 , t he dr i vi ng f or c e be c om e s z e r o.
F i nd t he t i m e , i n s e c onds , be f or e t h e s ys t e m c om e s t o r e s t a nd t he f or c e i n t he t ow - ba r dur i ng t hi s t i m e . [ 5]
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6 A pa r t i c l e P m ove s i n a s t r a i ght l i ne . T he ve l oc i t y v m s – 1 a t t i m e t s i s gi ve n by
v = 5 t ( t – 2) f or 0 ⩽ t ⩽ 4,
v = k f or 4 ⩽ t ⩽ 14,
v = 68 – 2 t f or 14 ⩽ t ⩽ 20,
w he r e k i s a c ons t a nt .
(a) F i nd k . [ 1]
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(b) S ke t c h t he ve l oc i t y–t i m e gr a ph f or 0 ⩽ t ⩽ 20. [ 3]
(c) F i nd t he s e t of va l ue s of t f or w hi c h t he a c c e l e r a t i on of P i s pos i t i ve . [ 2]
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(d) F i nd t he t ot a l di s t a nc e t r a ve l l e d by P i n t he i nt e r va l 0 ⩽ t ⩽ 20. [ 5]
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7A
B
P2.5 m
T w o pa r t i c l e s A a nd B , of m a s s e s 0. 8 kg a nd 0.2 kg r e s pe c t i ve l y , a r e c onne c t e d by a l i ght i n e xt e ns i bl e s t r i ng. P a r t i c l e A i s pl a c e d on a hor i z ont a l s ur f a c e . T he s t r i ng pa s s e s ove r a s m a l l s m oot h pul l e y P f i xe d a t t he e dge of t he s ur f a c e , a n d B ha ngs f r e e l y . T he hor i z ont a l s e c t i on of t he s t r i ng, A P , i s of l e ngt h 2.5 m ( s e e di a gr a m ) . T he pa r t i c l e s a r e r e l e a s e d f r om r e s t w i t h bot h s e c t i ons o f t he s t r i ng t a ut .
(a) G i ve n t ha t t he s ur f a c e i s s m oot h, f i nd t he t i m e t a ke n f or A t o r e a c h t he pul l e y . [ 5]
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(b) I t i s gi v e n i ns t e a d t h a t t he s ur f a c e i s r ough a nd t ha t t he s pe e d of A i m m e di a t e l y be f or e i t r e a c he s t he pul l e y i s v m s – 1 . T he w or k done a ga i ns t f r i c t i on a s A m ove s f r om r e s t t o t he pul l e y i s 2 J .
U s e a n e ne r gy m e t hod t o f i nd v . [ 4]
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Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity.
Cambridge Assessment International Education is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which itself is a department of the University of Cambridge.
Additional page
I f you us e t he f o l l ow i ng l i ne d pa ge t o c om pl e t e t he a ns w e r ( s ) t o a ny que s t i on ( s ) , t he que s t i on num be r ( s ) m us t be c l e a r l y s how n.
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