Phys 250 Ch6 p1 Work and Energy Energy ~ an ability to accomplish change Work: a measure of the change produced by a force Work = “a force through the displacement” portion of the force along displacement × displacement W = F x x =F cos  x x F cos  FF x FF W = F cos  x W = F x x F cos 90 = F  FF W = 0 Units: 1Newton. 1 meter = 1 joule = 1J 1 ft-lb =1.356 J

Phys 250 Ch6 p2 Example: A child pulls a toy 2.00 m across the floor by a string, applying a force of constant magnitude N. During the first meter, the string is parallel to the floor. During the second meter the string makes a 30º angle with the horizontal direction. What is the total work done by the child on the toy?

Phys 250 Ch6 p3 F x Work and Energy with varying forces Take average force, small sub-intervals  x i F1F1 x2x2 x3x3 x4x4 xNxN … F2F2 F3F3 Constant Force – near trivial example W = F. (x 2  x 1 ) F x x2x2 x1x1

Phys 250 Ch6 p4 Varying Force Example: Force of a Spring (GET OUT SOME SPRINGS!) |F| = kx (Hooke’s “Law”) k is the spring constant or force constant of that spring From un-stretched to stretched/compressed by x: area under curve = area of right triangle W = ½ “height”. “width” = ½ kx x = ½ kx 2 Example: How much work is required to extend an exercise spring by 45 cm if the spring constant k is 310 n/m? What force is required to stretch it this far? F x

Phys 250 Ch6 p5 Energy: the capacity to do work Kinetic Energy: energy associated with motion Potential Energy: energy associated with position Rest Energy, Thermal Energy, chemical energy... Kinetic Energy for an object under a constant force from motion in a straight line the work-energy theorem

Phys 250 Ch6 p6 Example: A baseball-player throws a kg baseball at a speed of 36.0 m/s. What is its kinetic energy? Example: How much work is done to move a 1840 kg Jaguar XJ6 automobile from rest to a speed of 27.0 m/s on a level road? If this takes place of a distance of 117 m, what is the average force?

Phys 250 Ch6 p7 Potential Energy energy associated with position example: gravitational potential energy Work done to raise an object a height h: W = mgh = Work done by gravity on object if the object descends a height h. identify source of work as Potential Energy PE = mgh other types of potential energy electrical, magnetic, gravitational, compression of spring... Example: How much potential energy does a 7.5 kg ceiling fan have with respect to the floor when it is 3.00 m above it?

Phys 250 Ch6 p8 Example: A 500 kg mass of a pile driver is dropped from a height of 3m onto a piling in the ground. The impact drives the piling 1.00 cm deeper into the ground. If the original potential energy of the mass is converted into work in driving the piling into the ground, what is the frictional force acting on the piling?

Phys 250 Ch6 p9 Elastic Potential Energy energy stored in stretching or compressing a spring Work done compressing: W = ½ k x 2 = work that can be extracted by releasing the spring PE = ½ k x 2 Example: A 1550 kg Pontiac Gran Prix is supported by 4 coil springs, each with a spring constant of 7.00E4 N/m. How much are the springs compressed by the weight of the car? How much energy is stored in this compression?