# Topic 4

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```Questions
Q1.
A 60 kg student weighs 600 N.
He does a bungee jump.
The bungee cord becomes straight and starts to stretch when he has fallen 50 m.
(a) Complete the sentence by putting a cross (
He first stops moving
(1)
A before all the energy has disappeared
B before the bungee cord starts to stretch
C when the bungee cord is stretched the most
D when the elastic potential energy is zero
(b) Complete the sentence by putting a cross (
When his speed is 10 m/s his momentum is
(1)
A 600 kg m/s
B 3 000 kg m/s
C 6 000 N m/s
D 30 000 N m/s
(c) (i) Calculate the change in gravitational potential energy as the student falls 50 m.
Give the unit.
(3)
change in gravitational potential energy = . . . . . . . . . . . . . . . . . . . . . . unit . . . . . . . . . . . . . . . . .
.....
(ii) State at what point in the bungee jump the student has maximum kinetic energy.
(1)
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(iii) Explain why his maximum kinetic energy is likely to be less than your answer to
(c)(i).
(2)
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(Total for Question = 8 marks)
Q2.
A pilot begins to land an aircraft.
(a) The height of the aircraft decreases from 200 m above the ground to 100 m.
(i) What happens to the gravitational potential energy of the aircraft?
Put a cross (
(1)
A it becomes zero
B it decreases
C it does not change
D it increases
(ii) The velocity of the aircraft remains constant.
What happens to the kinetic energy of the aircraft?
Put a cross (
(1)
A it becomes zero
B it decreases
C it does not change
D it increases
(b) The aircraft lands with its wheels on the runway as shown.
The aircraft is moving forwards.
(i) Draw an arrow on the diagram to show the direction of the momentum of the aircraft.
(1)
(ii) The velocity of the aircraft when it lands is 75 m/s.
The mass of the aircraft is 130 000 kg.
Calculate the momentum of the aircraft.
(2)
momentum = . . . . . . . . . . . . . . . . . . . . . . kg m/s
(iii) The aircraft comes to a stop.
State the momentum change of the aircraft from when it lands to when it stops.
(1)
change in momentum = . . . . . . . . . . . . . . . . . . . . . . kg m/s
(c) When the aircraft lands, the momentum of each passenger also changes.
(i) Explain why it is more comfortable for a passenger if the aircraft takes a longer time to
slow down.
(2)
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(ii) Suggest why some aircraft need a very long runway to land safely.
(2)
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(Total for Question is 10 marks)
Q3.
Andrew skis down a hill.
(a) Andrew starts from the top of the hill and his speed increases as he goes downhill.
He controls his speed and direction by using his skis.
He brings himself to a stop at the bottom of the hill.
Describe the energy changes that happen between starting and stopping.
(3)
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(b) Andrew returns to the top of the hill and starts again.
(i) His mass is 67 kg.
Show that his momentum is about 2000 kg m/s when his velocity is 31 m/s.
(2)
(ii) He falls over when his momentum is 2000 kg m/s.
After he falls over, he slows down by sliding across the snow.
It takes 2.3 s for his momentum to reduce to zero.
Calculate the average force on Andrew as he slows down.
(2)
force = . . . . . . . . . . . . . . . . . . . . . . N
(iii) Andrew is not injured by the fall even though he was moving quickly.
Use ideas about force and momentum to explain why he is not injured.
(2)
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(Total for Question is 9 marks)
Q4.
* The items in the box are packed in bubble wrap to protect them from damage.
Explain, by considering changes either in momentum or in kinetic energy, how bubble wrap
protects the items in a box from damage caused by a fall.
(6)
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Q5.
Momentum, energy and forces
A box with a mass of 0.8 kg is lifted from the floor and placed on a shelf.
The shelf is 1.8 m above the floor.
(a) (i) The box has gained gravitational potential energy.
Calculate the gain in gravitational potential energy.
Gravitational field strength = 10 N/kg
(2)
gain in gravitational potential energy = ......................................... J
(ii) The box falls off the shelf.
State the kinetic energy of the box just before it hits the floor.
(1)
....................................................................... J
(iii) Just before the box hits the floor it has a momentum of 4.8 kg m/s.
Calculate the velocity of the box just before it hits the floor.
(3)
velocity = ........................................ m/s
*(b) The items in the box are packed in bubble wrap to protect them from damage.
Explain, by considering changes either in momentum or in kinetic energy, how bubble wrap
protects the items in a box from damage caused by a fall.
(6)
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Q6.
Some students investigate a model of the craters produced by meteorite impacts.
They drop balls into a tray filled with sand.
They use six balls with different masses.
They drop each ball from the same height.
(a) (i) Which one of these graphs shows the relationship between the gravitational potential
energy (gpe) of the balls and their mass when they are all at the same height?
Put a cross (
(1)
(ii) Describe how the energy of a ball changes as it drops towards the sand.
(2)
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(b) This photograph shows the sand after several balls have hit it.
The students read this information in a textbook:
'When work is done, energy is transferred.'
Explain how work is done when the balls impact on the sand.
(2)
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(c) When one ball hits the sand, it has a velocity of 6.2 m/s.
It has a momentum of 0.46 kg m/s.
(i) Calculate the mass of the ball.
(3)
mass of ball = ........................................................... kg
(ii) The ball takes 0.17 s to come to rest after it hits the sand.
Calculate the average impact force.
(2)
average impact force = ........................................................... N
Mark Scheme
Q1.
(a)
C when the bungee
(1)
(b)
(c)(i)
(c)(ii)
(c)(iii)
cord is stretched the
most
A
600 kg m/s
(1)
Substitution: (1)
(3)
60 × 10 × 50 or 600 ×
50
give two marks for
Evaluation: (1)
working
30 000
j / joule
Unit: (1)
30 kJ for full marks
J / Nm
After falling 50 m /
tension starting to
(1)
when the cord becomes increase
straight/when cord
starts to stretch
at terminal velocity
ignore maximum
velocity/speed
(2)
any two of
not all GPE goes to KE
not all GPE is
transferred to KE (1)
maximum energy is
same (value) as GPE
before falling /speed
does not reach the
speed at which he
should fall
some {of the GPE
transfers to thermal
some lost as heat/sound
energy /work is done} (of rope or movement
(1)
through air)
due to drag (1)
(air) resistance / friction
ignore wind
Q2.
(a)(i) B it decreases
(a)(ii) C it does not change
Mark
(1)
(1)
(b)(i)
horizontal arrow (judge by eye),
pointing to the right anywhereon the
diagram
(1)
(b)(ii) substitution: (1)
130 000 × 75
give full marks for correct
evaluation: (1)
9 750 000 (kgm/s) (Ns)
(b)(iii) 9 750 000 kgm/s
Ignore minus sign
9.75 x 106 (kgm/s) (Ns)
same value as answer to (b)(ii)
Ignore minus sign
(c)(i)
(2)
(1)
(2)
An explanation linking two of the
following:
pressure is smaller/less
force is smaller/less (1)
momentum changes more
slowly (1)
lower deceleration (1)
use of the formula (1)
(c)(ii) Any two from:
slower deceleration force is
proportional to rate of change of
momentum/F= (mv – mu)/t
accept reverse argument for empty
aircraft
(2)
expert
heavier/more passengers/more cargo
has more mass (1)
has more momentum (1)
has more k.e. (1)
higher velocity
brakes need to do more work
(1)
higher speed/moving faster
Total marks for question = 10 marks
Q3.
(a)
Description including 3 of the
following:
(Gravitational) potential
energy (transferred) to KE(1)
(G)PE (transferred) to KE Allow
gravitational energy for GPE
Energy transferred to heat because of
Idea of energy transfer to
air resistance/ friction
heat/sound whilst descending
(1)
Chemical energy is transferred The energy goes to heat as he stops.
to heat energy in Andrew (1) Energy is transferred to the
surroundings
Idea of energy dissipated on
stopping (1)
(b)(i)
substitution (1)
Mark
(3)
67 × 31
2080, 2100
evaluation (1)
2077 (kg m/s)
working backwards using 2000
(v=) 29.85, 30
(m=) 64.52, 65
(b)(ii) substitution (1)
2000 ÷ 2.3
evaluation (1)
870 (N)
(b)(iii) an explanation linking two of the
following
(2)
67 X 31=2000 scores only one mark
900, 869.6, 869.5
903
force is reduced/ less /not as strong
(2)
(2)
slows down/changes momentum
Force on Andrew is quite small gradually
(1)
acceleration = 1.35 'g' or 13.5 m/s2
Because impact time is long
(1)
slows down (rate of) change of
momentum scores 2 marks
The acceleration/deceleration
is quite small (1)
Because impact distance is far
(1)
Total question = 8 marks
Q4.
Question
Number
QWC
*
Indicative Content
Mark
some of the following
points
(6)
Either momentum
• item must lose
momentum in order to
come to rest
• force of impact
depends on rate of
change of momentum
• if item is dropped
from greater height
then velocity at impact
is greater
• so momentum to
be lost is greater
• bubble wrap works
by increasing the time
taken for the item to
come to rest
• reduces the rate of
change of momentum
• this reduces the
force of impact to a
safe value
Or kinetic energy
• item must lose
kinetic energy in order
to come to rest
• force of impact
depends on work done
• if item is dropped
from greater height
then velocity at impact
is greater
• so kinetic energy to
be lost is greater
• loss of kinetic
energy equals work
done bringing item to
rest
• bubble wrap works
by increasing the
distance travelled for
the item to come to
rest
Level
1
0
1-2
• this reduces the
force of impact to a
safe value
No rewardable content
• a limited explanation of the cushioning
effect e.g. bubble wrap reduces the force of
impact
• the answer communicates ideas using
simple language and uses limited scientific
terminology
• spelling, punctuation and grammar are used
with limited accuracy
2
3-4
• some explanation linking cushioning effect
with either increased time of impact or
increased distance of impact e.g. bubble wrap
reduces the force of impact by increasing the
time of impact
• the answer communicates ideas showing
some evidence of clarity and organisation and
uses scientific terminology appropriately
3
5-6
• spelling, punctuation and grammar are used
with some accuracy
• a detailed explanation linking either force
with rate of change in momentum or energy
with work done and distance e.g. the bubble
wrap increases the time of impact which
reduces the rate of change of momentum
which reduces the force of impact
• the answer communicates ideas clearly and
coherently uses a range of scientific
terminology accurately
• spelling, punctuation and grammar are used
with few errors
Q5.
Question
Number
(a)(i)
Mark
substitution (1)
give full marks for
working
(2)
0.8 × 10 × 1.8
evaluation (1)
14.4 (J)
Question
Number
(a)(ii)
Mark
14.4 (J)
e.c.f from part (i)
(1)
Question
Number
(a)(iii)
Mark
substitution (1)
allow substitution and
transposition in either
(3)
4.8 = 0.8 × v
transposition (1)
v = 4.8/0.8
order
give full marks for
working
evaluation (1)
6 (m/s)
Question
Number
QWC
*(b)
Indicative Content
Mark
some of the following
points
(6)
Either momentum
• item must lose
momentum in order to
come to rest
• force of impact
depends on rate of
change of momentum
• if item is dropped
from greater height
then velocity at impact
is greater
• so momentum to
be lost is greater
• bubble wrap works
by increasing the time
taken for the item to
come to rest
• reduces the rate of
change of momentum
• this reduces the
force of impact to a
safe value
Or kinetic energy
• item must lose
kinetic energy in order
to come to rest
• force of impact
depends on work done
• if item is dropped
from greater height
then velocity at impact
is greater
• so kinetic energy to
be lost is greater
• loss of kinetic
energy equals work
done bringing item to
rest
• bubble wrap works
by increasing the
distance travelled for
the item to come to
rest
Level
1
0
1-2
• this reduces the
force of impact to a
safe value
No rewardable content
• a limited explanation of the cushioning
effect e.g. bubble wrap reduces the force of
impact
• the answer communicates ideas using
simple language and uses limited scientific
terminology
• spelling, punctuation and grammar are used
with limited accuracy
2
3-4
• some explanation linking cushioning effect
with either increased time of impact or
increased distance of impact e.g. bubble wrap
reduces the force of impact by increasing the
time of impact
• the answer communicates ideas showing
some evidence of clarity and organisation and
uses scientific terminology appropriately
3
5-6
• spelling, punctuation and grammar are used
with some accuracy
• a detailed explanation linking either force
with rate of change in momentum or energy
with work done and distance e.g. the bubble
wrap increases the time of impact which
reduces the rate of change of momentum
which reduces the force of impact
• the answer communicates ideas clearly and
coherently uses a range of scientific
terminology accurately
• spelling, punctuation and grammar are used
with few errors
Q6.