Question

Case 1: Lata cuts a potato into two halves, using a cutter which belongs to a Class II lever. She needed effort E\(_1\).
Case 2: Then she cuts one half of this potato again, but this time she needed effort E\(_2\).
If E\(_1\) > E\(_2\) then:
(a) In which case (1st or 2nd) was the potato closer to her hand applying the effort? (Assume normal reaction of the surface of the potato is same in both cases)
(b) Give a reason for your answer in (a) above.

Hint:

For a Class II lever (like a bottle opener or wheelbarrow), moving the load closer to the effort (away from the fulcrum) decreases your mechanical advantage, forcing you to apply more effort.

Answer 1

Step 1: Understanding the Concept:
A Class II lever has the Load situated between the Fulcrum and the Effort. Common examples include a paper cutter or a nutcracker.
Step 2: Key Formula or Approach:
The Principle of Levers states:
\[ \text{Effort} \times \text{Effort Arm} = \text{Load} \times \text{Load Arm} \]
\[ \text{Effort} (E) = \text{Load} (L) \times \frac{\text{Load Arm}}{\text{Effort Arm}} \]
Step 3: Detailed Explanation:
- The effort arm is the fixed length of the cutter (distance from fulcrum to hand).
- The load arm is the distance from the fulcrum to the potato.
- We are given \( E_1>E_2 \). Since the Load \( L \) is assumed constant (normal reaction), a higher effort \( E_1 \) implies a larger load arm (\( L.A._1 \)).
- In Case 1, the load arm was larger, meaning the potato was further from the fulcrum.
- Since the potato is between the fulcrum and the hand, being further from the fulcrum automatically means it is closer to the hand applying the effort.
Step 4: Final Answer:
The potato was closer to her hand in the \( 1^{st} \) case.
(b)
Step 1: Detailed Explanation:
In a Class II lever, the effort arm (length of handle) is constant. The required effort decreases as the load arm (distance of the load from the fulcrum) decreases.
Since \( E_2<E_1 \), the load arm in Case 2 must be smaller than in Case 1.
A smaller load arm means the potato is closer to the fulcrum in Case 2.
Consequently, in Case 1, where the load arm was larger, the potato must have been positioned closer to the effort point (the hand).
Step 2: Final Answer:
Because a larger effort corresponds to a larger load arm for a fixed effort arm, placing the load closer to the hand increases the effort required.