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27 Nov 2019

Let the clockwise torque caused by the force on the achilles tendon of the toddler exactly equals the counter clockwise torque of 1.53 from the normal force on her foot. What is the force on her Achilles tendon if the tendon is 3.3cm away.

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Jamar Ferry
Jamar FerryLv2
6 Sep 2019

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Related textbook solutions

Physics: Principles with Applications
7th Edition, 2013
Giancoli
ISBN: 9780321625922

Related questions

The tangential force method involves finding the component of the applied force that is perpendicular to the displacement from the pivot point to where the force is applied. This perpendicular component of the force is called the tangential force.
20061122120126329809921253700004765.png
(a) What is F_t, the magnitude of the tangential force that acts on the pole due to the tension in the rope?

Express your answer in terms of T and theta.

When using the tangential force method, you calculate the torque using the equation

\tau = f_{\rm t} d,

where d is the distance from the pivot to the point where the force is applied. The sign of the torque can be determined by checking which direction the tangential force would tend to cause the pole to rotate (where counterclockwise rotation implies positive torque).

(b) What is the magnitude of the torque tau on the pole, about point A, due to the tension in the rope?
Express your answer in terms ofT, L, and theta.

The moment arm method involves finding the effective moment arm of the force. To do this, imagine a line parallel to the force, running through the point at which the force is applied, and extending off to infinity in either direction. You may shift the force vector anywhere you like along this line without changing the torque, provided you do not change the direction of the force vector as you shift it. It is generally most convenient to shift the force vector to a point where the displacement from it to the desired pivot point is perpendicular to its direction. This displacement is called the moment arm.

For example, consider the force due to tension acting on the pole. Shift the force vector to the left, so that it acts at a point directly above point A in the figure. The moment arm of the force is the distance between the pivot and the tail of the shifted force vector. The magnitude of the torque about the pivot is the product of the moment arm and force, and the sign of the torque is again determined by the sense of the rotation of the pole it would cause.
20061122121536329809931322450004365.png
(c) Find R_m, the length of the moment arm of the force.
Express your answer in terms ofL and theta.
2006112212386329809938811512508683.png

(d)Now consider a woman standing on the ball of her foot as shown. A normal force of magnitude N acts upward on the ball of her foot. Achilles' tendon is attached to the back of the foot. The tendon pulls on the small bone in the rear of the foot with a forceF. This small bone has a length x, and the angle between this bone and the Achilles' tendon is phi. The horizontal displacement between the ball of the foot and the point P is D.
D oll
Find τp, the torque about point P due to the force applied by the Achilles' tendon. Express your answer in terms of F, ϕ, and x.

In Chapter 10 in the textbook, we saw that the Achilles tendon willstretch and then rebound, storing and returning energy during astep. We can model this motion as that of a mass on a spring. Thisis far from a perfect model, but it does give some insight. If a 60kg person stands on a low wall with her full weight on the ball ofone foot and the heel free to move, the stretch of the Achillestendon will cause her center of gravity to lower by about 2.5mm.

part a : What is the spring constant of her Achilles tendon?

part b: If she bounces a little, what is her oscillation period?

The Achilles tendon will stretch and then rebound, storing andreturning energy during a step. We can model this motion as that ofa mass on a spring. This is far from a perfect model, but it doesgive some insight. If a 60kg person stands on a low wall with herfull weight on the ball of one foot and the heel free to move, thestretch of the Achilles tendon will cause her center of gravity tolower by about 2.5mm.
A. What is the spring constant of her Achilles tendon?
B. If she bounces a little, what is her oscillation period?
C. When walking or running, the tendon spring begins to stretch asthe ball of the foot takes the weight of a stride, transformingkinetic energy into elastic potential energy. Ideally, the cycle ofthe motion will have advanced so that potential energy has justfinished being converted back to kinetic energy as the foot leavesthe ground. What fraction of an oscillation period should the timebetween landing and liftoff correspond to? Given the period youcalculated above, what is this time?
D. Sprinters running a short race keep their foot in contact withthe ground for about .10sec, some of which corresponds to the heelstrike and subsequent rolling forward of the foot. Given this, doesthe answer to part c make sense?

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