Take moment about point A.EMA =0MA =-F, x6+ F, x(5+4)Substitute F cos a for F, and Fsina for F,.M, =-F cosax6+F sin a x(5+4) .(1)......Differentiate the above equation with respect to angle.dM, d-F cosax6+Fsina×(5+4)dada= 6F sin a +9F cos aFor the maximum moment,6Fsin α + 9F cos α = 09tan a =a =-56.3Calculate the angle from positive x direction.a = 180– 56.3= 123.7°Therefore, the allowable angle for the required force is 123.7° The ball of a trailer hitch is subjected to a force F. If failure occurs when the moment of Faboutpoint A reaches 10.000 in.-lb. determine the largest value F may have and specify the value of afor which the moment about .A is the largest. Note that the value of Fyou determine must notproduce a moment about, A that exceeds 10.000 in.-Ib for any possible value of a.- 5 in. --- 4 in. -HAO6 in.FFigure P4.7

Objective: To determine the largest value of F. To determine the value of α.

The ball of a trailer hitch is subjected to a force F. If failure occurs when the moment of Fabout point A reaches 10.000 in.-Ib. determine the largest value Fmay have and specify the value of a for which the moment about .A is the largest. Note that the value of Fyou determine must not produce a moment about, A that exceeds 10.000 in.-lb for any possible value of a. 5 in. --- 4 in. - B HA O 6 in. F Figure P4.7

The ball of a trailer hitch is subjected to a force F. If failure occurs when the moment of Fabout point A reaches 10.000 in.-Ib. determine the largest value Fmay have and specify the value of a for which the moment about .A is the largest. Note that the value of Fyou determine must not produce a moment about, A that exceeds 10.000 in.-lb for any possible value of a. 5 in. --- 4 in. - B HA O 6 in. F Figure P4.7

International Edition---engineering Mechanics: Statics, 4th Edition

4th Edition

ISBN:9781305501607

Author:Andrew Pytel And Jaan Kiusalaas

Publisher:Andrew Pytel And Jaan Kiusalaas

Chapter2: Basic Operations With Force Systems

Section: Chapter Questions

Problem 2.66P: The flexible shaft AB of the wrench is bent into a horizontal arc with a radius of 24 in. The two...

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Concept explainers

Types of loading

In mechanical terminology, the term load indicates that external force/weight, either constant or variable, acts on a mechanical member/structure. The weight of an object of a specific material is also an external load, and the external force that works on a structure comes under the categories of loading. The external load generates its effects as stress and strain in the structure.

Question

Take moment about point A.
EMA =0
MA =-F, x6+ F, x(5+4)
Substitute F cos a for F, and Fsina for F,.
M, =-F cosax6+F sin a x(5+4) .
(1)
......
Differentiate the above equation with respect to angle.
dM, d-F cosax6+Fsina×(5+4)
da
da
= 6F sin a +9F cos a
For the maximum moment,
6Fsin α + 9F cos α = 0
9
tan a =
a =-56.3
Calculate the angle from positive x direction.
a = 180– 56.3
= 123.7°
Therefore, the allowable angle for the required force is 123.7°

The ball of a trailer hitch is subjected to a force F. If failure occurs when the moment of Fabout
point A reaches 10.000 in.-lb. determine the largest value F may have and specify the value of a
for which the moment about .A is the largest. Note that the value of Fyou determine must not
produce a moment about, A that exceeds 10.000 in.-Ib for any possible value of a.
- 5 in. --- 4 in. -
HAO
6 in.
F
Figure P4.7

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