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Chapter 11: Problem 14

United States currency is printed using intaglio presses that generate a printing pressure of \(8.0 \times 10^{4}\) lb/in. \(^{2}\) A \(\$ 20\) bill is 6.1 in. by 2.6 in. Calculate the magnitude of the force that the printing press applies to one side of the bill.

Short Answer

Expert verified
The force is 1,268,800 pounds.

Step by step solution

01

Identify the Given Values

We are given that the printing pressure is \(8.0 \times 10^{4}\) lb/in\(^{2}\), and the dimensions of the \(\$20\) bill are 6.1 inches by 2.6 inches.
02

Calculate the Area of the Bill

The area \(A\) of the bill can be calculated by multiplying its length and width. Thus, \(A = 6.1 \times 2.6\) square inches.
03

Perform the Multiplication for Area

Multiply 6.1 in by 2.6 in:\[A = 6.1 \times 2.6 = 15.86 \text{ in}^2\]
04

Use Pressure to Calculate Force

The force \(F\) applied by the press can be found by multiplying the pressure \(P\) by the area \(A\):\[F = P \times A = (8.0 \times 10^{4} \text{ lb/in}^{2}) \times 15.86 \text{ in}^{2}\]
05

Calculate the Force

Execute the multiplication to determine the force:\[F = 8.0 \times 10^{4} \times 15.86 \]Calculating:\[F = 1,268,800 \text{ lb}\]
06

Conclusion

The magnitude of the force applied to one side of the bill by the printing press is 1,268,800 pounds.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Pressure Calculations
Pressure is a measure of how much force is applied over a specific area. It's like thinking about how much weight is spread over a surface. Imagine pressing a finger down on a table. The tip of your finger exerts pressure due to the force applied and the area it covers. Pressure is commonly measured in units like pounds per square inch (lb/in虏).

To calculate pressure, you use the formula: \(P = \frac{F}{A}\), where:
  • **P** is the pressure.
  • **F** is the force applied.
  • **A** is the area over which the force is distributed.
Given the information about pressure in this exercise, \(8.0 \times 10^{4}\) lb/in虏, we will use this to calculate the force applied when we know the area of the bill.
Area Calculation
Understanding the area of a surface is crucial when calculating forces and pressures. In this exercise, the area of the currency bill represents the surface over which the printing press force is applied.

To find the area of a rectangular object like the bill, you multiply its length by its width. For the \$20\ bill, the dimensions are 6.1 inches by 2.6 inches. The calculation is as simple as \(A = \text{length} \times \text{width} = 6.1 \times 2.6\) square inches.

The result of this multiplication gives us an area of \15.86\ square inches. This area is then used in the next step to find out how much total force is being applied by the press.
Force Calculation
Force is the push or pull exerted on an object. In physics, we usually find force using the formula: \(F = P \times A\). This formula shows how force is related to pressure and area.

When calculating force, we take the given pressure (from the exercise, \(8.0 \times 10^{4}\) lb/in虏) and multiply it by the area of the object (from our previous calculation, \15.86\ in虏).

Performing the calculation, \(F = 8.0 \times 10^{4} \times 15.86\), we find that the force exerted is \1,268,800\ pounds. This tells us the strength of the printing press's impact on the bill, illustrating how both pressure and area play a role in exerting force.

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Most popular questions from this chapter

A pipe is horizontal and carries oil that has a viscosity of 0.14 \(\mathrm{Pa} \cdot \mathrm{s}\) The volume flow rate of the oil is \(5.3 \times 10^{-5} \mathrm{m}^{3} / \mathrm{s}\) . The length of the pipe is \(37 \mathrm{m},\) and its radius is 0.60 \(\mathrm{cm}\) . At the output end of the pipe the pressure is atmospheric pressure. What is the absolute pressure at the input end?

A log splitter uses a pump with hydraulic oil to push a piston, which is attached to a chisel. The pump can generate a pressure of \(2.0 \times 10^{7}\) Pa in the hydraulic oil, and the piston has a radius of 0.050 \(\mathrm{m}\) . In a stroke lasting 25 \(\mathrm{s}\) s, the piston moves 0.60 \(\mathrm{m} .\) What is the power needed to operate the log splitter's pump?

The density of ice is 917 \(\mathrm{kg} / \mathrm{m}^{3}\) , and the density of seawater is 1025 \(\mathrm{kg} / \mathrm{m}^{3}\) . A swimming polar bear climbs onto a piece of floating ice that has a volume of 5.2 \(\mathrm{m}^{3} .\) What is the weight of the heaviest bear that the ice can support without sinking completely beneath the water?

A paperweight, when weighed in air, has a weight of \(W=6.9 \mathrm{N}\) . When completely immersed in water, however, it has a weight of \(W_{\text { in water }}=4.3 \mathrm{N}\) . Find the volume of the paperweight.

A mercury barometer reads 747.0 mm on the roof of a building and 760.0 \(\mathrm{mm}\) on the ground. Assuming a constant value of 1.29 \(\mathrm{kg} / \mathrm{m}^{3}\) for the density of air, determine the height of the building.
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