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.

A 28-year-old male patient arrives at the clinic after a motorbike accident in which he sustained a deep laceration to his lateral forearm. On examination, he has lost the ability to feel fine touch and temperature sensations in part of his thumb, index, and lateral portion of the palm. He also complains of weakened grip strength. The physician suspects injury to a specific nerve and orders electromyography and nerve conduction studies. Further examination reveals that the nerve affected also provides motor innervation to some forearm flexors and muscles of the thenar eminence. Based on the location of the injury and the symptoms presented, the physician provides a diagnosis and begins treatment focused on nerve regeneration and occupational therapy. Question: Which of the following nerves is MOST likely injured in this patient?  

A 52-year-old patient presents to the neurology clinic with persistent headaches, nausea, and occasional visual disturbances. MRI imaging reveals a benign mass growing near the midline of the brain, just superior to the brainstem and nestled between the two halves of the thalamus. The physician explains that this mass is beginning to obstruct the normal flow of cerebrospinal fluid, leading to increased intracranial pressure. As a student observing the case, you are asked to predict which anatomical space is most likely being compressed and contributing to the patient’s symptoms.  

After suffering a minor stroke, a 67-year-old man begins to experience difficulty walking in a straight line and often overshoots when trying to reach for objects. Interestingly, his speech also becomes slurred, but his cognitive abilities and emotional expression remain largely unaffected. Imaging reveals damage localized primarily to a region in the posterior part of his brain. A medical student reviewing the case suggests that the symptoms likely result from impaired motor coordination rather than muscular weakness or cognitive dysfunction. Question: Based on the information provided, which of the following best explains the role of the affected brain region and the symptoms observed?