Work and Energy

Pull the overhead projector How much work do you do?

Force (Pull) Motion

How much work is done? Aside: What if a student pushes the projector sideways, and at the same time, the teacher pushes the projector downward? Surely the teacher does _ _ work.

How much work is done? Aside: What if a student pushes the projector sideways, and at the same time, the teacher pushes the projector downward? Surely the teacher does no work. To sort things out, use the _ _ _ _ _ _ _ _ _ of the force that is in the direction of the motion.

How much work is done? Aside: What if a student pushes the projector sideways, and at the same time, the teacher pushes the projector downward? Surely the teacher does no work. To sort things out, we use the component of the force that is in the direction of the motion.

Force (Pull) Motion  Force (Pull) Component of Force In direction of Motion = Fcos(  )  is the angle between the __________ and the ____________

Force (Pull) Motion  Force (Pull) Component of Force In direction of Motion = Fcos(  )  is the angle between the Force and the Motion.

The greater distance the force acts, the more work is done.

W = D Fcos(  ) This is how we deal with a force that is not in the direction of the motion

An example with numbers. The train at Memphis Kiddie Park in known to break down a lot. To haul the train back to the repair shed, the worker pulls it 7 meters. The train must move along the tracks, but the worker cannot stand on the tracks, so he pulls at an angle. The worker pulls with a force of 80 N, at an angle of 20˚ with the tracks.

TRAIN  Pull Top View

How much work did the worker do? What is the component of force that is along the motion? What are the units of work?

Calculate the Work W = D Fcos(  ) W = (7 m) (80 N) cos(20˚) W = (7 m) (75 N) W = 526 Joules

Types of Energy (Classification is satisfying, but here it does not reveal fundamental properties.) Mechanical Chemical Electromagnetic Thermal Nuclear Mass

Types of Mechanical Energy Kinetic Gravitational Elastic Sound (2nd semester) …

Kinetic All moving things have energy. More mass means more energy. More speed means LOTS more energy. KE = ( 1 / 2 )mv 2

Gravitational More height means more energy. How high is a stapler on a desk on the second floor? (1 m above floor? 6 m above ground? Only changes in height will matter.) More mass means more energy. GPE = mgh

Elastic More stretch (  x) means more energy. More compression (  x) means more energy. Tougher springs (greater spring constant) mean more energy. EPE = ( 1 / 2 ) k(  x) 2

What would you suppose “total energy” means? E = sum of all the types of _ _ _ _ _ _ that an object has.

What would you suppose “total energy” means? E = sum of all the types of Energy that an object has.

Relationship between Work and Total Energy How much work is done in lifting a 2 kg object 0.4 meters? The object starts at rest, ends at rest, and is lifted with the minimum force. W = D Fcos(  )  is the angle between the force and the motion. What is  in this question?

Calculate the work: W = D Fcos(  ) W = D (Mg) cos(0˚) W = (0.4 m) (2 kg) (9.8) 1 W = 7.84 J

Calculate the change in total energy for this system.  E = E 2 - E 1 = [GPE 2 + KE 2 ] - [GPE 1 + KE 1 ] = [GPE ] - [ ] = mgh 2 = (2)(9.8)(0.4) = 7.84 J …. Compare to the Work. W =  E

A student is walking in the cafeteria, carrying a tray of lunch. Explain why no work is done. Hint: “No work” implies “No Change in Total Energy”. Carrying the food sideways does not change the energy of the food and does not require work. Also, the force is upward, and has no component in the direction of the motion.

1 2 D = ? 1 Recall the exploration: How far does the ball slide in its sled?

Use Work - Energy Theorem W =  E Work = D Fcos(  ) = D Fcos(180˚) = D f(-1) = -D  k  N = -D  k  g  E = E 2 - E 1 = [0] - [GPE 1 ] = -MgH Set W =  E, giving: -D  Mg = -MgH D = H/  k Mass & Angle are not expected to matter. [To see why mass did matter, do it again but include the mass of the sled.]

Use the work energy theorem on a cart. The cart (0.4 kg) accelerates from 2 m/s to 3 m/s on a level table. It will take a 4 N force to do it, over a distance of 0.25 m. How much work was done on the cart? How much was the total energy changed?

Work done on the cart: W = D F cos(  ) W = (0.25 m) (4 N) cos(0˚) W = 1.0 Joules

Calculate the change in total energy  E = E 2 - E 1 = ( 1 / 2 )m(v 2 ) 2 - ( 1 / 2 )m(v 1 ) 2 = ( 1 / 2 )(.4)3 2 - ( 1 / 2 )(.4)2 2 = 1.8 J J = 1.0 J Compare to the work done.

Now you are ready for the worksheet: Work and Total Energy

Demonstration: Pendulum with an obstacle

What if no work is done? Doing work on a system can _ _ _ _ _ _ _ _ the total energy of the system.

What if no work is done? Doing work on a system can increase the total energy of the system. Friction can take energy _ _ _ of a system, or at least seem to. [It matters what you include in the system.]

What if no work is done? Doing work on a system can increase the total energy of the system. Friction can take energy out of a system, or at least seem to. [It matters what you include in the system.] …

What if no work is done? Doing work on a system can increase the total energy of the system. Friction can take energy out of a system, or at least seem to. [It matters what you include in the system.] So, … what happens to the equation if you set W = 0 ?

Conservation of Energy E 2 = E 1 This is one of the most scrutinized patterns in science. Some of the greatest patterns we see are also simple. We know of seven conservation laws, currently. These laws do not tell us what will happen. They do tell us what is possible.

Conservation Does this mean that the energy of an object cannot change? The energy of an object can change by work being done.

Conservation of energy - as a tool First we appreciate a new pattern in nature. Then, we exploit it.

Use Conservation of Energy Drop a 1 kg brick from a window at height 8 m. How fast does it hit the ground? No work is done on the earth-brick system, so E 2 = E 1 Try it

E 2 = E 1 mgh 2 + ( 1 / 2 )mv 2 2 = mgh 1 + ( 1 / 2 )mv (.5)(1)v 2 2 = (1)(9.8)(8) v 2 2 = 78.4 v 2 = 12.5 m/s This checks with the old method of v 2 =v o 2 +2a  y

If something heats up, it appears as though E 2 ≠ E 1. Which one appears to be greater? How much heat is made? Heat = E 1 - E 2 Example: slide a book, and heat = ( 1 / 2 )mv 2

Power Do the same job in less time and the work (select one): is more, less, the same?

Power Do the same job in less time and the work (select one): is more, less, the same? This does not seem right. You deserve credit for doing the work faster.

Power Do the same job in less time and the work (select one): is more, less, the same? This does not seem right. You deserve credit for doing the work faster. Power = Work ÷ _ _ _ _

Power Do the same job in less time and the work (select one): is more, less, the same? This does not seem right. You deserve credit for doing the work faster. Power = Work ÷ Time The units for power are _ _ _ _ _

Power Do the same job in less time and the work (select one): is more, less, the same? This does not seem right. You deserve credit for doing the work faster. Power = Work ÷ Time The units for power are Watts

What is the power of a person who pushes with 4 N over a distance of 30 m, in 2 seconds? W= FD = (4)(30) = 120 J P = W÷T = 120 J / 2 s = 60 W Notice that “W” can mean Work or Watts, (or even Weight).

Now you are ready for: Conceptual questions about energy Problem Solving: Energy.