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Machines — Physics STD 10 — Question

ICSE BoardEnglish MediumSTD 10PhysicsMachines5 Marks
Question
(i) (a) What is a machine?
(b) In reference to machine define effort and actual mechanical advantage.
(ii) Prove that efficiency of a machine is the ratio between mechanical advantage and the velocity ratio,
(iii) A machine displaces a load of 125 kgf through a distance 0.30 m, when an effort of 12.5 kgf acts through a distance of 4.0 m.
Calculate the (a) velocity ratio (b) mechanical advantage (c) % age efficiency of the machine
✓

Answer

(i) (a) Machine is a device by which we can overcome large resistance or gain speed or change the direction of effort applied, by applying comparatively a small force at a convenient point, and in a desired direction.
(b) Effort: Effort is the external force applied on a machine to overcome the load or resistance.
Actual mechanical advantage: Actual mechanical advantage is the ratio between the useful load moved to the effort applied.
(ii) Consider a machine which displaces a useful load ' $l$ ' through a distance ' $d$ ', when an effort ' B ' causes a displacement through distance D.
$\begin{aligned} \therefore \text { Output } & =\text { Work done in displacing the load }=l \times d \\ \text { Input } & =\text { Work done by the effort in causing the displacement }= E \times D \end{aligned}$
$\therefore$ Efficiency $=\eta=\frac{\text { Output }}{\text { Input }}=\frac{l \times d}{ E \times D }=\frac{l}{ E }\div \frac{D}{d}= MA \div VR$
$\therefore \eta=\frac{M A}{V R}$
$\therefore$ Efficiency of a machine is the ratio of mechanical advantage to the velocity ratio.
(iii) (a) Velocity ratio $=\frac{\text { Distance through which effort moves }}{\text { Distance through which the load moves }}=\frac{4.0 m}{0.3 m}=\frac{40}{3}=13.33$
(b) Mechanical advantage $=\frac{\text { Load }}{\text { Effort }}=\frac{125 kgf }{12.5 kgf }=10$
(c) $\%$ efficiency $=\frac{ MA }{ VR } \times 100=\frac{10}{\frac{40}{3}} \times 100=\frac{10 \times 100 \times 3}{40}=75 \%$

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