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1. the diagram shows a trolley moving down a gentle slope.

add forces to the diagram below to produce a free-body force diagram for the trolley.

(3)

the trolley is photographed by a multiflash technique. the result is shown below.

what evidence is there that the trolley is moving with constant velocity?

....................................................................................................................................(1)

state the acceleration of the trolley down the slope.

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what does the value of the acceleration indicate about the forces acting on the trolley?

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(total6marks)

2. this question rewarded those candidates who understood the use of labelled free-body forcediagrams as well as those who understood the relationship between the resultant force andacceleration of a body. many candidates gained all six marks, but some omitted all labels on thediagram whilst others thought the acceleration down the slope at constant velocity was equal to

g.

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3. the diagram shows a velocity-time graph for a ball bouncing vertically on a hard surface. theball was dropped at t= 0 s.

! . 0

0

" ! . 0

v # m s" $

0 . ! $ . 0 $ . ! % . 0 % . !t # s

at what time does the graph show the ball in contact with the ground for the third time?

...............................................................................................................................................(1)

the downward sloping lines on the graph are straight and parallel with each other. why?

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show that the height from which the ball was dropped is about $.% m.

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...............................................................................................................................................(2)

sketch a displacement-time curve on the axes below for the first second of the motion.

00 . ! $ . 0

t # s

& i s p l a c e m e n t # m

(3)

what is the displacement of the ball when it finally comes to rest?

...............................................................................................................................................(1)

(total 9 marks)

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4. t= %.$s $

represents acceleration of the ball

force on ball orgravitational field strengthoracceleration is constant oruniform %

relevant equation orcorrect area

substitution correct%

t # s00 . ! $ . 0

& i s p l a c e m e n t # m

displacement scale as shown above

first half of curve correctsecond half correct with reduced height '

"$.%! m (correct magnitudeanddirection)*look at candidate +s displacement origin $

[9]

5.

palaeontologists are able to deduce much about the behaviour of dinosaurs from the study offossilised footprints.

the tracks below show the path of a tyrannosaurus rexas it attacks a stationary triceratops.

$ 0 m

T y r a n n o s a u r u s R e x - t a t i o n a r yT r i c e r a t o p s

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the time between footprints is 0.% s. show that the maximum speed of the tyrannosaurus rexisabout $0 m s"$.

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...............................................................................................................................................(2)

tyrannosaurus rexis believed to have attacked its prey by charging and locking its /aws on theprey. tyrannosaurus rexwould be at its maximum speed when it hit the stationary prey.

this tyrannosaurus rexhas a mass of 000 kg. calculate its momentum /ust before it hits thetriceratops.

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momentum =1111111111111111111(2)

triceratopshas a mass of !000 kg. calculate their combined speed immediately after thecollision.

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combined speed =1111111111111111111(3)

the skull of tyrannosaurus rexis heavily reinforced to withstand the force produced in such acollision.

calculate the force exerted on the tyrannosaurus rexif the time taken to reach their combinedspeed after the collision is 0.'0 s.

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force =1111111111111111111(3)

(total 10 marks)

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6. '0 m 2 (! 3 0.% s)= 4. m s"$ %

(000 kg 3 4. m s"$) *allow $0 m s"$ as e.c.f.= 5 000 (kg m s"$) %

momentum before = momentum after

(000 kg 3 4. m s"$) 0 = (000 kg !000 kg) 3 = (000 kg 3 4. m s"$) 2 ($% 000 kg)= !. m s"$ *allow !.5 if e.c.f. of $0 m s"$ '

force = change in momentum 2 time= 000 kg 3 *4. m s"$"!. m s"$2 0.'0 s= 4' 000 n *45 000 n if $0 m s"$used '

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7. the diagram below shows a trolley running down a slope.

6

7

complete the diagram to show an experimental arrangement you could use to determine how thetrolley+s position varies with time.

(2)

the data is used to produce a velocity-time graph for the trolley. below isthe graph for themotion from point a to point b. time is taken to be 8ero as the trolley passes a, and the trolley

passes b 0.0 s later.

% . 0

$ . !

$ . 0

0 . !

0 0 . $ 0 0 . % 0 0 . ' 0 0 . 9 0 0 . ! 0 0 . 0 0 . 0

: e l o c i t y # m sv " $

; i m e # st

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the motion shown on the graph can be described by the equation = u at. use informationfrom the graph to determine values for uand a.

u= ..................................................

...............................................................................................................................................

a= ..................................................

...............................................................................................................................................(3)

determine the distance ab.

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ab = ...............................................................(3)

on the axes below sketch a graph to show how the displacementxof the trolley from point avaries with time t. add a scale to each axis.

x # m

t # s(3)

(total11marks)

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8. diagram