Work and Energy

WHY…? Curved paths (motion) Complicated motion is tough to handle with just Newton’s Laws

Definitions and Units Contrary to what you might think, solving word problems is no longer considered “work” in this class, solving word problems will hereafter be referred to as “play” or “fun.” Work, physical work, is an energy exchange, we will add it to a “system”…

Work and Energy Yes, we have equations for it… Work = Force times distance –Or more appropriately the “dot” product of a force vector and the displacement vector of the object it acts on. What are the units?

Work and Energy Joules! –You were probably thinking Newton’s times meters, huh? You are correct, we just have a special name for the units of work and energy. Since work is an energy exchange, they both have the same units.

Work and Energy In the real world you can exchange dollars for doughnuts, but in the physical world it’s more like dollars for euros, yen, pounds(!) etc. –Work, kinetic, potential, heat, sound, light… Let’s look at the dot product a little more…

Work F d  Were interested in the component of force that actually moves the object in the direction it goes. The other component, perpendicular to the displacement, is “wasted.”

Work F d  Fcos  Fsin 

Work F d  Fcos 

Work F d  Fcos  Yeah, memorize this one.

Let’s Apply this puppy. T leash displacement angle

Puppy Pull Ok, 1 – 2- 3 go Tension in leash = 30 N Angle with ground = 30 degrees Displacement along the ground = 30 meters (this puppy is stubborn)

So what’s the work? W= 30 N x 30 m x cos(30) = 779 Joules We did 780 joules of work on the puppy.

Energy So what is energy? The physical state of an object that gives it the capacity to do work. Ok, brass tacks time…

Energy You can probably mention two types, maybe more… Kinetic – translational, rotational Potential – gravitational, electrical, internal (temp) Let’s just do Translational Kinetic and Gravitational Potential for now and save the others for later in this course.

Kinetic Energy

Work and KE Work Kinetic energy theorem

Where’s this come from? Think back to kinematics

Apply! My truck is broken down, so you help me push it. We give it a push of 300 Newtons, parallel to the road, and quit after 20 meters. How much work did we do, on the system (my truck)?

How fast is it going? Let’s ignore friction right now. The mass of the Miata is 750kg. Start from rest

Video Break! Big Truck

Energy

Potential Energy Gravitational energy. Let’s think this one through. If I lift 100 N one meter what work did I do? Yeah, 100 Joules How fast is it moving now? Yeah, nothin’ What’s up? (besides the 100 N weight)

PE The energy went somewhere, where? We say the weight gained Potential energy equal to the change in vertical position, altitude, or height, times its weight (the force it took to get it there). Yep.

Work raising a weight How much work is done raising a bucket from a well? –Bucket 10 kg –Well 20 meters deep What work did the bucket raiser person do? What work did gravity do?

Conservative vs. Non- conservative forces So I lifted the 100N one meter, what happens when I drop it? It speeds up until it hits the ground. The work transforms into KE of the weight, so gravity is a conservative force. Conservative – we can get it back

Conservative vs. Non- conservative forces Think back to the puppy pull. Let’s make it a box now, even though I did work on the box, friction also did work on the box. Due to Newton’s IIId law, friction did negative work on the box! What happens when we let go of the leash? Will the box spontaneously spring back to where it was? NO! Friction is non-conservative. Non-conservative

Con vs non Conservative forces store the energy when you work against them. You can get it back later. –Gravity, electrical force, springs. Non-conservative Forces dissipate the energy of work done against them. You can’t get it back. It turns into; sound, heat etc. –Friction, airplane drag…

Enough! Let’s “play” Conservation of mechanical energy Yeah, this one too.

Block on a ramp No friction 10 kg block is 10 meters up on an incline. It starts from rest and slides to the bottom How fast is it going at the bottom? 10 meters 10 kg

Block on a ramp Try this one on-site,  k =.22, angle=30 deg 10 kg block is 10 meters up on an incline. It starts from rest and slides to the bottom How fast is it going at the bottom? 10 meters 10 kg f

Fin. Questions??

Review