Work, Power, Energy
Work, Power, Energy
Introduction to Biomechanics
Overview of key concepts: Work, Power, Energy
Learning objectives include:
Definitions and relationships between Work, Energy, Power
Fundamental Concepts
Linear Motion and Momentum
Explanation of how a force applied over time (impulse) affects momentum in linear motion.
Shift to explaining motion changes using work-energy relationships instead of Newtonian mechanics.
Importance of force in changing momentum and linear velocity:
Acceleration occurs when a constant mass experiences an external force.
Linear Kinetics reference to Newton's laws of motion.
Work
Definition of Work
Work is defined as a measure of energy transfer that occurs when an external force moves an object over a distance.
Formula for calculating work:
\text{Work} (Nm; \text{Joule}) = \text{Force} (N) \times \text{Displacement} (m)
Examples of Work
Scenario where a force of 1000 N is applied to a barbell:
If the displacement is zero (e.g., moving the barbell 70 cm down and back up), work done:
\text{Work} = 1000 N \times 0 = 0
Types of Work
Positive Work: Adds energy to a system.
Occurs when displacement is in the same direction as the applied force.
Negative Work: Removes energy from a system.
Occurs when displacement is opposite to the direction of the applied force.
Energy
Types of Energy
Focus on Mechanical Energy, which consists of:
Kinetic Energy (KE)
Potential Energy (PE), specifically:
Gravitational Potential Energy (GPE)
Strain Energy (SE)
Kinetic Energy
Kinetic Energy is the capacity to do work.
Formula for calculating Kinetic Energy:
\text{KE} (\text{Joule: Nm: kgm}^2/s^2) = \frac{1}{2} \times \text{Mass} \times \text{Velocity}^2
Example:
For a baseball thrown with a mass of 0.145 kg and a velocity of 40 m/s:
\text{KE} = \frac{1}{2} \times 0.145 kg \times (40 m/s)^2 = 116 J
Potential Energy
Related to the object's position relative to the Earth; calculated based on weight and height.
Formula for Potential Energy:
\text{PE} (Nm: J) = \text{Weight} (N) \times \text{Height} (m)
Example calculation:
For a weight of 70 kg at a height of 90 m:
\text{PE} = 70 N \times 9.81 m/s^2 \times 90 m = 61,803 J
Strain Energy
Definition: Potential energy due to deformation of an object.
Formula for Strain Energy:
\text{Strain Energy} = \frac{1}{2} \times k \times (\Delta X)^2
Where $k$ is stiffness (N/m) and $\Delta X$ is the change in length.
Example calculation:
For a stiffness of 10,000 N/m and deformation of 0.005 m:
\text{Strain Energy} = \frac{1}{2} \times 10,000 \times (0.005)^2 = 0.125 J
Work-Energy Relationship
Work is the sum of changes in energy:
\text{Work} = \Delta KE + \Delta PE + \Delta SE
Example scenario with lifting a barbell:
Work done in lifting a 1000 N barbell through a displacement of 0.7 m:
\text{Work} = 1000 N \times 0.7 m = 700 J
Changes in potential energy (PE) also yield:
\Delta PE = 1000 N \times (0.75 m - 0.05 m) = 700 J
Power
Definition of Power
Power is defined as the rate at which work is done.
Formula for Power:
\text{Power} (J/s; \text{Watt}) = \frac{\text{WORK}}{\Delta\text{time}}
Power can also be expressed as:
\text{Power} (J/s; \text{Watt}) = \text{Force} \times \frac{\text{Displacement}}{\Delta\text{time}} = \text{Force} \times \text{Velocity}
Examples of Power Calculations
Compare lifts:
Bill lifts a 1000 N barbell 1.5 m in 1.0 s, and Bob lifts a 1400 N barbell 2.0 m in 2.0 s to determine who is more powerful.
Calculation based on a pitch where a pitcher exerts a force of 100 N on a baseball:
Exploring how fast the baseball will go after displacement.
Scenario of Jon performing a snatch:
Lifts a 100 kg barbell in 0.50 s, covering a vertical distance of 2.0 m, to calculate average power output during lift.
Example Case Study - Archery
An archer draws a compound bow:
Arrow's mass = 23 g = 0.023 kg, final velocity = 88 m/s.
Bowstring displacement = 57 cm = 0.57 m, peak draw weight = 312 N.
Calculate:
Kinetic energy after release, work done by the bowstring, and average force exerted by the bowstring.
Summary & Questions
Recap of key concepts about Work, Power, Energy, and their interrelationships.
Open floor for any questions related to the topics discussed.