Wire Cutters A technician applies the 70-N gripping force to the handles of the wire cutters. What are the magnitudes of the cutting force on the electrical wire at and the force carried by the hinge pin at B? (See Figure 4.19.) Approach We are tasked to fi nd the forces at the cutting point and

Question

Wire Cutters

A technician applies the 70-N gripping force to the handles of the wire cutters. What are the magnitudes of the cutting force on the electrical wire at and the force carried by the hinge pin at B? (See Figure 4.19.)

Approach
We are tasked to fi nd the forces at the cutting point and the hinge. We assume that the weight of the wire cutters is negligible compared to the applied force. We then show the coordinate system and positive sign convention for the directions of forces and moments. The free body diagram is drawn for one jaw/handle assembly, which is a rigid body because it can rotate and the distances between the forces are significant to the problem. When a blade presses against the wire, the wire in turn pushes back on the blade following the principle of action–reaction. We label the jaw’s cutting force as [latex] F_{A}[/latex], and the force exerted by the hinge pin on the jaw/handle as [latex] F_{B}[/latex]. The 70-N gripping force is given, and it is also included on the free body diagram. (See Figure 4.20)

Accepted Answer

The cutting force is found by applying the equilibrium equations for a rigid body. The force balance requirement in the vertical direction becomes

[latex]F_{A}-F_{B}+ (70 N) = 0 \longleftarrow [\sum\limits_{i=1}^{N}{F_{y,i}=0} ] [/latex]

There are two unknowns, [latex]F_{A}[/latex] and[latex] F_{B}[/latex], and so an additional equation is needed. By summing moments about point B, we have

[latex](70 N)(90 mm) - F_{A}(20 mm) = 0 \longleftarrow [\sum\limits_{i=1}^{N}{M_{B,i}=0} ][/latex]

The negative sign indicates that [latex]F_{A} [/latex] produces a clockwise moment about point B. The cutting force is [latex]F_{A}[/latex] = 315 N, and, after back substitution, we find that [latex]F_{B} [/latex] =385 N. Because these numerical values are each positive, the directions shown at the outset on the free body diagram are correct.

Discussion
The wire cutters operate according to the principle of a lever. The cutting force is proportional to the force on the handles, and it is also related to the ratio of distances AB and BC. The mechanical advantage for a machine is defined as the ratio of the output and input forces, or in this case, (315 N)/ (70 N) = 4.5. The wire cutters magnify the gripping force by 450%.

[latex]F_{A} = 315 N[/latex]

[latex]F_{B} = 385 N[/latex]

Question 4.6: Wire Cutters A technician applies the 70-N gripping force to...

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