In multiple dimensions, the conservation of momentum applies in each direction independently. Hence, to solve collisions in multiple dimensions, we should write down the momentum conservation in each direction separately. To help understand collisions in multiple dimensions, consider an example.
A small car of mass 1,200 kg traveling east at 60 km/h collides at an intersection with a truck of mass 3,000 kg traveling due north at 40 km/h. The two vehicles are locked together. What is the...

The center-of-mass framework helps to easily describe the work done on rigid bodies. Since the internal forces in a rigid body do no work, they can be ignored, and the external forces can be considered in the work-energy theorem.
The work done by gravity to move a rigid body, or the work done by an opposing force to move a rigid body against gravity, can be calculated using the center-of-mass framework. It is the line integral of the force of gravity over the path, considered positive if...

Early Ischemia and Ionic ImbalanceWithin minutes of spinal cord injury, a secondary cascade begins, progressing over hours to weeks. Vascular damage reduces blood flow, causing ischemia and mitochondrial dysfunction. ATP depletion leads to ion pump failure, membrane depolarization, sodium influx, potassium efflux, and water accumulation, resulting in cellular swelling. Increased intracellular calcium further disrupts mitochondria and accelerates cellular injury.Excitotoxicity and Neuronal...

A decreased body temperature can occur in patients with hypothermia and frostbite. Heat loss with extended cold exposure overpowers the body's ability to create heat, resulting in hypothermia. Core temperature readings help classify hypothermia. Mild hypothermia is temperatures between 32 °C (89.6 °F) and 35°C (95 °F) and is caused by impaired thermoregulation. Moderate hypothermia is temperatures between 28 C (82.4 °F) and 32 °C (89.6 °F) caused by sustained extreme cold exposure, and severe...

Complications during healing arise when tissue repair is altered by local or systemic factors. These changes involve abnormal collagen deposition, altered biomechanics, and reduced vascular supply, impairing restoration of normal structure and function.Loss of FunctionScar tissue differs significantly from the original tissue it replaces. In the skin, fibrosis lacks adnexal structures such as hair follicles, sebaceous glands, and sweat glands. Their absence reduces tactile sensitivity, impairs...

Spinal cord injury progresses through two interconnected phases: primary injury and secondary injury.Primary InjuryPrimary injury happens at the moment of trauma and involves immediate mechanical damage to the spinal cord.Compression happens when broken vertebrae, herniated discs, or accumulating blood (such as a hematoma) press directly against the spinal cord, distorting its normal shape and function. In cases of contusion, the cord is bruised by a blunt force (like penetrating injuries or...