Question

A brass nameplate is 2.00 cm×10.0 cm×60.0 cm in size. A force F of 6.00×105 N acts on the upper left side and the bottom right side, as shown in the figure. Determine the shear strain hx​, which relates to the amount x of horizontal deformation of the top edge and the vertical height h of the nameplate. Determine the angle ϕ of deformation.

Answer 1

The shear strain, hₓ, is 0.005, and the angle of deformation, ϕ, is approximately 0.48 radians.

Step-by-step explanation:

To determine the shear strain, we can use the formula hₓ = x/h, where x is the horizontal deformation and h is the vertical height. Given that the nameplate is 60.0 cm in height, and the force is applied on the upper left and bottom right corners, causing a horizontal displacement of 2.00 cm, we can calculate hₓ as follows:

`\[ hₓ = (x)/(h) = \frac{2.00 \, \text{cm}}{60.0 \, \text{cm}} = 0.0333 \]`

To find the angle of deformation, ϕ, we can use the tangent of ϕ, which is given by the formula
`\(\tan(ϕ) = (x)/(h)\)`. Substituting the values, we get:

`\[ \tan(ϕ) = \frac{2.00 \, \text{cm}}{60.0 \, \text{cm}} = 0.0333 \]`

Taking the arctangent of both sides, we find ϕ ≈ 0.48 radians.

Therefore, the shear strain, hₓ, is 0.0333, and the angle of deformation, ϕ, is approximately 0.48 radians.

Answer 2

The shear strain hx can be determined using the formula hx = Δx / h. The angle ϕ of deformation can be determined using the formula ϕ = atan(Δx / h).

The shear strain hx can be determined using the formula:

hx = Δx / h

where Δx is the horizontal deformation of the top edge and h is the vertical height of the nameplate.

The angle ϕ of deformation can be determined using the formula:

ϕ = atan(Δx / h)

Given the force F and the dimensions of the brass nameplate, the shear strain and angle of deformation can be calculated.

When a deforming force is applied to a surface at a straight angle, the result is tensile stress. Shear stress, on the other hand, results from the application of a deforming force parallel to the surface.

It is a shift in angular position within a form. When scissors cut through paper, for instance, the shear strain is so great that the paper gives and tears at the strained areas.