Lifting Machines – Mechanical Advantage vs Velocity Ratio For actual (real) machines with frictional losses, the mechanical advantage (MA) is __________ the velocity ratio (VR).
-
Aequal to
-
Bless than
-
Cgreater than
-
Dunrelated to
-
Ealways the reciprocal of
Answer
Correct Answer: less than
Explanation
Introduction / Context: In machine theory, the velocity ratio (VR) is a geometric/kinematic property, while the mechanical advantage (MA) depends on actual forces and is reduced by friction. Efficiency bridges the two.
Given Data / Assumptions:
- Efficiency η = MA / VR.
- For real machines, 0 < η < 1 due to losses.
Concept / Approach: Rearranging efficiency gives MA = η * VR. Since η < 1 in real machines, MA < VR.
Step-by-Step Solution: Start: η = MA / VR. Rearrange: MA = η * VR. With η < 1 ⇒ MA < VR.
Verification / Alternative check: Ideal machine has η = 1 ⇒ MA = VR; adding friction reduces MA below VR.
Why Other Options Are Wrong: Equal to: only for ideal machines. Greater than or reciprocal: contradicts η < 1. Unrelated: incorrect; η links them directly.
Common Pitfalls: Confusing MA with VR or ignoring efficiency.
Final Answer: less than