derive the relationship between MA,VRandñ,
Answers
Let a machine overcome a load L by the application of an effort E. In time t, let the displacement of effort of d
E
ad the displacement of load be d
L
.
Work input =Effort× displacement of effort
=E×d
E
Work output =Load× displacement of load
=L×d
L
Efficiency=
Work input
Work output
=
E×d
E
L×d
L
=
E
L
×
d
E
d
L
=
E
L
×
d
E
/d
L
1
But
Effort(E)
Load(L)
=M.A.
and
d
L
d
E
=V.R.
∴Efficiency η=
V.R.
M.A.
or M.A.=V.R.×η
Thus, the mechanical advantage of a machine is equal to the product of its efficiency and Velocity Ratio
Answer:
Let a machine overcome a load L by the application of an effort E. In time t, let the displacement of effort of d
E
ad the displacement of load be d
L
.
Work input =Effort× displacement of effort
=E×d
E
Work output =Load× displacement of load
=L×d
L
Efficiency=
Work input
Work output
=
E×d
E
L×d
L
=
E
L
×
d
E
d
L
=
E
L
×
d
E
/d
L
1
But
Effort(E)
Load(L)
=M.A.
and
d
L
d
E
=V.R.
∴Efficiency η=
V.R.
M.A.
or M.A.=V.R.×η
Thus, the mechanical advantage of a machine is equal to the product of its efficiency and Velocity Ratio.