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

(a) In which case was the potato closer to her hand?
The potato was closer to her hand in Case 1.
(b) Reason:
Step 1: Understanding the Lever System:
A cutter is a Class II lever, where the Load (the resistance from the potato) is between the Fulcrum (the pivot of the cutter) and the Effort (the force applied by the hand).
Step 2: Principle of Levers:
The principle of moments for a lever in equilibrium is:
\[ \text{Effort} \times \text{Effort Arm} = \text{Load} \times \text{Load Arm} \] This can be rearranged to find the effort required:
\[ \text{Effort} = \frac{\text{Load} \times \text{Load Arm}}{\text{Effort Arm}} \] Step 3: Applying the given conditions:
- The Effort Arm is the distance from the fulcrum to the hand, which we can assume remains constant.
- The question states to assume the normal reaction (which is the Load) is the same in both cases. So, Load\(_1\) = Load\(_2\).
- With the Load and Effort Arm being constant, the formula simplifies to:
\[ \text{Effort} \propto \text{Load Arm} \] - We are given that \(E_1>E_2\). Since the effort is directly proportional to the load arm, this implies that the Load Arm in Case 1 was greater than the Load Arm in Case 2.
\[ \text{Load Arm}_1>\text{Load Arm}_2 \] Step 4: Conclusion:
The Load Arm is the distance from the fulcrum to the potato. A larger load arm means the potato is placed further from the fulcrum. Since the hand is at the other end of the lever, placing the potato further from the fulcrum means placing it closer to the hand. Therefore, the potato was closer to the hand in Case 1, which required a greater effort.