C. Numerical Problems
1. An effort of 45 N is applied on a machine through a
displacement of 8 m. As a result of it, a load of 270 N is
moved through a distance of 1.0 m. Calculate velocity
ratio, mechanical advantage and efficiency of the
machine.
Answers
Answer:
F1 = 45 N
d1 = 8 m
F2 = 270 N
d2 = 10 m
To find:
1) velocity ratio = VR =?
2) mechanical advantage = M.A. =?
3) efficiency of the machine = η =?
Explanation:
1)
The velocity ratio is the ratio of a distance through which any part of a machine moves to that the driving part moves during the same time.
\displaystyle Velocity \ ratio = \frac{distance \ of \ effort}{distance \ moved \ by \ load}Velocity ratio=
distance moved by load
distance of effort
VR = \frac{8}{10}
10/8
VR = 0.8
2)
The mechanical advantage the ratio of the force produced by a machine to the force applied to it, utilized in assessing the performance of a machine.
M.A. = \displaystyle \frac{Load}{Effect}
Effect/
Load
= \displaystyle \frac{270}{45}
45/270
M.A. = 6
3)
The efficiency of the machine is that the percent of work put into a machine by the input work that becomes work done by the machine output work.
\displaystyle \eta =\frac{mechanical \ \ advantage}{velocity\ \ ratio}η=
velocity ratio
mechanical advantage
= \displaystyle {\frac{0.8}{6}{ \times 100}
η = 13.33 %