6834 Lecture Notes - Lecture 6: Muscle Tone, Stretch Reflex, Anti-Gravity

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rosesnake902

21 Jun 2018

School

University of Canberra

Department

University of Canberra

Course

6834

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all

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TICS 2: Torques and centre of mass

- Force vs torque

oForce that acts through the centre of an object is called centric force

oA force that doesn’t act through the centre of an object is called eccentric force and

causes the object to rotate

oThis turning moment due to force is called a torque

- Torque

oTorque: rotary effect of a force about an axis

oT= Fd_|_ (perpendicular distance – momarm length)

oThe magnitude of force and the length of the moment arm affect the amount of

torque

oNote: moment arm is the perpendicular distance from the forces line of action to

the axis of rotation

Torque around hip is greater than at knee because of moment arm length

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Document Summary

Torque around hip is greater than at knee because of moment arm length. 2nd law of equilibrium this is in a static movement o o. Sticking point is where moment arm is the greatest. Gravity: centre of gravity (centre of mass. Point around which the bodys mass is equally distributed. Sum of torques produced by the bodys segments is equal to zero (2nd law of equilibrium) Calculating com and segmental com: indirect methods. Sum of all segment torques/body weights gives the position of the. This has to be done for all the directions ie in 2d has to be done for the x and y direction. Weights of segments based on cadaver based studies. Mobility vs stability: the stability of a body in equilibrium depends on three factors. The position of the line of gravity relative to the limits of the base. The height of the centre of gravity relative to the base: understanding of this can aid athletes.

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.

(a) What is , the magnitude of the tangential force that acts on the pole due to the tension in the rope?

Express your answer in terms of

and

.

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

$\tau = f_{\rm t} d$ ,

where

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

on the pole, about point A, due to the tension in the rope?

Express your answer in terms of

, and

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.

, the length of the moment arm of the force.

Express your answer in terms of

and

(d)Now consider a woman standing on the ball of her foot as shown. A normal force of magnitude

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 force

. This small bone has a length

, and the angle between this bone and the Achilles' tendon is

. The horizontal displacement between the ball of the foot and the point P is

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.

byzantiumarmadillo929

Express your answer in terms of

and

.

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

$\tau = f_{\rm t} d$ ,

where

on the pole, about point A, due to the tension in the rope?

Express your answer in terms of

, and

, the length of the moment arm of the force.

Express your answer in terms of

and

(d)Now consider a woman standing on the ball of her foot as shown. A normal force of magnitude

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 force

. This small bone has a length

, and the angle between this bone and the Achilles' tendon is

. The horizontal displacement between the ball of the foot and the point P is

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.

turquoiseworm20

This magnetic resonance image of a patient's brain shows a tumor, which is highlighted in red.

Imagine you are a doctor who has just received a magnetic resonance image of your patent’s brain. The brain has a tumor How large is the tumor?

To be precise, what is the area of the red region? The red cross-section of the tumor has an irregular shape, and therefore it is unlikely that you would be able o find a set of equations or inequalities for the region and then be able to calculate its area by conventional means. You could approximate the area by chopping the region into tiny squares (a Riemann sum approach), but this method always gives an answer with some error.

Instead of trying to measure the area of the region directly, we can use a device called a rolling planimeter to calculate the area of the region exactly, simply by measuring its boundary. In this project you investigate how a planimeter works, and you use Green’s theorem to show the device calculates area correctly.

A rolling planimeter is a device that measures the area of a planar region by tracing out the boundary of that region. To measure the area of a region, we simply run the tracer of the planimeter around the boundary of the region. The planimeter measures the number of turns through which the wheel rotates as we (race the boundary; the area of the shape is proportional to this number of wheel ruins. We can derive the precise proportionality equation using Green’s theorem. As the (racer moves around the boundary of the region, the tracer arm rotates and the roller moves back and forth (but does no; rotate).

(a) A rolling planimeter. The pivot allows the tracer arm to rotate. The roller itself does not rotate; it only moves back and forth. (b) An interior view of a rolling planimeter. Notice that the wheel cannot rum if the planimeter is moving back and forth th the tracer arm perpendicular to the roller.

Let C denote the boundary of region D. the area to be calculated. As the tracer traverses curve C, assume the roller moves along the y-axis (since the roller does not rotate, one can assume it moves along a straight line). Use the coordinates (x, y) to represent points on boundary C, and coordinates (0, y) to represent the position of the pivot. As the planimeter traces C the pivot moves along the y-axis while the tracer arm rotates on the pivot. Watch a short animation of a planimeter in action.

Begin the analysis by considering the motion of the tracer as it moves from point (x, y) counterclockwise to point that is close to (x, y). The pivot also moves, from point (0, y) to nearby point (0, y + dy). How much does the wheel turn as a result of this motion? To answer this question, break the motion into two parts. First, roll the pivot along they-axis from without rotating the tracer arm. The tracer arm then ends up a point while maintaining a constant angle with the x-axis. Second, rotate the tracer arm by an angle d θθ without moving the roller. Now the tracer is at point Let 1 be the distance from the pivot to the wheel and let L be the distance from the pivot to the tracer (the length of the tracer arm).

6.49 Mathematical analysis of the motion of the planimeter.

Conclude that the sea of D equals the length of the air am multiplied by the total rolling distance of the wheel. You now know how a planimeter works and you have used Green’s theorem to justify that it works. To calculate the area of planar region D, use a planimeter to trace the boundary of the region .

The area of region is the length of the tracer arm multiplied by the distance wheel rolled

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6834 Lecture Notes - Lecture 6: Muscle Tone, Stretch Reflex, Anti-Gravity

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