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Figures for Part E are not shown Answered keeping the student’s benefit in mind …. is assumed to be the figure
Figures for Part E are not shown
Answered keeping the student’s benefit in mind
…. is assumed to be the figure
See lessThe tangential force method involves finding the component of the applied force that is perpendicular to the displacement…
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 tRead more
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.
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.
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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