Engineering Mechanics

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(^180) „„„„„ A Textbook of Engineering Mechanics
Effort required to run the machine at no load
Substituting the value of W = 0 in the law of the machine (for no load condition),
P = 4.8 N Ans.
Effort required to run the machine at a load of 900 N
Substituting the value of W = 900 N in the law of machine,
1
900 4.8 54.8 N
18
P=× + =^ Ans.
10.17. MAXIMUM MECHANICAL ADVANTAGE OF A LIFTING MACHINE
We know that mechanical advantage of a lifting machine,
M.A.
W
P


For maximum mechanical advantage, substituting the value of P = mW + C in the above
equation,
11
Max. M.A.
W
mW C C m
m
W





    • ... NeglectingC
      W
      ⎛⎞
      ⎜⎟
      ⎝⎠
      10.18. MAXIMUM EFFICIENCY OF A LIFTING MACHINE
      We know that efficiency of a lifting machine,
      Mechanical advantage
      Velocity ratio V.R. V.R.
      W
      P W
      P
      η= = =
      ×
      For *maximum efficiency, substituting the value of P = mW + C in the above equation,
      11
      Max.
      ()V.R V.R.
      V.R.
      W
      mW C C m
      m
      W
      η= = =
      +× ⎛⎞ ×
      ⎜⎟+×
      ⎝⎠
      ... NeglectingC
      W
      ⎛⎞
      ⎜⎟
      ⎝⎠
      Example 10.8. The law of a machine is given by the relation :
      P = 0.04 W + 7.5
      where (P) is the effort required to lift a load (W), both expressed in newtons. What is the mechanical
      advantage and efficiency of the machine, when the load is 2 kN and velocity ratio is 40? What is the
      maximum efficiency of the machine?
      If (F) is the effort lost in friction, find the relation between F and W. Also find the value of F,
      when W is 2 kN.
      Solution. Given: Law of machine P = 0.04 W + 7.5 ; Load (W) = 2 kN = 2000 N and velocity
      ratio (V.R.) = 40.






  • We know that efficiency of a lifting machine,
    M.A.
    V.R.
    η=
    A little consideration will show that the efficiency will be maximum, when the mechanical advantage
    will be maximum.
    or
    Max. Max. M.A.
    V.R.
    η=
    1
    m V.R.


    × ...
    Max. M.A.^1
    m
    ⎛⎞=
    ⎜⎟⎝⎠Q



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