SME
Grade 8 Science · Physical Science
Kinetic and potential energy
Use this for “A 200 kg coaster car drops from 30 m to 12 m. How much kinetic energy does it have, and how fast is it going?”
Diagram
PE + KE = 23,520 J + 35,280 J
= 58,800 J
PE = m × g × h
= 200 kg × 9.8 m/s² × 12 m
= 23,520 J
KE = ½ × m × v²
= ½ × 200 kg × (18.783 m/s)²
= 35,280 J
Going down, potential energy turns into kinetic energy; the total stays the same
This is an example. Type your own values to start a new problem.
m
Mass
example · kg
H
Top height
example · m
h
Height now
example · m
PE
Potential energy
calculated · J
KE
Kinetic energy
calculated · J
E
Total energy
calculated · J
v
Speed
worked out (not typed)
Formulas
PE
=
m
×
9.8
×
h
(potential
energy
=
mass
×
9.8
×
height
now)
23,520 = 200 × 9.8 × 12
E
=
m
×
9.8
×
H
(total
energy
=
mass
×
9.8
×
top
height)
58,800 = 200 × 9.8 × 30
PE
+
KE
=
E
(potential
energy
+
kinetic
energy
=
total
energy)
23,520 + 35,280 = 58,800
KE
=
1
2
×
m
×
v
2
(kinetic
energy
=
1/2
×
mass
×
speed²)
35,280
=
1
2
×
200
×
18.783
2
Assumptions
•
The car starts at rest at the top, so all its energy is potential energy: m × g × h, with g = 9.8 N/kg.
•
As it drops, potential energy becomes kinetic energy: 1/2 × m × v². The total stays the same.
•
Friction and air are too small to count here; on a real coaster they turn some energy into heat, so each hill is lower than the last.
•
Energy is in joules (J): 1 J lifts 1 newton by 1 meter.
Step-by-step
WE KNOW
m = 200 kg (mass), H = 30 m (top height), h = 12 m (height now)
FIND
potential energy (PE), total energy (E), kinetic energy (KE), speed (v)
Step 1 · Find potential energy (PE)
Use PE = m × 9.8 × h (potential energy = mass × 9.8 × height now)
Each kilogram lifted each meter stores 9.8 J.
PE = 200 × 9.8 × 12
PE = 1,960 × 12
PE = 23,520 J
Step 2 · Find total energy (E)
Use E = m × 9.8 × H (total energy = mass × 9.8 × top height)
At the top it is all potential energy.
E
=
200
×
9.8
×
30
E
=
1,960
×
30
E
=
58,800
J
Step 3 · Find kinetic energy (KE)
Use PE + KE = E (potential energy + kinetic energy = total energy)
What is not potential energy is kinetic energy.
23,520 + KE = 58,800
KE = 58,800 − 23,520
KE = 35,280 J
Step 4 · Find speed (v)
Use KE = 1/2 × m × v² (kinetic energy = 1/2 × mass × speed²)
Double
the
kinetic
energy
and
divide
by
the
mass:
that
is
v
2
.
Take
its
square
root.
35,280
=
1
2
×
200
v
²
v
=
√(2
×
35,280
200
)
v
=
√(
70,560
200
)
v
=
√
352.8
v
≈
18.783
m/s
Check
Put the numbers back in. Both sides should match.
23,520 = 200 × 9.8 × 12 ✓
58,800 = 200 × 9.8 × 30 ✓
23,520 + 35,280 = 58,800 ✓
35,280
≈
1
2
×
200
×
18.783
2
✓
Topic check
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