[5 Mark Question Answer]

Question 15 Marks

To which order do the following levers belong and why?
(i) Railway signal, (ii) a man cutting bread with knife, (iii) a boy writing on a piece of paper,
(iv) nut-cracker, (v) handle of water pump, (vi) see-saw, (vii) forceps, (viii) a man rowing a boat,
(ix) lock and key, ( x ) opening of a soda water bottle, (xi) closing a door, (xii) motor car foot brake,
(xiii) nail cutter, (xiv) a fishing rod, (xv) a lemon squeezer.

Answer

Levers of Ist order
(i) Railway signal
(ii) Handle of water pump
(iii) See-saw
(iv) Motor car foot brake
(v) Nail cutter
Levers of IInd order
(i) Nut-cracker
(ii) A man rowing a boat
(iii) Lock and key
(iv) Opening of soda-water bottle
(v) A lemon squeezer.
(vi) Closing a door
Levers of IIIrd order
(i) A man cutting bread with knife
(ii) A boy writing on a piece of paper
(iii) Foreeps
(iv) A fishing rod

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Question 25 Marks

(i) Define machine and write functions of a machine.
(ii) Describe mechanical advantage and its types.
(iii) (a) Derive relation between the efficiency, mechanical advantage, and the velocity ratio of a practical machine.
(b) Derive relation between ideal mechanical advantage and velocity ratio for a perfect machine

Answer

(i) 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.
Functions of a machine are:
(a) A machine can multiply force.
(b) A machine can increase speed.
(c) A machine can change the direction of effort applied.
(ii) Mechanical advantage means advantage given by the machine, in terms of effort applied and load lifted by it. If a machine lifts a comparatively large load, compared to effort applied, then it has a positive mechanical advantage.
Mechanical advantage can be classified under two classes
(a) Ideal mechanical advantage: Ideal mechanical advantage is the ratio between the total load (useful load + resistance due to friction and movable parts of machine) moved to the effort applied.
(b) Actual mechanical advantage : Actual mechanical advantage is the ratio between the useful load moved to the effort applied.
(iii) Consider a perfect machine (whose parts are weightless and frictionless) in which an effort ' E ' causes a displacement 'D', when total load ' $L$ ', is displaced through a distance ' $d$ '.
$\therefore$ Output of the machine $=L \times d$
Input of the machine $=E \times D$.
By the principle of a perfect machine,
Output of the machine $=$ Input of the machine
$\begin{aligned} & L \times d=E \times D \\ \Rightarrow & \frac{L}{E}=\frac{D}{d} \\ \therefore & I M A = V R \end{aligned}$
However, if $L=l+x$, where $T$ is the useful load and $x$ is the resistance due to the movable parts of the machine and friction, etc., then from the above expression :
$\frac{L}{E}=\frac{D}{d} \Rightarrow \frac{l+x}{E}=\frac{D}{d}$
$\Rightarrow \frac{l}{E}+\frac{x}{E}=\frac{D}{d}$
$AMA +\frac{x}{E}= VR$
$\therefore \frac{x}{E}= VR - AMA$
$x= E ( VR - AMA )$
But $ V R=I M A$
$\therefore x=E($ IMA - AMA $)$

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Question 35 Marks

(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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Question 45 Marks

(i) (a) What is a pulley?
(b) What is single fixed pulley system?.
(c) What is single movable pulley system?
(ii) A pulley system has five pulleys in all and is 90% efficient.
Calculate:
(a) the mechanical advantage
(b) the effort required to lift a load of 1000 N
(c) the resistance due to the movable parts of the machine and friction
(iii) Give reasons why single fixed pulley is commonly used.

Answer

(i) (a) A pulley is a flat circular disc having a groove in its edge and capable of rotating about a fixed point passing through its centre and is commonly called axle.
(b) It consists of a single pulley. It is attached to some high platform and around its groove passes a rope. One end of the rope is attached to the load and the effort is applied at the other end.
(c) It consists of two pulleys A and B. The pulley A is fixed on some high platform, such as a hook in the ceiling. The pulley B is movable, ie., it moves up and down, along with the load, in addition to rotating around its own axis.
(ii) Velocity ratio $=$ Number of pulleys $=5$
$\eta=90 \%$
(a) $\eta=\frac{M . A}{V R}$
or, M.A. $=\eta \times VR =\frac{90}{100} \times 5=4.5$
(b) $l=1000 N$
M.A. $=\frac{l}{ E }$
or $E =\frac{l}{ MA }=\frac{1000 N}{4.5}=222.2 N$
(c) If R is the resistance due to the movable parts of the machine and friction, then
$M . A .=VR-\frac{x}{E} \Rightarrow x=E(VR-MA)=222.2 N(5-4.5)=111.1 N$
(iii) Reasons for using single fixed pulley:
(a) It is always easier to apply effort in the downward direction rather than in the upward direction. Thus, the pulley helps in changing the direction of effort,
(b) One can use one's own body weight, while applying the effort in the downward direction.

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Physics [5 Mark Question Answer]

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