Ch3 part c By Mashael Saud

We will review briefly the theory of deformation and then examine the damaging effects of forces on bones and tissue Longitudinal Stretch and Compression. Let us consider the effect of a stretching force F applied to a bar (Fig. 5.1). The applied force is transmitted to every part of the body, and it tends to pull the material apart. This force, however, is resisted by the cohesive force that holds the material together.

The material breaks when the applied force exceeds the cohesive force. If the force in Fig. 5.1 is reversed, the bar is compressed, and its length is reduced. Similar considerations show that initially the compression is elastic, but a sufficiently large force will produce permanent deformation and then breakage.

Stress S is the internal force per unit area acting on the material; it is defined as: Here F is the applied force and A is the area on which the force is applied. The force applied to the bar in Fig. 5.1 causes the bar to elongate by an amountΔL

>The combined energy in the two legs is twice this value, or 385 J. This is the amount of energy in the impact of a 70-kg person jumping from a height of 56 cm (1.8 ft), given by the product mgh. (Here m is the mass of the person, g is the gravitational acceleration, and h is the height.) If all this energy is absorbed by the leg bones, they may fracture.

It is certainly possible to jump safely from a height considerably greater than 56 cm if, on landing, the joints of the body bend and the energy of the fall is redistributed to reduce the chance of fracture. The calculation does however point out the possibility of injury in a fall from even a small height. Similar considerations can be used to calculate the possibility of bone fracture in running.

5.4. Impulsive Forces: In a sudden collision, a large force is exerted for a short period of time on the colliding object. Impulsive force: Impulsive force: is The force starts at zero, increases to some maximum value, and then decreases to zero again such a short- duration. The duration of the collision: The time interval (t 2 -t 1 =Δt) during which the force acts on the body.

The general characteristic of such a collision force as a function of time is shown in Fig. 5.4.

* Because the collision takes place in a short period of time, it is usually difficult to determine the exact magnitude of the force during the collision. However, it is relatively easy to calculate the average value of the impulsive force F av. It can be obtained simply from the relationship between force and momentum; that is,

Note that: For a given momentum change, the magnitude of the impulsive force is inversely proportional to the collision time; that is, the collision force is larger in a fast collision than in a slower collision.

5.5 Fracture Due to a fall: Impulsive Force Considerations: In the preceding section, we calculated the injurious effects of collisions from energy considerations. Similar calculations can be performed using the concept of impulsive force. The magnitude of the force that causes the damage is computed from Eq

*Thus, falling into soft sand is less damaging than falling on a hard concrete surface. When a person falls from a height h, his/her velocity on impact with the ground, neglecting air friction is By multiplying equation with m:

Now comes to the difficult part of the problem : 1) Estimate of the collision duration. 2)If the impact surface is hard, such as concrete, and if the person falls with his/her joints rigidly locked, the collision time is estimated to be about 10 − 2 sec. 3)The collision time is considerably longer if the person bends his/her knees or falls on a soft surface.

Problem Problem :

Example: If the person of 70 kg falls flat on his/her heels, the area of impact may be about 2 cm 2, what is the force that will cause fracture? Then calculate the height at which that fracture will be happened? Solution From Table 5.1, the force per unit area that may cause a bone fracture is 10 9 dyn/cm 2.

5.6. Airbags: Inflating Collision Protection Devices:5.6. Airbags: Inflating Collision Protection Devices: The impact force may also be calculated from the distance the center of mass of the body travels during the collision under the action of the impulsive force. This is illustrated by examining the inflatable safety device used in automobiles (see Fig. 5.5).

An inflatable bag is located in the dashboard of the car. In a collision, the bag expands suddenly and cushions the impact of the passenger. The forward motion of the passenger must be stopped in about 30 cm of motion if contact with the hard surface s of the car is to be avoided. The average deceleration (see Eq. 3.6) is given by

5.7. Whiplash Injury: *Neck bones are rather delicate and can be fractured by even a moderate force. *Fortunately the neck muscles are relatively strong and are capable of absorbing a considerable amount of energy. If, however, the impact is sudden, as in a rear- end collision, the body is accelerated in the forward direction by the back of the seat, and the unsupported neck is then suddenly yanked back at full speed.

*Here the muscles do not respond fast enough and all the energy is absorbed by the neck bones, causing the well-known whiplash injury (see Fig. 5.6).

5.8. Falling from Great Height: There have been reports of people who jumped out of airplanes with parachutes that failed to open and yet survived because they landed on soft snow. It was found in these cases that the body made about a 1-m-deep depression in the surface of the snow on impact. The credibility of these reports can be verified by calculating the impact force that acts on the body during the landing.

The decelerating impact force acts over a distance of about 1 m, the average value of this force remains below the magnitude for serious injury even at the terminal falling velocity of 62.5 m/sec (140 mph).

5.9. Osteoarthritis and Exercise: Definition: Osteoarthritis is a joint disease characterized by a degenerative wearing out of the components of the joint among them the synovial membrane and cartilage tissue. Osteoarthritis is the commonly suspected damage resulting from such repetitive impact. As a result of such wear and tear the joint loses flexibility and strength accompanied by pain and stiffness.

Eventually the underlying bone may also start eroding. It is not surprising that an injured joint is more likely to be subsequently subject to wear and tear. As shown in Chapter 2, Table 2.1, the coefficient of kinetic friction (μ k ) of an intact joint is about The coefficient of friction for unduplicated bones is a hundred times higher.

Osteoarthritis is a major cause of disability at an older age. Knees are the most commonly affected joint. After the age of 65, about 60% of men and 75% of women are to some extent affected by this condition. The emerging conclusion is that joint injury is most strongly correlated with subsequent development of osteoarthritis.