Chapter 18: Q. 44 (page 512)

A 15 $°$ C, 2.0-cm-diameter aluminum bar just barely slips between two rigid steel walls 10.0 cm apart. If the bar is warmed to 25 $°$ C, how much force does it exert on each wall?

Short Answer

Expert verified

The accurate answer is $14.5 k n$

Step by step solution

Description

A 15 $°$ C, 2.0-cm-diameter aluminum bar just barely slips between two rigid steel walls 10.0 cm apart.

The young module depicts

$p = \frac{F}{A} = Y \frac{∆ L}{L}$

Finding the result

The description provided that

$F = A Y \frac{∆ L}{L} = \frac{π}{4} D^{2} Y \frac{∆ L}{L}$

From the expression for linear thermal expansion is:

$\frac{∆ L}{L} = α ∆ T$

Therefore, the final expansion will be:

$F = \frac{{πD}^{2}}{4} Y α ∆ T$

The table of 18.4 depicts that the coefficient of linear thermal expansion of Aluminium is almost $23 . 10^{- 5} 1 / k$ .

The table of 14.3 depicts that Aluminium's young modules is $Y = 20 . 10^{10} N / m^{2}$ .

Thus, $F = \frac{π \cdot 0 . 02^{2}}{4} \cdot 20 \cdot 10^{10} \cdot 2.3 \cdot 10^{- 5} \cdot 10 = 14500 N$

Therefore, If the bar is warmed to 25 $°$ C, the force of $14.5 k N$ , it exert on each wall.

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A 15 $°$ C, 2.0-cm-diameter aluminum bar just barely slips between two rigid steel walls 10.0 cm apart. If the bar is warmed to 25 $°$ C, how much force does it exert on each wall?

Short Answer

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Finding the result

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A 15°C, 2.0-cm-diameter aluminum bar just barely slips between two rigid steel walls 10.0 cm apart. If the bar is warmed to 25°C, how much force does it exert on each wall?

Short Answer

Step by step solution

Description

Finding the result

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Conservation of Energy and Momentum

Circular Motion and Gravitation

Particle Model of Matter

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Magnetism

Study anywhere. Anytime. Across all devices.

A 15 $°$ C, 2.0-cm-diameter aluminum bar just barely slips between two rigid steel walls 10.0 cm apart. If the bar is warmed to 25 $°$ C, how much force does it exert on each wall?