Velocity triangle insight In orthogonal cutting, consider the standard velocity triangle that relates cutting velocity (V), chip velocity along the tool face (Vc), and shear velocity along the shear plane (Vs). The vector sum of cutting velocity and chip velocity is __________ the shear velocity.

Introduction / Context:
Understanding the velocity triangle helps in analyzing chip flow and energy partitions in machining. Each velocity corresponds to a distinct physical interface: work-tool, chip-tool, and shear plane within the work material.

Given Data / Assumptions:

• Orthogonal cutting with a defined rake angle.
• Steady state cutting and continuous chip formation.
• Conventional sign and vector directions (Merchant diagram).

Concept / Approach:
The well-known vector relationship is V = Vs + Vc (vector sum). That is, the cutting velocity equals the vector sum of shear and chip velocities, not vice versa. Consequently, if one were to sum V and Vc, the resulting vector would not equal Vs and will generally have a larger magnitude than Vs due to triangle inequality.

Step-by-Step Solution:

Verification / Alternative check:
Draw a representative triangle for a positive rake angle; measure magnitudes to see |V + Vc| > |Vs| typically holds.

Why Other Options Are Wrong:
Equal to: incorrect by the fundamental relation (V = Vs + Vc).Less than: contradicts the triangle inequality for typical geometries.Undefined without rake angle: directions depend on geometry, but the algebraic relation and inequality stand in general.Opposite to: incorrect; the vectors are not opposite by definition.

Common Pitfalls:
Confusing which pair sums to which; always anchor the triangle on the physical interfaces to avoid sign/direction errors.

Final Answer:

more than