Introduction to Biomechanics

Course Title: SES08105

Lecture Outline

The lecture on projectile motion encompasses various critical components, including:

1. Definition of projectile motion.

2. Factors affecting projectile motion.

3. Practical applied examples.

4. Revision questions for consolidating knowledge.

Definition of a Projectile

A projectile is defined as a body that is propelled, projected, or dropped into the air. Upon entering this state, the projectile experiences only two forces:

• Gravity: The force acting downward.

• Air Resistance: The opposing force that acts against the direction of motion, although it is often neglected in basic calculations.

Characteristics of Projectile Motion

In the absence of air resistance, projectile motion is characterised by:

• Constant Horizontal Velocity: This means the horizontal speed does not change due to the absence of horizontal forces acting on the projectile.

• Changing Vertical Velocity: The vertical velocity is influenced by gravity and changes as the projectile ascends or descends.

Vertical and Horizontal Components of a Projectile

The horizontal and vertical components of a projectile's motion are independent of each other. This means they can be analysed separately:

• Horizontal Component (Vh): Not affected by gravity, hence constant.

• Vertical Component (Vv): Affected by gravity, leading to acceleration downwards.

Equations of Motion for Projectiles

The understanding of both vertical and horizontal components permits the use of various equations of motion. The equations essential for calculating projectile motion include:

1. $s = ut + \frac{1}{2} at^2$ (displacement)

2. $v = u + at$ (final velocity)

3. $v^2 = u^2 + 2as$ (final velocity squared)

4. $s = ut$ (when acceleration is zero)
   Where:

• $s$ = displacement

• $v$ = final velocity

• $u$ = initial velocity

• $t$ = time

Example Problem Analysis

Problem Statement

A golf ball is struck with an initial horizontal and vertical velocity of $12 m/s$ and lands $120 m$ away.

Calculation of Time in Air

Using the relationship $v = \frac{s}{t}$:

• Given that $s = 120 m$ and $v = 12 m/s$:

• Rearranging the equation gives: $t = \frac{s}{v}$.

• Therefore, $t = \frac{120 m}{12 m/s} = 10 s$.

Calculation of Vertical Height Reached

To find the vertical height using the displacement formula with gravity taken into account:

• Given parameters:

  • $u = 12 m/s$

  • $t = 5 s$

  • $a = 9.81 m/s^2$ (acceleration due to gravity)

• The formula utilised is:
  $s = ut + \frac{1}{2} at^2$

• Substituting in values:

  • $s = 12 m/s (5 s) + \frac{1}{2} (9.81 m/s^2)(5 s)^2$

  • This yields:

  • $s = 60 m + 122.625 m = 182.625 m$

Factors Influencing the Range of Projectiles

Key factors that significantly influence projectile range include:

1. Velocity at Release: Initial speed of the projectile at launch.

2. Angle of Release: The angle at which the projectile is launched from the horizontal.

3. Height of Release: The initial height from which the projectile is released.

Angle of Release

• For maximum range, with the release height and landing height equal, the optimal angle is 45 degrees.

• When the release height is greater than the landing height, an angle of release less than 45 degrees is optimal.

• Conversely, when the release height is lower than the landing height, an angle of release greater than 45 degrees should be employed.

Shotput Throw Kinematics

Example Values of Experienced Shot-putters

For instance, an experienced shot-putter may exhibit parameters such as:

• Distance Thrown: 15.9 m

• Release Velocity: 11.9 m/s

• Release Angle: 34.1 degrees

• Release Height: 2.11 m (Linthorne, 2001)

Goals of Projection Beyond Range

While optimising range is vital, other key goals include:

• Accuracy: Essential in sports where precision is crucial.

• Speed: Importance in sports requiring rapid, dynamic movements.

• Transition: The ability to adapt movements based on varied regulations or game scenarios (e.g., golf shots, baseball pitches, rugby passes).

Re-distribution of Mass Around the Center of Mass (CoM)

When the human body acts as a projectile, it will follow a parabolic path. However,:

• Changes in body configuration can influence performance as the centre of mass cannot be altered once in flight.

• Internal forces may change the distribution of mass relative to the CoM to impact flight dynamics.

Evolution of High Jump Technique

The evolution of high jump techniques illustrates:

• For a given peak height of the CoM, lowering certain body parts can lead to others going higher. This principle is essential in refining techniques such as the Fosbury Flop, which emphasises optimal bar clearance.

Air Resistance and its Effects

Air resistance significantly affects the trajectory and range of projectiles. It is important to note:

• With air resistance, projectiles like a badminton shuttlecock experience altered trajectories that do not conform to parabolic patterns.

• Drag: A force acting in the direction of airflow that reduces speed.

• Lift: A component of force acting perpendicular to drag which helps maintain flight.

Factors Contributing to Air Resistance

Factors influencing air resistance include:

1. Fluid Density: The density of air or the fluid through which the projectile is moving.

2. Cross-sectional Area: The area of the body that is exposed to the flow of air.

3. Velocity: The speed of the object relative to the air.

4. Shape/Smoothness: The aerodynamic nature of the projectile greatly influences drag.

5. Orientation: The angle at which the body faces against airflow.

6. Spin (Magnus Effect): Spin can affect the trajectory of projectiles, enabling curves in the flight path.

Magnus Effect

The Magnus Effect refers to the phenomenon where a spinning object deviates in trajectory in the direction of the spin due to a lift force generated during its flight.

Summary of Lecture

In conclusion, projectile motion is defined as the motion of objects influenced primarily by gravity and affected by air resistance. The essential factors impacting projectile motion include:

• Release Velocity: Speed imparted when the projectile is launched.

• Release Angle: The angle at which the projectile is projected.

• Release Height: The height at which the projectile is launched.

• Re-distribution of mass around the centre of mass for performance improvement: Influences overall flight dynamics.

• Air resistance: Presented through drag acting along the airflow direction and lift acting perpendicularly to drag.

Future Tests and Projects

• An announcement mentions the upcoming summative test scheduled for Friday, October 18th at 12:00 PM (Noon). Students should initiate the test between 12:00 PM and 12:10 PM to ensure the full time allocation of 30 minutes for answering 15 questions.

• Students are also encouraged to start contemplating their scientific poster projects, with workshops aiming for project finalisations occurring in week 7.