Presented by: Group 4
Overview of key concepts: Work, Energy, Conservation of Energy, and Power in Mechanical Systems
Definition: Work is the application of force across a distance.
Energy expended when an object is moved against a resisting force.
Fundamental concept crucial to physics and engineering, with broader implications.
Force and Displacement:
Work requires a force causing an object to move; without movement, no work is done even if force is applied.
Direction of Force Matters:
The force must align with the direction of displacement for work to be done.
Only the component of the force in the direction of motion contributes to work when at an angle.
Work (W) is measured in joules (J)
Force (F) is measured in newtons (N)
Distance (d) is measured in meters (m)
Formula: W = F × d × cos(θ)
θ: Angle between the force and motion direction in degrees.
Definition: Energy is the capacity of objects or substances to perform work or create changes in the environment.
Two Types of Energy:
Kinetic Energy
Potential Energy
Definition: Energy possessed by a moving object.
Factors: Speed (velocity), mass impact energy - faster or heavier = more kinetic energy.
Formula:
KE = ( \frac{1}{2} mv^2 )
KE = Kinetic energy (in joules, J)
m = Mass (in kilograms, kg)
v = Velocity (in meters per second, m/s)
Definition: Energy an object holds due to its position, state, or configuration.
Related to object’s capacity to do work based on location or structure.
Example: Falling object or released compressed spring releases potential energy.
Gravitational Potential Energy Formula:
PE_gravitational = mgh
PE = Gravitational potential energy (in joules, J)
m = Mass (in kg)
g = Acceleration due to gravity (9.81 m/s² on Earth)
h = Height above reference point (in meters, m)
Principle: Energy cannot be created or destroyed; it can only be transformed from one type to another.
Examples include:
Falling objects
Roller coasters
Bouncing balls
Definition: Power measures the rate of doing work; a result of force and motion.
Power can be expressed as the product of force and velocity or torque and angular velocity.
General Formula:
P = W / t
P = Power (in Watts, W)
W = Work done (in Joules, J)
t = Time taken (in seconds, s)
Force and Velocity:
P = F × v
F = Force applied (in Newtons, N)
v = Velocity (in meters per second, m/s)
Torque and Angular Velocity (Rotational Systems):
P = T × w
T = Torque (in Newton-meters, Nm)
w = Angular velocity (in radians per second, rad/s)