why is the derivative taken? 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 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+ F sin a ×(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°

To understand the above solution, consider a polynomial equation as shown below.

Answered: why is the derivative taken?

Engineering

Mechanical Engineering

why is the derivative taken?

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Conduction and Convection

When energy travels from one object to another it is said to have undergone heat transfer. Heat transfer is nothing but the transfer of thermal energy or internal energy from one thing to another, like e.g., when a vessel with water, kept on top of a burner, heats up because of the flame underneath it.

Question

why is the derivative taken?

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

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+ F sin a ×(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°

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