A lever AB of length 1.8 m is pivoted at a point C and he point C is at a distance 60 cm from the point A. If 80 N load is applied at point A, then find the effort required to lift the load:

CONCEPT:

Lever:

• An ideal lever is essentially a light (i.e. of negligible mass) rod pivoted at a point along its length. This point is called the fulcrum.
• Levers are the most basic machines that are used to do some work with minimal effort.
• If two forces F1 and F2 are acting on the lever as shown in the figure at distances d1 and d2 respectively from the fulcrum, then from the rotational equilibrium,

⇒ F1d1 = F2d2

⇒ (load arm)×load = (effort arm)×effort

Mechanical advantage:

• It is defined as the ratio of the load applied on the lever to the effort applied.

\(⇒ MA=\frac{F_1}{F_2}=\frac{d_2}{d_1}\)

• Example of lever:
  • The beam of a balance
  • Seesaw

CALCULATION:

Given AB = 1.8 m, AC = d₁ = 60 cm = 0.6 m, BC = d2 = 120 cm = 1.2 m, and F₁ = 80 N

We know that If two forces F1 and F2 are acting on the lever as shown in the figure at distances d1 and d2 respectively from the fulcrum, then from the rotational equilibrium,

⇒ F1d1 = F2d2

⇒ 80 × 0.6 = F₂ × 1.2

\(\Rightarrow F_2=\frac{80\times06}{1.2}\)

⇒ F2 = 40 N

• Hence, option 3 is correct.