MASS AND WEIGHT.pptx in introduction to medical mechanics

Introduction to medical mechanics

1. MASS AND WEIGHT

2. D efinition of terms Mass Mass is a fundamental property of matter that measures the amount of substance in an object. It is a scalar quantity and is typically measured in kilograms (kg) in the International System of Units (SI). Mass is an intrinsic property of an object and does not change with location or gravitational environment. Weight Weight is the gravitational force exerted on an object due to the gravitational attraction of another massive body, such as Earth. It is a vector quantity and is measured in newtons (N). Weight depends on both the mass of the object and the gravitational acceleration at the location where the object is situated.

3. Definition of terms Relationship The weight of an object (W) can be calculated using the formula: W=m⋅g where m is the mass of the object and g is the gravitational acceleration at the location of the object. On Earth's surface, g is approximately 9.81 m/s2.

4. Definition of terms

5. Law of gravity The Law of Gravity, formulated by Sir Isaac Newton in the 17th century, is a fundamental principle in physics that describes the gravitational attraction between objects with mass. Here's an explanation of the key aspects of the Law of Gravity: Statement of the Law Gravitational Force : Every mass in the universe attracts every other mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. Mathematical Formulation : Mathematically, the gravitational force F between two objects with masses m1​ and m2​, separated by a distance r, is given by: F = G{m1 m2}/{r^2}​​ where: F is the gravitational force between the masses, G is the gravitational constant (G≈6.67430×10−11 m^3kg^−1s^−2) m1​ and m2 are the masses of the two objects, r is the distance between the centers of the masses.

6. Key Principles and Implications Universal Gravitation : The law states that every mass exerts a gravitational pull on every other mass in the universe. This means gravity is a universal force that acts between all objects with mass, no matter how large or small. Inverse-Square Law : The gravitational force decreases with the square of the distance between the masses. This means if you double the distance between two objects, the gravitational force between them decreases by a factor of four. Proportional to Mass : The gravitational force is directly proportional to the product of the masses of the objects involved. This means larger masses exert a stronger gravitational force than smaller masses.

7. Law of gravity

8. CENTRE OF GRAVITY Every molecule in an object has a weight. The sum of these downward forces will give a single resultant force for the weight of any object. When gravity pulls an object towards the Earth, it always appears to pull at the same point on an object. So, an object behaves as if its whole weight was a single force which acts through some point called the center of gravity. Therefore, the center of gravity is defined as: A point from which the all of weight of a body or system may be considered or appears to act. This is not to be confused with the center of mass, since this is the mean position of mass of an object. Although for many objects, these two points are in exactly the same place; they are only the same when the gravitational field is uniform across an object.

9. CENTRE OF GRAVITY

10. CENTRE OF GRAVITY The center of gravity is the point where the sum of all gravitational forces acting on the body, due to the mass distribution of the body, is equal to zero . In a uniform gravitational field (like near the Earth's surface), the center of gravity is typically located at the geometric center of the object, assuming the object has uniform density . For irregularly shaped objects or objects with non-uniform density, the center of gravity may not coincide with the geometric center. It depends on the distribution of mass within the object . Importance : The center of gravity is crucial in various fields such as physics, engineering, and biomechanics. It is used to analyze stability, balance, and motion of objects. For example, in designing vehicles or structures, locating the center of gravity is important to ensure stability . The center of gravity can be calculated through mathematical formulas for simple shapes or by balancing methods for more complex shapes. It can also be found experimentally by suspending the object and observing where it balances.

11. Centre of Gravity in the Human Body

12. Centre of Gravity in the Human Body In the anatomical position, the COG lies approximately anterior to the second sacral vertebra, at the center of the pelvis. However, since human beings do not remain fixed in the anatomical position, the precise location of the COG is always shifting with each movement of the body and limbs. The proportion of body weight of the limbs, trunk, and head will also affect the location of the COG every time we move body positions. It is seen that in males, the center of gravity is in a slightly higher position due to larger shoulder mass.

13. Stability Stability refers to the ability of a body to restore to its original static equilibrium, after it has been slightly displaced. The stability of an object is determined by two factors: 1. The position of its center of gravity 2.The surface area of its base Racing cars have really low centers of gravity so that they can corner rapidly without turning over. Increasing the area of the base will also increase the stability of an object, the bigger the area the more stable the object. Rugby players will stand with their feet well apart if they are standing if they expect to be tackled. Stability analysis involves assessing how a system responds to disturbances , and whether it returns to its original state (stable), moves to a new state (unstable), or remains in the perturbed state (neutral).

14. Stability

15. Stable Bodies Definition: A stable body is one that, when displaced from its equilibrium position, experiences a restoring force or torque that brings it back toward equilibrium . Characteristics: Lower center of gravity: Objects with a lower center of gravity are typically more stable because they are less likely to topple over . Wide base of support: A wider base provides stability by distributing the weight more evenly and reducing the likelihood of tipping . Example : A wide, flat-bottomed bowl is stable because its center of gravity is low and its base provides support.

16. Unstable Bodies Definition : An unstable body is one that, when displaced slightly from its equilibrium position, experiences a force or torque that further displaces it away from equilibrium . Characteristics: Higher center of gravity: Objects with a higher center of gravity are prone to tipping over when disturbed . Narrow base of support: A narrow base makes an object more likely to tip over because it concentrates the weight onto a smaller area . Example : A tall, narrow vase is unstable because its center of gravity is high and its base is narrow.

17. Neutral stability Neutral stability refers to a condition where a system returns to its equilibrium position after being perturbed, but without oscillating around it. In other words, it indicates that the system neither amplifies nor dampens disturbances, resulting in a return to equilibrium without any additional motion beyond the initial displacement . Characteristics: No Oscillations : After a disturbance, the system moves directly back to its equilibrium position without oscillating around it . Balance of Forces : The restoring forces or influences exactly balance out the perturbing forces, resulting in no net change in the system's state once equilibrium is regained . Marginal Stability : The system is on the borderline between stable and unstable behavior. While it returns to equilibrium, any slight deviation from equilibrium could lead to instability.

18. Circular motion Circular motion refers to the movement of an object along the circumference of a circle or a circular path. This type of motion is characterized by a constant distance from a fixed point (the center of the circle) and a constant speed, although the direction of motion continuously changes.

19. Circular motion

20. Circular motion

21. Circular motion

22. Circular motion

23. Circular motion

24. Dynamics of Circular Motion Inertia and Circular Motion: An object in circular motion tends to continue moving tangentially unless acted upon by a centripetal force, due to inertia . Uniform Circular Motion: Occurs when an object moves at a constant speed along a circular path. The magnitude of the velocity remains constant, but the direction changes continuously . Non-uniform Circular Motion: Occurs when the speed of the object changes while moving along the circular path. The centripetal force required varies with the speed and radius of the circular path.

25. Examples

26. Examples