Kinetic and potential energy

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Kinetic and potential energy
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1 Kinetic energy (KE)

• A force F acts on an object of mass m, increasing
  its velocity from u to v over a distance s

u
v
F
F
s
Kinetic energy (KE) gained
work done by force
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1 Kinetic energy (KE)
u
v
F
F
s
KE gained
W Fs
?
F ma
v2 ? u2 2as

? KE gained Fs
ma
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1 Kinetic energy (KE)
u
v
F
F
s
KE gained
When the objects velocity is u
KE
When the objects velocity is v
KE
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1 Kinetic energy (KE)
Simulation
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2 Gravitational potential energy (PE)

• PE is the energy an object possesses due to its
  position above the ground.

mg
h
A box of mass m is lifted a height h above the
ground.
Force needed to lift box weight
mg
mg
Work done force ? distance lifted
mgh (PE gained by box) (unit J)
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Gravitational potential energy (PE)
Points to note in calculating PE
Only the height lifted against gravity matters,
NOT the actual distance moved.
less force, but longer distance
g
mass m
mass m
h
both have the same PE at the top!!
PE mgh
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Gravitational potential energy (PE)
Simulation
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Example 3
KEpassenger car vs KEtruck
(a) Find the KE of a passenger car of mass 1000
kg travelling at (i) 70 km h1, (ii) 100 km h1.
(i) KEpassenger car at 70 km h1
189 000 J
0.189 MJ
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Example 3
(a) Find the KE of a passenger car of mass 1000
kg travelling at (i) 70 km h1, (ii) 100 km h1.
KE of car at 70 km h?1 0.189 MJ
(ii) KEpassenger car at 100 km h1
386 000 J
0.386 MJ
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Example 3
(b) Find the KE of a 10-tonnes truck (10 000 kg)
travelling at 70 km h1.
KE of car at 70 km h?1 0.189 MJ
KEtruck at 70 km h1
1.89 MJ
1 890 000 J
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Example 4
A car of mass 1500 kg is travelling at 20 m s1
(72 km h 1).
(a) What is the kinetic energy of the car?
300 000 J
0.3 MJ
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Example 4
(b) Brakes are applied to stop the car. If the
braking force is 7500 N (equal to half the weight
of the car), what is the braking distance?
Data KE of car 0.3 MJ
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Example 4
KE of car 0.3 MJ braking force 7500 N
To stop the car,
work done by braking force KE of the car
F 7500 N
force is ?ve because forward is taken as ve
?7500 ? s 0 ? 300 000
s 40 m
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Example 5
A 2-kg box is lifted 1 m from the floor to a
table top and then to a shelf 1 m above the
table. What is the gravitational potential energy
the box gains
(a) at the table top, (b) on the shelf?
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Example 5
(a) PE gain of box at the table top
mgh
2 ? 10 ? 1 20 J
(b) PE gain of box on the shelf
mgh
2 ? 10 ? 2 40 J
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Q1
A 0.2-kg stone is thrown with 5 m s?1. Find the
gain in KE of it.
5 m s?1
Initial KE (KE1)
0.2
52
2.5
Final KE (KE2)
0.2
302
90
30 m s?1
87.5
KE gain KE2 ? KE1 ____ J
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Q2
Pauline of mass 50 kg goes hiking. After walking
for 5 km, she is 20 m vertically above her
starting point.
(a) What is her potential energy gained?
Potential energy gained mgh ____ ? 10 ? _____
_________ J
50
20
10 000
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Q2
(b) If she takes a steeper route and keeps the
start and end points the same, will her PE gain
be different? Why?
Her PE gain will be _______________. It is
because both her _________________ and
______________ displacement are the same.
the same
weight
vertical