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Ch. 12 - Static Equilibrium; Elasticity and Fracture
Giancoli Douglas - Physics for Scientists and Engineers 5th edition
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook
All textbooksGiancoli Douglas 5th editionCh. 12 - Static Equilibrium; Elasticity and FractureProblem 6
Chapter 12, Problem 6

Figure 12–53 shows a pair of forceps used to hold a thin plastic rod firmly. If the thumb and finger each squeeze with a force FT = FF = 11.0 N, what force do the forceps jaws exert on the plastic rod?
Illustration of forceps gripping a plastic rod, showing forces applied and measurements labeled.

Verified step by step guidance
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Analyze the problem: The forceps act as a type of lever, where the thumb and finger apply forces at one end, and the jaws exert a force on the plastic rod at the other end. The forces applied by the thumb and finger are equal and opposite, creating a torque about the pivot point of the forceps.
Identify the pivot point: The pivot point is the location where the forceps rotate. The forces applied by the thumb and finger create torques about this pivot point, and the force exerted by the jaws on the plastic rod is the result of these torques.
Set up the torque equation: The torque due to the thumb and finger forces must balance the torque exerted by the jaws on the plastic rod. Use the equation for torque: τ = F × d, where F is the force and d is the perpendicular distance from the pivot point to the line of action of the force.
Express the relationship: Let d_T and d_J represent the distances from the pivot point to the thumb/finger forces and the jaws, respectively. The torque balance equation is: F_T × d_T = F_J × d_J, where F_J is the force exerted by the jaws on the plastic rod.
Solve for F_J: Rearrange the equation to find the force exerted by the jaws: F_J = (F_T × d_T) / d_J. Substitute the given values for F_T (11.0 N) and the distances (d_T and d_J) to calculate the force exerted by the jaws.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Newton's Third Law of Motion

Newton's Third Law states that for every action, there is an equal and opposite reaction. This principle is crucial in understanding how forces interact in the system of the forceps and the plastic rod. When the thumb and finger apply forces to the rod, the rod exerts an equal and opposite force back on the forceps, which helps determine the resultant force exerted on the rod.
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Force Transmission in Mechanical Systems

In mechanical systems like forceps, forces applied at one point can be transmitted and amplified at another point. The configuration of the forceps allows the forces applied by the thumb and finger to be concentrated at the jaws, resulting in a greater effective force on the plastic rod. Understanding this concept is essential for calculating the total force exerted on the rod.
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Equilibrium of Forces

The concept of equilibrium involves the balance of forces acting on an object. In this scenario, the forces exerted by the thumb and finger must be analyzed to determine the net force acting on the plastic rod. If the system is in equilibrium, the total force exerted by the forceps on the rod will equal the sum of the forces applied by the thumb and finger, allowing for a straightforward calculation of the resultant force.
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Related Practice
Textbook Question

A shop sign weighing 215 N hangs from the end of a uniform 135-N beam as shown in Fig. 12–59. Find the tension in the supporting wire (at 35.0°), and the horizontal and vertical forces exerted by the hinge on the beam at the wall.

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Textbook Question

Calculate the mass m needed in order to suspend the leg shown in Fig. 12–50. Assume the leg (with cast) has a mass of 15.0 kg, and its cg is 35.0 cm from the hip joint; the cord holding the sling is 78.0 cm from the hip joint.

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Textbook Question

Three children are trying to balance on a seesaw, which includes a fulcrum rock acting as a pivot at the center, and a very light board 3.2 m long (Fig. 12–60). Two playmates are already on either end. Boy A has a mass of 45 kg, and boy B a mass of 35 kg. Where should girl C, whose mass is 25 kg, place herself so as to balance the seesaw?

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Textbook Question

(II) The force required to pull the cork out of the top of a wine bottle is in the range of 200 to 400 N. What range of forces F is required to open a wine bottle with the bottle opener shown in Fig. 12–58?

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