WHEEL AND AXLE
 
 
It is a simple machine and is used to lift heavy loads. It has a wheel of larger radius (R) and an axle of smaller radius (r) fixed on the same shaft. Wheel and axle are free to rotate about its shaft.
MECHANICAL ADVANTAGE OF WHEEL AND AXLE
 
The effort is applied to the rim of the wheel and the load is raised by a rope wound around the axle.
In one rotation wheel covers a distance of 2pR
In one rotation load is raised by a distance of 2pr
If we neglect force of friction,
Output = input
W x 2
pr = P x 2pR
W/P = 2pR/2pr
W/P = R/r
Since [W/P = M.A.]
M.A. = R/r
OR
M.A. = radius of wheel / radius of axle
This expression indicates that in order to increase the mechanical advantage
Radius of :wheel must have a large value.
Radius of axle must be smaller than that of wheel.
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WEDGE
 
Wedge is also a type of simple machines. It is used in levers as a fulcrum. It is also used for splitting the wood in to small pieces. It is used as an Ax.
CONSTRUCTION OF
WEDGE
 
A wedge is made of two inclined planes joined together. The effort ‘P’ is applied on the top of the wedge placed over a wood log. The wedge enters the wood and splits it. The reaction forces R1 & R2 are acting perpendicular on the inclined planes of the wedge. These forces and resultant frictional forces are responsible for keeping the wedge inside the wood firmly.
MECHANICAL ADVANTAGE OF WEDGE
 
Let us consider that the wedge is in equilibrium under the action of forces three forces R1, P and R2 and neglecting frictional forces. According to figure below the forces P, R1 and R2 are represented by the sides of D XYZ such that effort P the reaction R1 and R2 are represented by XY, YZ, ZX which are the sides of ,D XYZ respectively.
Mechanical advantage(M.A). = load/effort
For equal sides of wedge i.e. = R1 = R2 = R
M.A. = R/P
M.A = ZX/XY
Triangle ABC and triangle XYZ are similar, therefore,
ZX=AC and XY=BC
M.A. = AC/BC
Mechanical advantage = length of inclined surface of wedge/thickness of wedge
From above expression it is clear that if the thickness of the wedge is decreased the mechanical advantage of the wedge will increase & if the wedge is more sharper , then the mechanical advantage will increase.
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