Physics Chapter 2: Statics and Torque

Principles of Physics

• Presented by Dr. Mohaned Mohammed, School of Biotechnology, Badr University, Assiut.
• Introduces the concepts of Statics and Torque.

Chapter Two: Statics and Torque

• Focuses on the principles of Statics and Torque in physics.

Torque

• 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 the direction of r.
• Torque is zero if the force passes through the pivot point.
• The force (F) 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.

Static Equilibrium

• A body is considered in mechanical equilibrium if two conditions are met:
  • The resultant external force equals zero (ΣF = 0).
  • The resultant external torque equals zero about any axis (Στ = 0).
• If these conditions aren't met, the body will rotate.
• A body is static if its linear and angular velocities are zero.

Conditions for Static Equilibrium

• The center of mass is the average position of an object's parts, weighted by their masses.
• For a body to be in stable equilibrium under gravity, the center of mass must be directly above the base of support.
• In a stable body, the reaction force (F₁) upwards cancels the body weight (Fw) downwards, acting along the same line with opposite directions.
• Unstable bodies rotate around a pivot point.

Equilibrium in the Human Body

• The center of gravity for an upright person with their arms at their sides is approximately 56% of their height from the soles of their feet.
• The center of mass changes position if the shape of the body changes, even if the mass remains constant.
• The body compensates for uneven loads by adjusting limb positions to keep the center of gravity balanced over the feet.
• Amputees may need prosthetic limbs to help maintain stability.

The Action of an External Force on Human Body Stability

• Example illustrating calculating the force required to cause a person to topple while standing at attention.
• Calculates this using torques applied to the body.

Example 2

• Calculates the force required to topple a person in a standing position, accounting for their mass, height, and foot width.

Example 3

• Calculates the force each hand exerts to hold a pole in a balanced position, given the weight of the pole and the distance from the hands to the center of gravity of the pole.

Muscles

• Skeletal muscles consist of numerous parallel fibers.
• Muscle force depends on the number of contracting fibers.
• Tendons connect muscles to bones.
• Most muscles end in a single tendon, except biceps and triceps.

Levers

• A lever is a rigid bar that rotates around a fixed point called the fulcrum.
• Levers have three components: fulcrum, input force (effort), and output force (load).
• Levers are useful for moving or lifting loads.
• There are three classes of levers:
  • Class 1: Fulcrum is between the input and output forces (e.g., claw hammer).
  • Class 2: Output force is between the input force and the fulcrum (e.g., wheelbarrow).
  • Class 3: Input force is between the output force and the fulcrum (e.g., human arm).

Forces and Torques in Muscles and Joints

• Skeletal muscles generate forces significantly larger than forces applied to the limbs.
• This is because tendons attach close to joints, providing mechanical advantage in transferring force.

Example

• Calculates the force required from the biceps muscle to hold a forearm and load.
• Compares the calculated force to the combined weight of the forearm and load.

Discussion

• The biceps exerts 7.38 times the supported weight.
• Changing the angle between the forearm and upper arm affects the biceps force.
• The force is variable depending on biceps muscle length.

Example

• Calculates the force needed in the back muscles to support an upper body and box.
• Calculates the force exerted by the vertebrae at the pivot point.

Problem Solving Strategy

• A free body diagram is used to visualize all the forces acting on the body.
• The net force must be zero (ΣF= 0).
• The net torque must be zero (Σt = 0).

Problem 9.32

• Calculates the force needed by the neck muscles to keep the head held erect.
• Determining the force exerted by the head's pivot point.

Problem 12.41

• Determining the magnitudes (tension) in the deltoid muscle of the arm.
• Determining the magnitude of the shoulder's force acting on the upper arm.

Problem 12.42

• Finding values of T, R, and u (position) for a person standing on tiptoe with a given gravitational force acting on them.