A Pop-A-Shot ball with an inside diameter of 6.39 in. and wall thickness of 0.044 in. is constructed from a polymer that has a yield strength of 3.34 ksi. If the ball is inflated to a pressure of 5.4 psi, determine the factor of safety with respect to the yield strength.

A wooden ruler with length L = 12 in. carries loads Px = 15 lb and Py = 6 lb. The ruler has a rectangular cross section with a thickness of 0.200 in. and a height of 1.205 in. Determine normal stress σx on the bottom surface of the ruler at B.

A vessel is loaded by internal pressure p = 110 kPa, horizontal force Px = 100 N, vertical force Py = 180 N, and torque T = 6 N·m acting in the directions shown. Determine the normal stress σx at H on the outside of the vessel.Vessel geometry    height, h = 54 mm    outside diameter = 54 mm    inside diameter = 48 mm    wall thickness = 3 mm    cross sectional area = 480.66 mm2    Ix = Iz = 156,820 mm4    J = 313,630 mm4    Q = 3,906 mm3

A basketball with an inside diameter of 8.78 in. and wall thickness of 0.051 in. is constructed from a polymer that has a yield strength of 3.32 ksi. If the ball is inflated to a pressure of 7.6 psi, determine the factor of safety with respect to the yield strength.

During a histology practicum, a Science  student observes a microscope slide showing a cross-section of a peripheral nerve. The instructor asks the student to identify the structure that surrounds a bundle of nerve fibers (fascicle). The student recalls that individual axons are protected by a delicate connective tissue, and multiple axons are grouped into fascicles that require a stronger, selective barrier. The instructor explains that this middle connective tissue layer is semipermeable and plays a crucial role in maintaining the blood-nerve barrier, protecting nerve fibers from toxins and inflammation. Damage to this layer can compromise nerve function and increase susceptibility to neuropathies. Question: Which structure is the student describing?  

An unpressurized vessel is loaded by horizontal force Px = 80 N, vertical force Py = 150 N, and torque T = 3 N·m acting in the directions shown. Determine the magnitude of shear stress τxy at H on the outside of the vessel.Vessel geometry    height, h = 54 mm    outside diameter = 54 mm    inside diameter = 48 mm    wall thickness = 3 mm    cross sectional area = 480.66 mm2    Ix = Iz = 156,820 mm4    J = 313,630 mm4    Q = 3,906 mm3

An unpressurized vessel is loaded by horizontal force Px = 70 N, vertical force Py = 160 N, and torque T = 5 N·m acting in the directions shown. Determine the magnitude of shear stress τxy at H on the outside of the vessel.Vessel geometry    height, h = 51 mm    outside diameter = 51 mm    inside diameter = 47 mm    wall thickness = 2 mm    cross sectional area = 307.88 mm2    Ix = Iz = 92,555 mm4    J = 185,110 mm4    Q = 2,402.3 mm3

An unpressurized vessel is loaded by horizontal force Px = 70 N, vertical force Py = 160 N, and torque T = 6 N·m acting in the directions shown. Determine the magnitude of shear stress τyz at K on the outside of the vessel.Vessel geometry    height, h = 55 mm    outside diameter = 55 mm    inside diameter = 49 mm    wall thickness = 3 mm    cross sectional area = 490.09 mm2    Ix = Iz = 166,200 mm4    J = 332,400 mm4    Q = 4,060.5 mm3

An unpressurized vessel is loaded by horizontal force Px = 90 N, vertical force Py = 190 N, and torque T = 3 N·m acting in the directions shown. Determine the magnitude of shear stress τyz at K on the outside of the vessel.Vessel geometry    height, h = 52 mm    outside diameter = 52 mm    inside diameter = 48 mm    wall thickness = 2 mm    cross sectional area = 314.16 mm2    Ix = Iz = 98,332 mm4    J = 196,660 mm4    Q = 2,501.3 mm3

For the following cylindrical vessel at surface A, the hoop stress is considered to be in the x direction.