The tangential force method involves finding the component of theapplied force that is perpendicular to the displacemen…
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Question “The tangential force method involves finding the component of theapplied force that is perpendicular to the displacemen…”
theapplied force that is perpendicular to the displacement from
thepivot point to where the force is applied. This
perpendicularcomponent of the force is called the tangential
force.
(a) What is , the magnitude of the tangential
forcethat acts on the pole due to the tension in the rope?
of and .
When using the tangential force method, you calculate the
torqueusing the equation
where is the distance from the pivot
tothe point where the force is applied. The sign of the torque can
bedetermined by checking which direction the tangential force
wouldtend to cause the pole to rotate (where counterclockwise
rotationimplies positive torque).
(b) What is the magnitude of the torque on the pole, about point A, due to
thetension in the rope?
of, , and .
The moment arm method involves finding the effective moment
armof the force. To do this, imagine a line parallel to the
force,running through the point at which the force is applied,
andextending off to infinity in either direction. You may shift
theforce vector anywhere you like along this line without changing
thetorque, provided you do not change the direction of the
forcevector as you shift it. It is generally most convenient to
shiftthe force vector to a point where the displacement from it to
thedesired pivot point is perpendicular to its direction.
Thisdisplacement 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
pointdirectly above the point A in the figure. The moment arm of
theforce is the distance between the pivot and the tail of the
shiftedforce vector. The magnitude of the torque about the pivot is
theproduct of the moment arm and force, and the sign of the torque
isagain determined by the sense of the rotation of the pole it
wouldcause.
of and .
Now consider a woman standing on the ball of her foot as shown.
Anormal force of magnitude acts upward on the ball of her foot.
TheAchilles’ tendon is attached to the back of the foot. The
tendonpulls 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
theAchilles’ tendon is . The horizontal displacement between
theball of the foot and the point P is .
torqueabout point P due to the force of magnitude in the Achilles’ tendon. Which of the
followingstatements is correct?

Answer
This problem can be solved using the moment arm and tangential force methods.
To solve for the tangential part of the force, first use the trigonometric functions.
To solve for tension force torque, you can use the torque equation from the tangential force method. Next, use the trigonometric functions to solve the moment arm.
Identify the best solution for your problem.
The tangential force method is based on finding the component perpendicular the displacement of the pivot point to the place where the force is applied. The tangential force is the perpendicular component.
The torque equation for the tangential force method uses is.
\tau = {F_{\rm{t}}}dHere, {F_{\rm{t}}}
Moment arm is a method of finding the effective moment arms of the force. The moment arm is the displacement.
The moment arm method uses the torque equation.
\tau = F{R_{\rm{m}}}Here, F
The trigonometric identity can be described as follows:
\cos \theta = \frac{{{\rm{adjacent}}}}{{{\rm{hypotenuse}}}}Here, \theta
(a)
To find the tangential force {F_{\rm{t}}}, draw the sketch of the diagram
To solve for the Tangential component of the Tension force T, use the cosine function
Substitute $math_tag_7
\begin{array}{c}\\\cos \theta = \frac{{{F_{\rm{t}}}}}{T}\\\\{F_{\rm{t}}} = T\cos \theta \\\end{array}(b)
Use the torque equation for tangential force method.
Substitute $math_tag_10
\begin{array}{c}\\\tau = \left( {T\cos \theta } \right)L\\\\ = TL\cos \theta \\\end{array}(c)
Refer to the diagram in the $math_tag_12 question
To solve the {R_{\rm{m}}}, use the cosine function
Substitute $math_tag_14
\begin{array}{c}\\\cos \theta = \frac{{{R_{\rm{m}}}}}{L}\\\\{R_{\rm{m}}} = L\cos \theta \\\end{array}Use the torque equation method for moment arm.
Substitute $math_tag_7
\tau = TL\cos \theta(d)
Parts b and c show that we can get the same torque using either method
\tau = TL\cos \thetaThis means that both methods can be used for this section, as they each lead to the same answer.
Ans: Part A
The magnitude of the tangential force acting on the pole because of the tension in the rope is $math_tag_19
Conclusion
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