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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 12.13
Chapter 12, Problem 12.13

(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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Identify the lever type used in the bottle opener. Most bottle openers use a class 2 lever, where the load (cork) is between the fulcrum (pivot point of the opener) and the effort (force applied by the user).
Determine the distances from the fulcrum to where the force is applied (effort arm) and from the fulcrum to the cork (load arm). These distances are crucial for calculating the mechanical advantage of the lever.
Calculate the mechanical advantage (MA) of the lever using the formula: MA = \(\frac{\text{length of effort arm}\)}{\(\text{length of load arm}\)}. This ratio tells you how much the lever amplifies the input force.
Apply the concept of mechanical advantage to find the range of forces required to pull the cork. Since the mechanical advantage allows the user to apply less force than the force required to pull the cork directly, divide the direct force range (200 to 400 N) by the mechanical advantage.
Consider any additional factors that might affect the force required, such as friction at the fulcrum or deformation of the cork, and adjust your force range estimate accordingly.

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Key Concepts

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

Force

Force is a vector quantity that represents an interaction that causes an object to change its velocity, direction, or shape. It is measured in newtons (N) and can be calculated using Newton's second law, F = ma, where 'm' is mass and 'a' is acceleration. In the context of opening a wine bottle, the force applied must overcome the resistance of the cork.
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Mechanical Advantage

Mechanical advantage is a measure of the force amplification achieved by using a tool, such as a lever or a bottle opener. It is defined as the ratio of the output force exerted by the tool to the input force applied to it. A bottle opener typically provides mechanical advantage, allowing a smaller input force to generate a larger output force to remove the cork.
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Torque

Torque is a measure of the rotational force applied to an object, calculated as the product of the force and the distance from the pivot point (lever arm). In the case of a bottle opener, applying force at a distance from the cork creates torque, which helps to loosen and remove the cork. Understanding torque is essential for determining the effectiveness of the opener in relation to the force required.
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Related Practice
Textbook Question

A 2300-kg trailer is attached to a stationary truck at point B, Fig. 12–64. Determine the normal force exerted by the road on the rear tires at A, and the vertical force exerted on the trailer by the support B.

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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

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?

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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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