Question

A lever of length $9\text{cm}$ has its load arm $5\text{cm}$ long and the effort arm $9\text{cm}$ long:
(a) Which class does the lever belong to?
(b) What will be the mechanical advantage and velocity ratio if the efficiency becomes $50\%$?

Answer 1

Given:
Length of lever = 9 cm; Load arm = 5 cm; Effort arm = 9 cm.

$\left(a\right)$ $\because$ Effort arm $>$ Load arm and Effort arm $=$ Length of arm
$\therefore$ Fulcrum is at one end, the effort is at another end and load is in between.
⇒ It is a class $\text{II}$ lever.

$\left(b\right)$ For an ideal lever :
Mechanical advantage, $\text{MA}=\frac{\text{Effort arm}}{\text{Load arm}}=\frac{9}{5}$
$\text{MA}=1.8$
And, velocity ratio,
$\text{VR}=\frac{\text{velocity of effort point}}{\text{velocity of load point}}$
$=\frac{\text{Effort arm}}{\text{Load arm}}=1.8$
But for a real lever with the efficiency of $50\%$,
${\text{MA}}^{\prime }=\eta \times \text{VR}=0.5\times 1.8$
${\text{MA}}^{\prime }=0.9$
$\text{VR}$ remains the same $(\text{VR =1.8)}$ as the lever is rigid and does not vary with efficiency.