Chapter 7 - Work and Energy Definition of Work [units] Work done by a constant force (e.g friction,weight) Work done by a varying force (e.g. a spring) Work in 3 dimensions – General Definition Work and Kinetic Energy Definition of Kinetic Energy Work-Energy Principle

Definitions Work - The means of transferring energy by the application of a force. Work is the product of the magnitude of displacement times the component of that force in the direction of the displacement. Work is a scalar Energy - The state of one or more objects. A scalar quantity, it defines the ability to do work.

Units Joule (J) N-m kg-m2/s2 Erg Dyne-cm g-cm2/s2 Energy [M-L2/T2] Ft-lb slug-ft2/s2

Problem 1 A 1500 kg car accelerates uniformly from rest to a speed of 10 m/s in 3 s. Find the work done on the car in this time

How much work is done by this guy? Walking at a constant speed

Problem 3 m = 50 kg displacement = 40 m force applied = 100 N 37o angle wrt floor mk = 0.1 Find net work done moving the crate

Vector Multiplication – Scalar Product

A more elegant definition for work

Problem 4 How much work is done pulling the wagon 100 m in the direction shown by the boy applying the force:

Work done by a varying force

Work in three dimensions

Problem 5 Fx (N) 3 2 1 10 15 x (m) 5 How much work is done by this force?

Hooke’s Law and the work to compress/extend a spring

Kinetic Energy and the Work-Energy Principle

And you can show this with calculus too!

Problem 6 A 3 kg mass has an initial velocity, v = (5i - 3j) m/s. What is the kinetic energy at this time? The velocity changes to (8i + 4j) m/s. What is the change in kinetic energy? How much work was done?

Problem 7 A 2 kg block is attached to a light spring of force constant 500 N/m. The block is pulled 5 cm to the right and of equilibrium. How much work is required to move the block? If released from rest, find the speed of the block as it passes back through the equilibrium position if the horizontal surface is frictionless. the coefficient of friction is 0.35.