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Wednesday, March 25, 2015


In Business Accounting and Bookkeeping, Statistics

What is the importance of statistics in accounting?

statistics and accounting both are very similar to each other regarding their uses, because both are tools of decision making. To take decision regarding average, standard and marginal you have to take help from statistics even if you are accountant.
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In Sports

What rugby statistics are most important?

Tackles made Turnovers for and against Line-out won on own ball and opposition penalties conceded advantage lines achieved points for points against possession kicked-away
5 Fascinating Email Statistics
In Email

5 Fascinating Email Statistics

Statistics can be an amazing look into the world. Some can be easy to understand while others can be quite surprising. The email marketing researcher ExactTarget has composed … (MORE)
In Education

Why is accounting important?

Answer We need accounting because it's the only way for business's to grow and flourish. Accounting is the backbone of the business financial world. Accounting was crea… (MORE)
In Microsoft Office

Is Excel important in accounting role?

While there are specialised accounting software applications, Excel would be also very important as it deals with lots of calculations and it has a lot of financial capabiliti… (MORE)
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Saturday, March 21, 2015

LEANING LADDER

Worked example 10.3: Leaning ladder

Question: A uniform ladder of mass $m = 40 {\rm kg}$ and length $l=10 {\rm m}$ is leaned against a smooth vertical wall. A person of mass $M=80 {\rm kg}$ stands on the ladder a distance $x=7 {\rm m}$ from the bottom, as measured along the ladder. The foot of the ladder is $d=1.2 {\rm m}$ from the bottom of the wall. What is the force exerted by the wall on the ladder? What is the normal force exerted by the floor on the ladder?
\begin{figure*} \epsfysize =2.5in \centerline{\epsffile{ladder1.eps}} \end{figure*}
Answer: The angle $\theta$ subtended by the ladder with the ground satisfies
\begin{displaymath} \theta = \cos^{-1}(d/l)= \cos^{-1}(1.2/10) = 83.11^\circ. \end{displaymath}

Let $S$ be the normal reaction at the wall, let $R$ be the normal reaction at the ground, and let $f$ be the frictional force exerted by the ground on the ladder, as shown in the diagram. Consider the torque acting on the ladder about the point where it meets the ground. Only three forces contribute to this torque: the weight, $m g$, of the ladder, which acts half-way along the ladder; the weight, $M g$, of the person, which acts a distance $x$ along the ladder; and the reaction, $S$, at the wall, which acts at the top of the ladder. The lever arms associated with these three forces are $(l/2) \cos\theta$, $x \cos\theta$, and $l \sin\theta$, respectively. Note that the reaction force acts to twist the ladder in the opposite sense to the two weights. Hence, setting the net torque to zero, we obtain
\begin{displaymath} m g \frac{l}{2} \cos\theta + M g x \cos\theta - S l \sin\theta = 0, \end{displaymath}

which yields
\begin{displaymath} S = \frac{(m g/2 + M g x/l)}{\tan\theta} = \frac{(0.5\tim... ...80\times 9.81\times 7/10)}{\tan 83.11^\circ} = 90.09 {\rm N}. \end{displaymath}

The condition that zero net vertical force acts on the ladder yields
\begin{displaymath} R - m g - M g = 0. \end{displaymath}

Hence,
\begin{displaymath} R = (m+M) g = (40+80)\times 9.81 = 1177.2 {\rm N}. \end{displaymath}
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