Considered Formula;
$$\text {i)}\quad M.A = \frac {L}{E}$$ $$\qquad \text {Where}~~M.A \to Mechanical~advantage,\quad L \to Load \\\qquad E \to Effort$$ $$\text {ii)}\quad V.R = \frac {Ed}{Ld}$$ $$\qquad \text {Where}~~V.R \to Velocity~ratio,\quad Ed \to Effort~distance \\\qquad Ld \to Load~distance$$ $$\text {iii)}\quad \epsilon = \frac {M.A}{V.R} \times 100%$$ $$\qquad \text {Where}~~\epsilon \to Efficiency,\quad M.A \to Mechanical~advantage \\\qquad V.R \to Velocity~ratio$$Example 1
A simple machine raises a load of 100N by using a force 50N. Calculate the mechanical advantage.
Solution
Data given
Load (L) = 100 N
Effort (E) = 50 m
Mechanical advantage (M.A) =?
$$~~~~~~~~~~~~~~~~~~~~~~~~~~~~M.A = \frac {L}{E}$$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = \frac {100}{50}$$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = 2$$
The mechanical advantage = 2
Example 2
A force of 20N raises a load of 100kg. Calculate mechanical advantage of the machine.
Solution
Data given
$$\text {Load (L) = Weight} = m \times g = 100 \times 10~N = 1000~N$$Effort (E) = 20 N
Mechanical advantage (M.A) =?
$$~~~~~~~~~~~~~~~~~~~~~~~~~~~~M.A = \frac {L}{E}$$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = \frac {1000}{20}$$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = 50$$
The mechanical advantage = 50
Example 3
When a machine pressed by effort moved down a distance of 100 cm, while the load is raised through 25 cm at the same time. Find the velocity ratio.
Solution
Data given
Effort distance (Ed) = 100 cm
Load distance (Ld) = 25 cm
Velocity ratio (V.R) =?
$$~~~~~~~~~~~~~~~~~~~~~~~~~~~~V.R = \frac {Ed}{Ld}$$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = \frac {100}{25}$$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = 4$$
The velocity ratio = 4
Example 4
In a certain machine a force of 10N moves down a distance of 0.05 m in order to raise a load of 100N through a height of 0.5cm calculated the velocity ratio (V.R) of the machine.
Solution
Data given
Effort distance (Ed) = 0.05 m = (0.05 x 100) cm = 5 cm
Load distance (Ld) = 0.5 cm
Velocity ratio (V.R) =?
$$~~~~~~~~~~~~~~~~~~~~~~~~~~~~V.R = \frac {Ed}{Ld}$$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = \frac {5 \times 10}{0.5 \times 10}$$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = \frac {50}{5}$$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = 10$$
The velocity ratio = 10
Example 5
In a certain machine a force of 10N moves
down a distance of 5 cm in order to raise a load of 80N through a height of
0.5cm, calculated the
i)
M.A
ii) V.R
iii) Efficiency of the machine.
Solution
Data given
Effort (E) = 10 N
Load (L) = 80 N
Effort distance (Ed) = 5 cm
Load distance (Ld) = 0.5 cm
Velocity ratio (V.R) =?
i)
Mechanical advantage (M.A) = ?
$$~~~~~~~~~~~~~~~~~~~~~~~~~~~~M.A= \frac {L}{E}$$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = \frac {80}{10}$$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = 8$$
The mechanical advantage = 8
ii)
Velocity ratio (V.R) = ?
$$~~~~~~~~~~~~~~~~~~~~~~~~~~~~V.R = \frac {Ed}{Ld}$$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = \frac {5}{0.5}$$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = \frac {5 \times 10}{0.5 \times 10}$$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = \frac {50}{5}$$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = 10$$
The velocity ratio = 10
iii)
Efficiency (ε) = ?
$$~~~~~~~~~~~~~~~~~~~~~~~~~~~~\epsilon = \frac {M.A}{V.R} \times 100 \%$$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = \frac {8}{10} \times 100 \%$$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = 80%$$
The efficiency of the machine = 80%
Example 6
When an effort of 50N is applied through 6 m on a machine, whose efficiency is 75%, such that load is overcome through 1.5 m. calculate the
i)
Velocity ratio
ii) Mechanical advantage
iii) Load of which the machine overcome
Solution
Data given
Effort (E) = 50 N
Effort distance (Ed) = 6 cm
Load distance (Ld) = 1.5 cm
Efficiency (ε) = 75%
Mechanical advantage (M.A) = ?
Velocity ratio (V.R) = ?
ii)
Velocity ratio (V.R) = ?
$$~~~~~~~~~~~~~~~~~~~~~~~~~~~~V.R = \frac {Ed}{Ld}$$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = \frac {6}{1.5}$$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = \frac {6 \times 10}{1.5 \times 10}$$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = \frac {60}{15}$$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = 4$$
The velocity ratio = 4
iii)
Mechanical advantage (M.A) = ?
$$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\epsilon = \frac {M.A}{V.R} \times 100 \%$$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~75\% = \frac {M.A}{4} \times 100 \%$$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~300\% = 100% \times M.A$$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~M.A = \frac {300 \%}{100 \%}$$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~= 3$$
The Mechanical advantage = 3
iii)
Load (L) = ?
$$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~M.A= \frac {L}{E}$$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~3= \frac {L}{50}$$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~L= 3 \times 50$$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~= 150$$
The load of which the machine overcome = 150 N
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