SME
Human Anatomy & Physiology
Musculoskeletal system
Use this for “A 20 N weight is held 32 cm from the elbow, and the biceps attaches 4 cm from it. How hard must the biceps pull?”
Diagram
Moments about the elbow: FM dM = L dL.
FM
=
640
4
=
160
N.
Arrows to one scale; the shortest are lengthened to be seen.
This is an example. Type your own values to start a new problem.
FM (N)
×
dM (cm)
=
L (N)
×
dL (cm)
MA
Mechanical advantage
calculated
Formulas
FM
×
dM
=
L
×
dL
160 × 4 = 20 × 32
MA
=
dM
dL
0.125
=
4
32
Assumptions
•
The elbow is the fulcrum and the forearm is held level and still.
•
The biceps pulls straight up and the load hangs straight down.
•
The forearm’s own weight is left out here; the joint forces page adds it.
Step-by-step
WE KNOW
L = 20 N, dL = 32 cm, dM = 4 cm
FIND
muscle force (FM), mechanical advantage (MA)
Step 1 · Find muscle force (FM)
Use FM × dM = L × dL
Moments about the elbow balance: the loads’ moments over the muscle’s arm.
FM
=
L
× dL
dM
FM
=
20 × 32
4
FM
=
640
4
FM = 160 N
Step 2 · Find mechanical advantage (MA)
Use MA = dM ÷ dL
The muscle’s arm over the load’s arm: below 1 for a third-class lever.
MA
=
4
32
MA = 0.125
Check
Put the numbers back in. Both sides should match.
160 × 4 = 20 × 32 ✓
0.125
=
4
32
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.