Principles of Physics Chapter 2

Study Notes

The lecture is on principles of physics by Dr. Mohaned Mohammed from the School of Biotechnology, Badr University in Assiut.

The magnitude of torque (τ) equals the applied force (F) times the length of the arm (r) perpendicular to the force.
|τ| = |F × r| = rF sin θ
Where θ is the angle between the force and r.
Torque is zero if the force passes through the pivot point.
Force is measured in Newtons (N) and torque is measured in Newton-meters (N⋅m).
The direction of torque can be determined using the right-hand rule.

A body is in mechanical equilibrium if two conditions are met:
- The resultant external force is zero (ΣF = 0).
- The resultant external torque about any axis is zero (Στ = 0).
Otherwise, the body will rotate.
A body is said to be static if its linear and angular velocities are zero.

The center of mass is the average position of all parts of an object, weighted by their masses.
If the gravity is constant across an object, then the center of mass is considered the center of gravity.
A body is in stable equilibrium under the action of gravity if its center of mass is directly above its base of support.
In a stable body, the reaction force (F₁) upwards cancels the weight force (Fw) downwards as they act in a straight line in opposite directions.
When an object rotates (unstable), there are two key conditions to consider.

The center of gravity for a standing person with arms at their side is approx. 56% of their height from the soles of their feet.
The center of mass changes if the shape of the body changes, even if the mass remains the same.
When an uneven load is carried, the body adjusts by bending and extending different limbs to keep the center of gravity over the feet.
People who have lost an arm often experience spinal distortions due to continuous compensatory bending.
Artificial limbs can help restore balanced weight distribution in amputees.

Example 1 calculates the force needed to topple a person standing at attention, considering torques around a pivot point, and the person's mass and gravitational acceleration.
Example 2 calculates the force necessary to topple a person considering their height, foot width, mass, and the gravitational acceleration to calculate the force.
Example 3, calculates forces exerted by the hands to balance a bar on hands.

Examples will calculate forces for various scenarios related to equilibrium and torques.

Skeletal muscles consist of thousands of parallel fibers.
Muscle force depends on the number of contracting fibers.
Tendons attach muscles to bones
Most muscles end in one tendon, but some (like biceps and triceps) end in multiple tendons, each anchored to different bones.

A lever is a rigid bar that rotates about a fixed point (fulcrum).
Three parts of a lever: fulcrum, input force (effort), and output force (load).
If a lever is in equilibrium, the torque produced by the applied force equals the torque produced by the load.
Mechanical advantage is the ratio of the weight to the applied force, and depends on the location of the fulcrum relative to the load and effort.
Three classes of levers: class 1 (fulcrum between effort & load), class 2 (load between effort & fulcrum), class 3 (effort between load & fulcrum)

Muscles exert significantly greater forces within the body compared to the force they apply on the outside world.
This is due to the arrangement of tendons near the joints, creating mechanical advantages for applying forces.

This example involves calculating muscular forces needed to support a load while considering the arm's posture and weight distribution. Includes calculations related to forces and torques involved.

Includes a discussion of the examples and how the discussed concepts are applied to the real-world scenario of human movement and equilibrium. Includes notes on human muscular force.

A method for solving physics problems related to equilibrium by establishing equilibrium equations related to forces and or torques.

A problem involving calculating the force exerted by neck muscles to keep the head erect.
Another related to a person holding a box on their back and finding the force exerted by the spine and neck muscles.