School › Skeleton › Ages 15–16
Bone tissue and bones as levers
Compact and spongy bone, bone cells and remodelling, growth plates, and calculating muscle and joint forces with torques. With a model-forearm investigation.
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Compact bone is dense and resists compression; its structural unit is the osteon, rings of calcified matrix around a central canal carrying blood vessels and nerves. Spongy bone is a lattice of trabeculae that form along lines of stress and make bones lighter.[4]
Bone matrix is a composite: collagen fibres give flexibility so bone is not brittle, and hydroxyapatite crystals, formed from calcium phosphate and calcium carbonate, give hardness and strength.[4]
Bone is living tissue that is constantly remodelled: osteoblasts form new bone, osteocytes maintain the matrix and osteoclasts break bone down. In the teens much more bone is deposited than removed, and bone mass usually peaks by the mid- to late 20s.[4][6]
Long bones lengthen at the epiphyseal (growth) plate, a layer of cartilage that is ossified as growth continues. Growth in length continues until early adulthood; afterwards only the epiphyseal line remains.[5]
Long bones act as levers and joints as fulcrums; a bone moves only when a muscle spanning the joint contracts.[2][3]
For a forearm held still, the torques about the elbow balance: FB × r1 = warm × r2 + wload × r3. With the biceps attached 4.00 cm from the elbow, a 2.50 kg forearm (centre of gravity 16.0 cm) and a 4.00 kg book at 38.0 cm, FB = 470 N: about 7.4 times the 63.7 N weight supported. The elbow joint pushes with about 407 N.[7]
So muscles exert far larger forces inside the body than the limbs apply to the outside world: the arm is a lever with a mechanical advantage less than one.[7]
Try it: A model forearm: how big is the 'biceps' force?
You need
- A 50 cm wooden ruler (the forearm)
- A clamp stand with a pivot or a nail/hinge through one end of the ruler (the elbow)
- A 0–10 N newton meter (the biceps)
- String loops
- 100 g masses with a hanger
- Safety glasses
Safety
Wear safety glasses in case a string or the newton meter springs loose. Keep feet and hands clear under the hanging masses and do not exceed the newton meter's range. Clamp the stand firmly to the bench.
What to do
- Fix the ruler so it can turn about a pivot at the 0 cm end. Hook the newton meter vertically at 10 cm (r₁) and adjust it so the ruler is horizontal.
- With no mass hung, record the newton meter reading F₀ (it supports the ruler's own weight).
- Hang 100 g (weight ≈ 0.98 N) at d = 15, 20, 25, 30, 35 and 40 cm. Each time keep the ruler horizontal and record F. Calculate F − F₀.
- Predict F − F₀ from torques: (F − F₀) × r₁ = W × d. Compare measured and predicted values.
- Plot F − F₀ against d. Is it a straight line through the origin? Estimate your uncertainties (newton meter resolution, reading the distance, keeping the ruler level).
What happens, and why?
Balancing torques about the pivot gives F × r₁ = W × d, so the 'muscle' force is the load multiplied by d / r₁. With r₁ much smaller than d, the muscle must pull several times harder than the weight it holds, just as the biceps does: in the textbook example it is about 470 N for a 63.7 N load. Long bones act as levers and joints as fulcrums.[7][2]
Play: Muscle force calculator
Use F × r = W × d (forearm weight ignored) to find the muscle force, then pick the right answer box.
Your best score is kept only on this device. Nothing is sent anywhere.
Quiz
Other ages: Ages 6–7 · Ages 10–11