A square steel plate is 10.0 cm on a side and 0.500 cm thick. (a) Find the shear strain that results if a force of magnitude 9.0×10 5 N is applied to each of the four sides, parallel to the side. (b) Find the displacement x (in centimeters).

Welcome back everybody. We are looking at an aluminum box here and we are told that a tangential force is applied on both ends of this aluminum box. Now this tangential force is equal to three times 10 to the fifth. Newtons, we are tasked with finding two different things here. We are tasked with finding what the shear strain of the box is and we are tasked with finding what the displacement of the boxes. And we are also told just as I note that the dimension of the box is six by six by six centimeters. So let's start out here with the shear strain. Well, we know that the sheer module is which I'm just going to denote by S is equal to the tangential force over the area of the cross section of the box, divided by the displacement over the height of one of the sides of the boxes. Now the displacement over the height is actually equal to our shear strain. So our sheer modulates, then is equal to force over area over our shear strain, which rearranging this equation. We then get that our shear strain is equal to our tangential force over our area of a cross section of the boss box. Times our sheer modulates which we know all these values. So let's go ahead and plug those values in. Our shear strain is equal to our tangential force of three times 10 to the fifth, divided by area of a cross section. Cross section of a cube is just a square. So we're just gonna do six centimeters or 60.6 m squared times the sheer module list for aluminum, which when you look it up is just 2.5 times 10 to the 10th pascal's. Which when you plug this into your calculator, we get that our shear strain is 3.3 times 10 to the negative third. Great. Now moving on to part two here, we need to find the displacement. Well, we established earlier that our shear strain is equal to displacement over height, meaning that our displacement is just equal to our shear strain times the height of one of the sides of the box is plugging in values. Here we get that. This is 3.3 times 10 to the negative third times a height of one of the sides, which is six centimeters or 0.6 m. Which when you plug this into your calculator, you get 0.198 micro meters. So now we have found both the shear strain and the displacement which corresponds to uh Sorry, answer choice. C Thank you all so much for watching. Hope this video helped. We will see you all in the next one

Table of contents

Skip topic navigation

0. Math Review31m
- Math Review
  31m
1. Intro to Physics Units1h 29m
2. 1D Motion / Kinematics3h 56m
3. Vectors2h 43m
4. 2D Kinematics1h 42m
5. Projectile Motion3h 6m
6. Intro to Forces (Dynamics)3h 22m
7. Friction, Inclines, Systems2h 44m
8. Centripetal Forces & Gravitation7h 26m
9. Work & Energy1h 59m
10. Conservation of Energy2h 54m
11. Momentum & Impulse3h 40m
12. Rotational Kinematics2h 59m
13. Rotational Inertia & Energy7h 4m
14. Torque & Rotational Dynamics2h 5m
15. Rotational Equilibrium3h 39m
16. Angular Momentum3h 6m
17. Periodic Motion2h 9m
18. Waves & Sound3h 40m
19. Fluid Mechanics4h 27m
20. Heat and Temperature3h 7m
21. Kinetic Theory of Ideal Gases1h 50m
22. The First Law of Thermodynamics1h 26m
23. The Second Law of Thermodynamics3h 11m
24. Electric Force & Field; Gauss' Law3h 42m
25. Electric Potential1h 51m
26. Capacitors & Dielectrics2h 2m
27. Resistors & DC Circuits3h 8m
28. Magnetic Fields and Forces2h 23m
29. Sources of Magnetic Field2h 30m
30. Induction and Inductance3h 38m
31. Alternating Current2h 37m
32. Electromagnetic Waves2h 14m
33. Geometric Optics2h 57m
34. Wave Optics1h 15m
35. Special Relativity2h 10m

19. Fluid Mechanics

Density

Physics

19. Fluid Mechanics

Density

Previous problemNext problem

3:01 minutes

Problem 36

Textbook Question

A square steel plate is 10.0 cm on a side and 0.500 cm thick. (a) Find the shear strain that results if a force of magnitude 9.0×10⁵ N is applied to each of the four sides, parallel to the side. (b) Find the displacement x (in centimeters).

Verified step by step guidance

Understand the problem: We need to find the shear strain and the displacement of a square steel plate when a force is applied parallel to its sides.

Recall the formula for shear strain (γ), which is the ratio of the displacement (x) to the original length (L): γ = x / L.

Use the formula for shear stress (τ), which is the force (F) applied divided by the area (A) it is applied to: τ = F / A. Here, A is the area of one side of the square plate.

The shear modulus (G) relates shear stress and shear strain: τ = G * γ. Rearrange this to find the shear strain: γ = τ / G.

To find the displacement (x), use the relationship γ = x / L, where L is the side length of the plate. Rearrange to find x: x = γ * L.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above

Video duration:

Play a video:

Was this helpful?

Key Concepts

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

Shear Stress

Shear stress is the force per unit area acting parallel to the surface of a material. It is calculated by dividing the applied force by the area over which the force is distributed. In this problem, the shear stress is crucial for determining the shear strain, as it directly influences how the material deforms under the applied force.

Shear Strain

Shear strain is a measure of how much a material deforms in response to shear stress. It is defined as the displacement of a layer of the material divided by its original length. Understanding shear strain is essential for calculating the deformation of the steel plate when subjected to the given force, as it quantifies the angular distortion experienced by the material.

Shear Modulus

The shear modulus, also known as the modulus of rigidity, is a material property that describes its response to shear stress. It is the ratio of shear stress to shear strain and provides insight into the material's stiffness. For this problem, knowing the shear modulus of steel allows us to relate the applied force to the resulting shear strain and displacement, enabling the calculation of the plate's deformation.

Watch next

Master Intro to Density with a bite sized video explanation from Patrick

Start learning

Related Videos

Related Practice

Multiple Choice

You have three objects in front of you. Object A has a volume of

4 {cm}^{3}

. object B has a volume of

7 {cm}^{3}

. and object C has a volume of

10 {cm}^{3}

. They all have the same mass. What is the correct ranking of the objects from most dense to least dense?

562

views

Multiple Choice

Suppose a cubic box contains so much air at

0 ℃

that the mass of the air inside is equal to the mass of

1 . 0 L

of water. What would be the side length of such a box?

613

views

Multiple Choice

Different materials in the body have different densities, and therefore will tend to make a person float or sink to different extents. Which bodily material is most buoyant (helps you stay afloat the most)?

582

views

Textbook Question

A brass wire is to withstand a tensile force of 350 N without breaking. What minimum diameter must the wire have?

1255

views

Textbook Question

In the Challenger Deep of the Marianas Trench, the depth of seawater is 10.9 km and the pressure is 1.16×10⁸ Pa (about 1.15×10³ atm). If a cubic meter of water is taken from the surface to this depth, what is the change in its volume? (Normal atmospheric pressure is about 1.0×10⁵ Pa. Assume that k for seawater is the same as the freshwater value given in Table 11.2.)

1919

views

Textbook Question

A specimen of oil having an initial volume of 600 cm³ is subjected to a pressure increase of 3.6×10⁶ Pa, and the volume is found to decrease by 0.45 cm³. What is the bulk modulus of the material and the compressibility?

1736

views

Textbook Question

A solid gold bar is pulled up from the hold of the sunken RMS Titanic. The bulk modulus of lead is one-fourth that of gold. Find the ratio of the volume change of a solid lead bar to that of a gold bar of equal volume for the same pressure change.

901

views

Textbook Question

A nylon rope used by mountaineers elongates 1.10 m under the weight of a 65.0 kg climber. If the rope is 45.0 m in length and 7.0 mm in diameter, what is Young's modulus for nylon?

876

views

Show more practices

Download the Mobile app

Privacy

Do not sell my personal information

Accessibility

Patent notice

Sitemap

A square steel plate is 10.0 cm on a side and 0.500 cm thick. (a) Find the shear strain that results if a force of magnitude 9.0×105 N is applied to each of the four sides, parallel to the side. (b) Find the displacement x (in centimeters).

Key Concepts

Shear Stress

Shear Strain

Shear Modulus

Watch next

A square steel plate is 10.0 cm on a side and 0.500 cm thick. (a) Find the shear strain that results if a force of magnitude 9.0×10⁵ N is applied to each of the four sides, parallel to the side. (b) Find the displacement x (in centimeters).