SME
Grade 8 Science · Problem type
A pendulum trades energy
Use this for “Where is the pendulum fastest, and where does it have the most potential energy?”
Diagram
PE + KE = 3.92 J + 5.88 J = 9.8 J
PE = m × g × h
= 2 kg × 9.8 m/s² × 0.2 m = 3.92 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
Formulas
PE
=
m
×
9.8
×
h
(potential
energy
=
mass
×
9.8
×
height
now)
3.92 = 2 × 9.8 × 0.2
E
=
m
×
9.8
×
H
(total
energy
=
mass
×
9.8
×
top
height)
9.8 = 2 × 9.8 × 0.5
PE
+
KE
=
E
(potential
energy
+
kinetic
energy
=
total
energy)
3.92 + 5.88 = 9.8
Assumptions
•
The bob is let go from rest at height H.
•
At the bottom all its energy is kinetic: it is fastest there. At each end it stops for an instant: all potential.
•
Without air it would rise to the same height each swing; air takes a little energy, so each swing is a little lower.
Step-by-step
WE KNOW
m = 2 kg (mass), H = 0.5 m (top height), h = 0.2 m (height now)
FIND
potential energy (PE), total energy (E), kinetic energy (KE)
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 = 2 × 9.8 × 0.2
PE = 19.6 × 0.2
PE = 3.92 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
=
2
×
9.8
×
0.5
E
=
19.6
×
0.5
E
=
9.8
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.
3.92 + KE = 9.8
KE = 9.8 − 3.92
KE = 5.88 J
Check
Put the numbers back in. Both sides should match.
3.92 = 2 × 9.8 × 0.2 ✓
9.8 = 2 × 9.8 × 0.5 ✓
3.92 + 5.88 = 9.8 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.