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Home/ Questions/The tangential force method involves finding the component of the applied force that is perpendicular to the displacement...
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lyytutoria
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lyytutoriaExpert
Asked: April 10, 20222022-04-10T08:42:43+00:00 2022-04-10T08:42:43+00:00In: Physics

The tangential force method involves finding the component of the applied force that is perpendicular to the displacement…

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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.

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The tangential force method involves finding the component of theapplied force that is perpendicular to the displacemen...
(a) What is Ft, the magnitude of the tangential forcethat acts on the pole due to the tension in the rope?

Express your answer in terms of T and θ .
When using the tangential force method, you calculate the torque using the equation

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                                                             τ=Ftd,

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 counter clockwise rotation implies positive torque).

(b) What is the magnitude of the torque τ on the pole, about point A, due to the tension in the rope?

Express your answer in terms of T, L and θ.

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 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 the 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.

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The tangential force method involves finding the component of theapplied force that is perpendicular to the displacemen...

(c) Find Rm1, the length of the moment arm of theforce.
Express your answer in terms of L and θ.
Now consider a woman standing on the ball of her foot as shown. Anormal force of magnitude N acts upward on the ball of her foot. The Achilles’ tendon is attached to the back of the foot. The tendonpulls on the small bone in the rear of the foot with a force F. This small bone has a length , and the angle between this bone and the Achilles’ tendon is Φ. The horizontal displacement between the ball of the foot and the point P is D.  

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The tangential force method involves finding the component of theapplied force that is perpendicular to the displacemen...
 
(d) Suppose you were asked to find the torque about point P due to the force of magnitude F in the Achilles’ tendon. Which of the following statements is correct?
 
  The tangential force method must be used.
  The moment arm method must be used.
  Eithermethod may be used.
  Neithermethod can be used.

♦ Relevant knowledge
If you are applying the force of a self-closing door make sure you apply the force towards edges of doors in order to decrease the force tangential to it. The torque needed for opening the door is identical, however, the force tangential changes when you push the door towards the hinge, or through a slight angles to the doors.

 

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    lyytutoria Expert
    2022-04-15T05:03:37+00:00Added an answer on April 15, 2022 at 5:03 am
    Concepts and Reason

    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.

    Fundamentals

    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.

                                                        τ=Ftd

    Here, Ft is the tangential force,an d is the distance from the pivot point to the point where force is applied.​

    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.

                                                                   τ=FRm

    Here F,​ is the force, and Rm is the moment arm.

    The trigonometric identity can be described as follows:

                                         ​cos θ=adjacent/hypotenuse​

    Here, θ is the angle,addjacent is the side adjacent to the angle θ, and hypotenuse is the longest side of the right-angled triangle.

    (a) To find the Ft​ tangential force, draw the diagram.


    F Adjacent
Т
Hypotenuse
90 0
Diagram : The diagram showing the forces and
angle for the pole and rope system

    To solve for the Tangential component of the Tension force T, use the cosine function

    Substitute T

         cos θ=Ft/T ​​

         Ft​ =T cos θ​

    ​

    (b) Use the torque equation for tangential force method.

    Substitute T cos θ for Ft, and L for d in the equation τ=Ftd

    τ=(T cos θ) L

    =T L cos θ

     

     

    (c) Refer the diagram in the question with Rm. The Rm is the adjacent to the angle θ and L is the hypotenuse.

    Use cosine function to solve for the Rm

    Substitute L for hypotenuse, and Rm for adjacent in the equation

    cos θ=adjacent/hypotenuse and rearrange to solve for Rm.

    cos θ= Rm / L

    Rm=L cos θ

    Use the torque equation of moment arm method.

    Substitute T for F and L cos θ  for d in the equation τ=FRm

    τ=T L cos θ

    (d) From part b and c, it is clear that using ether method,we get the same torque

    τ=T L cos θ

    Thus,for this part also either can be used as both tthe method leads to same answer.

    Ans: Part A

    The magnitude of the tangential force acting on the pole because of the tension in the rope is Ft = T cos θ

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  2. tonytutoria
    2022-04-10T09:00:47+00:00Added an answer on April 10, 2022 at 9:00 am
    Concepts and Reason

    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.

    Fundamentals

    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.

    [katex]\tau = {F_{\rm{t}}}d[/katex]

    Here, [katex]{F_{\rm{t}}}[/katex]

    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.

    [katex]\tau = F{R_{\rm{m}}}[/katex]

    Here, [katex]F[/katex]

    The trigonometric identity can be described as follows:

    [katex]\cos \theta = \frac{{{\rm{adjacent}}}}{{{\rm{hypotenuse}}}}[/katex]

    Here, [katex]\theta[/katex]

    (a)

    To find the [katex]{F_{\rm{t}}}[/katex] tangential force, draw the diagram.


    F Adjacent
Т
Hypotenuse
90 0
Diagram : The diagram showing the forces and
angle for the pole and rope system

    To solve for the Tangential component of the Tension force [katex]T[/katex], use the cosine function

    Substitute [katex]T[/katex]

    [katex]\begin{array}{c}\\\cos \theta = \frac{{{F_{\rm{t}}}}}{T}\\\\{F_{\rm{t}}} = T\cos \theta \\\end{array}[/katex]

    (b)

    Use the torque equation for tangential force method.

    Substitute [katex]{F_{\rm{t}}}[/katex]0

    [katex]{F_{\rm{t}}}[/katex]1

    (c)

    Refer to the diagram in the [katex]{F_{\rm{t}}}[/katex]2 question

    To solve the [katex]{F_{\rm{t}}}[/katex]2 problem, use cosine function

    Substitute [katex]{F_{\rm{t}}}[/katex]4

    [katex]{F_{\rm{t}}}[/katex]5

    Use the torque equation method for moment arm.

    Substitute [katex]T[/katex]

    [katex]{F_{\rm{t}}}[/katex]7

    (d)

    Parts b and c show that we can get the same torque using either method

    [katex]{F_{\rm{t}}}[/katex]7

    This 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’s length is [katex]{F_{\rm{t}}}[/katex]9

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