Consider the hinge on the drawbridge of the previous problem.(a) Compute the force on the hinge FH(x) as a function of the archaeologist's location x. Compute both the horizontaland vertical components of the force. Your result should be two functions of the unknown variable x. Express yourresult only in terms of the parameters L, h, W, and w.(b) Suppose the rope has been reinforced so that it can support up to 1000 lbs without breaking. If the hinge canwithstand a maximum force of 500 lbs without breaking, is it safe for the archaeologist to cross?Don't guess. Justify your response with a calculation.If it is safe to cross, what is the margin of safety? I.e., how much less is the maximum force on the hinge than theupper limit of 500 lbs?If it is not safe to cross, how far can the archaeologist walk before the hinge gives out?

Considering :Tx=TcosθTy=TsinθNow, writing the equation for force and torqueΣFx=0that is,…

Consider the hinge on the drawbridge of the previous problem. (a) Compute the force on the hinge FH(x) as a function of the archaeologist's location x. Compute both the horizontal and vertical components of the force. Your result should be two functions of the unknown variable x. Express your result only in terms of the parameters L, h, W, and w. (b) Suppose the rope has been reinforced so that it can support up to 1000 Ibs without breaking. If the hinge can withstand a maximum force of 500 Ibs without breaking, is it safe for the archaeologist to cross? Don't guess. Justify your response with a calculation. If it is safe to cross, what is the margin of safety? I.e., how much less is the maximum force on the hinge than the upper limit of 500 lbs? If it is not safe to cross, how far can the archaeologist walk before the hinge gives out?

Consider the hinge on the drawbridge of the previous problem. (a) Compute the force on the hinge FH(x) as a function of the archaeologist's location x. Compute both the horizontal and vertical components of the force. Your result should be two functions of the unknown variable x. Express your result only in terms of the parameters L, h, W, and w. (b) Suppose the rope has been reinforced so that it can support up to 1000 Ibs without breaking. If the hinge can withstand a maximum force of 500 Ibs without breaking, is it safe for the archaeologist to cross? Don't guess. Justify your response with a calculation. If it is safe to cross, what is the margin of safety? I.e., how much less is the maximum force on the hinge than the upper limit of 500 lbs? If it is not safe to cross, how far can the archaeologist walk before the hinge gives out?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Rigid Body

A rigid body is an object which does not change its shape or undergo any significant deformation due to an external force or movement. Mathematically speaking, the distance between any two points inside the body doesn't change in any situation.

Rigid Body Dynamics

Rigid bodies are defined as inelastic shapes with negligible deformation, giving them an unchanging center of mass. It is also generally assumed that the mass of a rigid body is uniformly distributed. This property of rigid bodies comes in handy when we deal with concepts like momentum, angular momentum, force and torque. The study of these properties – viz., force, torque, momentum, and angular momentum – of a rigid body, is collectively known as rigid body dynamics (RBD).

Question

Consider the hinge on the drawbridge of the previous problem.
(a) Compute the force on the hinge FH(x) as a function of the archaeologist's location x. Compute both the horizontal
and vertical components of the force. Your result should be two functions of the unknown variable x. Express your
result only in terms of the parameters L, h, W, and w.
(b) Suppose the rope has been reinforced so that it can support up to 1000 lbs without breaking. If the hinge can
withstand a maximum force of 500 lbs without breaking, is it safe for the archaeologist to cross?
Don't guess. Justify your response with a calculation.
If it is safe to cross, what is the margin of safety? I.e., how much less is the maximum force on the hinge than the
upper limit of 500 lbs?
If it is not safe to cross, how far can the archaeologist walk before the hinge gives out?

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