Q63P Four bricks of length L, identic... [FREE SOLUTION]

Chapter 12: Q63P (page 351)

Four bricks of length L, identical and uniform, are stacked on top of oneanother (Fig. 12-71) in such a way that part of each extends beyond the one beneath. Find, in terms of L, the maximum values of (a) $a_{1}$ , (b) $a_{2}$ , (c) $a_{3}$ , (d) $a_{4}$ , and (e) $h$ , such that the stack is in equilibrium, on the verge of falling.

Short Answer

Expert verified

Maximum values of

$\begin{array}{l} (a) 鈥� a_{1} = \frac{L}{2} \\ (b) 鈥� a_{2} = \frac{L}{4} \\ (c) 鈥� a_{3} = \frac{L}{6} \\ (d) 鈥� a_{4} = \frac{L}{8} \\ (e) 鈥� h = \frac{25 L}{24} \end{array}$

Step by step solution

Understanding the given information

The length of the bricks is L.

Concept and formula used in the given question

For the given equilibrium,you can find the distance of bricks in terms of L. The formulas used are given below.

$\begin{array}{l} 蟿 = 0 \\ N e t f o r c e = 0 \end{array}$

(a) Calculation for the a1

You know the condition of equilibrium in which the moment of force, and torque is zero.

The Center of mass of the top brick cannot be extended further to the right $L/2$ ; otherwise, it will fall. So maximum value of $a_{1}$ is

$a_{1} = \frac{L}{2}$

(b) Calculation for the a2

$N_{2} = 2mg$

Moment of force

$\begin{array}{l} 鈭� 蟿 = 0 \\ 鈭� a_{2} (N_{2}) + \frac{L}{2} (m g) = 0 \\ a_{2} = \frac{L}{4} \end{array}$

(c) Calculation for the a3

$N_{3} = 3 m g$

Moment of force

$\begin{array}{l} 鈭� 蟿 = 0 \\ 鈭� a_{3} (N_{3}) + \frac{L}{2} (m g) = 0 \\ a_{3} = \frac{L}{6} \end{array}$

(d) Calculation for the a4

$N_{4} = 4mg$

Moment of force

$\begin{array}{l} 鈭� 蟿 = 0 \\ 鈭� a_{4} (N_{4}) + \frac{L}{2} (m g) = 0 \\ a_{4} = \frac{L}{8} \end{array}$

(e) Calculation for the h

$\begin{matrix} h = a_{1} + a_{2} + a_{3} + a_{4} \\ = \frac{L}{2} + \frac{L}{4} + \frac{L}{6} + \frac{L}{8} \\ = \frac{25 L}{24} \end{matrix}$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Short Answer

Step by step solution

Understanding the given information

Concept and formula used in the given question

(a) Calculation for the a1

(b) Calculation for the a2

(c) Calculation for the a3

(d) Calculation for the a4

(e) Calculation for the h

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Scientific Method Physics

Wave Optics

Thermodynamics

Linear Momentum

Further Mechanics and Thermal Physics

Fluids

Study anywhere. Anytime. Across all devices.