SME
Grade 11 Science · Problem type
Hanging in an elevator
Use this for “A 3 kg lamp hangs from the ceiling of an elevator speeding up at 2 m/s² going up. What is the tension in its cord?”
Diagram
Weight = m × g = 3 × 9.8 = 29.4 N
Net force = Tension − Weight = 35.4 − 29.4 = 6 N
a = Net force/m = 6/3 = 2 m/s²
This is an example. Type your own values to start a new problem.
T (N)
−
W (N)
=
m (kg)
×
a (m/s²)
Fₙₑₜ
Net force
calculated
Formulas
W
=
m
×
9.8
29.4 = 3 × 9.8
a
=
Fₙₑₜ/
m
2
=
6
3
Fₙₑₜ
=
T
−
W
6 = 35.4 − 29.4
Assumptions
•
Only two forces: the cord’s tension up and the weight down.
•
Up is +: a > 0 when it speeds up going up or slows going down.
•
The tension is more than the weight when a > 0, less when a < 0.
Step-by-step
WE KNOW
m = 3 kg, a = 2 m/s²
FIND
weight (W), net force (Fₙₑₜ), tension in the cord (T)
Step 1 · Find weight (W)
Use W = m × 9.8
Earth pulls each kilogram with 9.8 N.
W
=
3
×
9.8
W
=
29.4
N
Step 2 · Find net force (Fₙₑₜ)
Use a = Fₙₑₜ/m
The net force is the mass times the acceleration.
Fₙₑₜ
=
m
×
a
Fₙₑₜ = 3 × 2
Fₙₑₜ = 6 N
Step 3 · Find tension in the cord (T)
Use Fₙₑₜ = T − W
The cord holds up the weight and also gives the net force.
T
=
Fₙₑₜ
+
W
T
=
6
+
29.4
T
=
35.4
N
Check
Put the numbers back in. Both sides should match.
29.4 = 3 × 9.8 ✓
2
=
6
3
✓
6 = 35.4 − 29.4 ✓
Topic check
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