A square steel plate is 10.1 cm on a side and 0.545 cm thick. 3) You are prepari

Question

A square steel plate is 10.1 cm on a side and 0.545 cm thick.

3) You are preparing some apparatus for a visit to a newly discovered planet Caasi having oceans of glycerine and a surface acceleration due to gravity of 3.95 m/s2. If your apparatus floats in the oceans on earth with 50.0% of its volume submerged, what percentage will be submerged in the glycerine oceans of Caasi?
________________ %

A square steel plate is 10.1 cm on a side and 0.545 cm thick. (a) Find the shear strain that results if a force of magnitude 9.6 X 105 N is applied to each of the four sides, parallel to the side. 1 _____________ (b) Find the displacement x in centimeters. 2_____________ cm 3) You are preparing some apparatus for a visit to a newly discovered planet Caasi having oceans of glycerine and a surface acceleration due to gravity of 3.95 m/s2. If your apparatus floats in the oceans on earth with 50.0% of its volume submerged, what percentage will be submerged in the glycerine oceans of Caasi? ________________ %

Explanation / Answer

Shear modulus = 7.5 * 10^10 Pa

F = .96 * 10^6 N

A = cross-sectional area of plate = (10.1 * 10.1) cm^2 = 102.01cm^2
= 0.010 m^2

I = Initial length = thickness of plate = 0.545 cm = 0.00545m

Displacement of both the top face and the bottom face = x

Shear modulus = (F/A) / (x / I)

7.5 * 10^10 = (.96 * 10^6 / 0.01) / (x / 0.00545)

7.5 * 10^10 = 96,000,000 / (x / 0.00545)

7.5 * 10^10 =523200/x

7.5 * 10^10 x = 523200

x = 1.12 * 10^ -5 m = 6.976 * 10^-6 m

Therefore, the top and bottom faces are displaced by 6.976 * 10^-6 m

The total displacement of the plate = the displacements of both top and bottom faces of the plates
= (6.976 * 10^-6 m +6.976 * 10^-6 m ) cm
= 1.39510^-5 m

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.