Question

A crowbar 2m long is pivoted about a point of 10cm from its tip.
(i) Calculate the mechanical advantage of the crowbar.
(ii) What is the least force which must be applied at the other end to displace a load of 100kgf?

Answer 1

Hint:We know mechanical advantage is the ratio of load to the effort of the machine or we can say it is the ratio of the output of the machine to the input of the machine. Velocity ratio is also defined as velocity of effort to the velocity of load which is equivalent to mechanical advantage.

Formula used:
Mechanical advantage (M.A) $ = \;\dfrac{{{\rm{Load(L)}}}}{{{\rm{Effort(E)}}}}$

Complete step by step answer:
The machine is a device which multiplies the force or multiplies the speed, or it changes the direction of effort. Some terms are related to machines like load, effort, velocity ratio, mechanical advantage and efficiency.
According to question given data,
Load arm $ = \;10{\rm{cm = 0}}{\rm{.1m}}$
$\therefore \;{\rm{Effort arm = (2 - 0}}{\rm{.1)m = 1}}{\rm{.9m}}$
(i) We used the above formula to calculate the mechanical advantage of crowbar:
M.A = V.R
$ \Rightarrow \;{\rm{V}}{\rm{.R}}\;{\rm{ = }}\dfrac{{{\rm{Effort arm}}}}{{{\rm{Load arm}}}}\; = \dfrac{{1.9}}{{0.1}}\; = \,19$
$\therefore \;{\rm{M}}{\rm{.A}}\,{\rm{ = }}\;{\rm{19}}$
(ii) Given the load $ = \;100{\rm{kgf}}$
$\therefore \;{\rm{M}}{\rm{.A}}\;{\rm{ = }}\dfrac{{{\rm{Load}}}}{{{\rm{Effort}}}}$
$ \Rightarrow \;{\rm{Effort = }}{\rm{M}}{\rm{.A}} \times {\rm{Load}}$
$ \Rightarrow \;{\rm{Effort = }}\;{\rm{19}} \times {\rm{100}}\,{\rm{ = 1900kgf}}$
The least force which is applied at the other end to displace a load = 1900kgf

Additional information:The ratio of load lifted by a machine to the forced effort applied on a machine is called mechanical advantage of the machine. More considerable the value of mechanical advantage of a machine, more accessible is the work done.

Note:Load is the output which is overcome by machine whereas the effort is the input to the machine. Mechanical Advantage (M.A.), efficiency$(\eta )$ and velocity ratio are interconnected with each other. The mechanical advantage of the machine is the product of its efficiency and velocity ratio. Therefore, ${\rm{M}}{\rm{.A = }}\,{\rm{V}}{\rm{.R}} \times \eta $.