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This lecture focuses on the fundamental concepts of work and energy in physics. It covers the definitions of energy as a capacity for action and work as energy transfer due to force. The discussion includes various forms of energy such as mechanical, kinetic, and potential energies, as well as practical applications through problem-solving. Key principles like Newton's laws and the work-energy theorem are explored, providing valuable insights into mechanical work and energy transformations. Through examples and questions, the concepts are made accessible for a deeper understanding of physical activity.
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PHYS16 – Lecture 15 Work and Energy October 13, 2010
Agenda • Administration • Homework for Week 5 • Exam • What have we learned so far? What do we still need to know? • Energy • Mechanical Work
Description of Motion – What else do we need? • We have: • Laws of Calculus – Displacement, Velocity and Acceleration • Newton’s Laws – F=ma • Concept of Momentum
Definition of Energy • Energy • A quantity whose expenditure or transformation allows for physical activity • An ability to drive motion • A capacity for action • Scalar Quantity • Unit = Joule (J) = kg·m2/s2 • Comes in many forms • Thermal • Chemical • Mechanical!!!!!
Mechanical Energy • Kinetic Energy (K)– energy stored in the movement of an object • Potential Energy (U) – energy stored in the configuration of a system • Gravitational Potential Energy • Spring Potential Energy
Energy can be transformed • Wyle E. Coyote • http://www.youtube.com/watch?v=Jnj8mc04r9E&feature=related
Practice Question • A 0.50 kg vase falls from 3.0 m. What is the kinetic energy of the vase just before it hits the ground? A) 0 J B) 15 J C) 1.5 J D) 2.3 J
Practice Question • A 0.50 kg vase falls from 3.0 m. What is the potential energy of the vase before it falls? A) 0 J B) 15 J C) 1.5 J D) 2.3 J
Definition of Work • Mechanical Work (W) – energy transferred to an object due to the action of a force (+) transfer to object (-) transfer from object
Aside on Dot Product • Dot Product is one way to multiply two vectors • Basically just multiply components and add • Dot Product is a scalar A B
Aside on Dot Product • Dot Product is one way to multiply two vectors • Basically just multiply components and add • Dot Product is a scalar A B
Aside on Dot Product • Dot Product is one way to multiply two vectors • Basically just multiply components and add • Dot Product is a scalar • Or multiply magnitudes and cosine angle between the vectors A θ=56° B
Work with a Constant Force • Force = Constant, then can take force outside integral
Work with a Variable Force • Force = Constant, then can take force outside integral Fx x
Practice Question • I pull a 4.0 kg sled a distance of 5.0 m. I pull the sled using a rope at a 30.0 degree angle with a force of 5.0 N. What is the work done by me? A) 0 J B) 20 J C) 25 J D) 22 J
Practice Question • A force is given by Fx = 3x2+2. What is the work done by the force for moving an object from x=0.0 m to x=4.0 m? A) 72 J B) 50 J C) 0 J D) 200 J
Work – Energy Theorem • Work = the transfer of Energy • Energy = the ability to do work Work done by External Force Change in Energy to the system
Work and grav. potential energy • If I lift an object, how much work did I do on the object? • Use work-energy theorem to derive gravitational potential energy Force and displacement are both downward
Work and spring potential energy • If mass on a spring moves, how much work is done by spring? • Use work-energy theorem to derive spring potential energy Work done by system is negative Force and displacement are in opposite directions
Work and Kinetic energy • If an object speeds up, how much work is done on object? • Use work-energy theorem to derive kinetic energy Assume K=mv2/2 and prove left side = right side Just multiply and divide by dt since dt/dt=1 Now take derivative and remember to use chain rule
