Balance in a sprinter’s foot *Balance in a sprinter’s foot
The figure below shows the external forces acting on the rear foot of a sprinter just an instant
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before the starting time of her race (still at rest): the ground reaction R at the tip of the foot;
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the tension on the Achilles tendon T, which makes a known angle α with the ground; and finally
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the force F exerted by the tibia on the ankle which is directed towards the ground and forms an
angle β with the vertical. The magnitude of the normal reaction on the ground can be computed
by computing the equilibrium of the entire sprinter (not just her foot). If we assume that she is
leaning symmetrically on her two feet then each reaction to the ground compensates for half his
⃗ mg
weight, orR=R= 2 =221Nforayoungsprinterofmassm=45kg.
1. Project all the forces acting on the foot into the base ⃗ex,⃗ey. ⃗
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3. Deduce the modulus of the force T as a function of R, x1, x2 and α. Obtain the numerical
value.
4. Write the translational equilibrium condition for the sprinter’s foot.
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5. Deduce the magnitude and angle of inclination of the force F . Obtain the numerical value.
Data: x1 =4.25cm, x2 =9.55cm,α=59o
2. We want to determine the modulus of tension T by writing the rotational equilibrium of the sprinter’s foot. Which point should we choose for the calculation of the moments? Identify the lever arms corresponding to the different moments on the diagram and calculate them.