WORK AND ENERGY PS Chapter 4 Work Work

WORK AND ENERGY PS Chapter 4

Work ■ Work is a product of the force applied and the distance over which the work is applied – W=Fd – In order for work to have been done, the object receiving the force must move ■ Proof (very , very likely to be on your test…) – W=Fd, If the object does not move, d=0 ■ W=F(0)=0 – No work is done

Deriving the Units for Work ■ W=Fd – W(? )=F(N)xd(m) – W=N*m – Recall that N=kg*m/s 2 – So, W=kg*m/s 2*m=kg*m 2/s 2 ■ We have a name for this unit – Called Joule (J) – 1 J=1 kg*m 2/s 2 ■ As you will see, Joules are the unit for energy – To do work, you must expend energy

Example problem-Work ■ You and a friend are driving when you run out of gas 100 m from the nearest gas pump. To get the car to the gas pump, you put the car in neutral and together push with 1080 N to the gas pump. How much work did the two of you do? ■ 2. 4 x 105 J

Practice #1 ■ You apply a force of 60 N to an object to move it 5 m. How much work did you do? ■ 300 J

Practice #2 ■ Your lazy friend sits in a chair on wheels and asks you to push them to their next class which is 10 m away. You agree to do so as long as they pay you $1 per Joule expended. They accept because they were not paying attention in class and have no idea what you are talking about. You push on the chair with a force of 400 N to their class. How much do they owe you? ■ $4000

Practice #3 ■ An object has a mass of 100 kg. You push on the object for 30 m it accelerates at 2 m/s 2. How much work did you do on the object? ■ 6000 J

Machines ■ Any object that changes the force or increases the motion from work – The purpose of a machine is to make work easier ■ 6 simple machines – Lever, pulley, screw, inclined plane (ramp), wheel and axle, wedge

Compound Machines ■ A combination of 2 or more simple machines

Efficiency ■

Example Problem-Efficiency ■ What is the efficiency of a machine that can move a 50 J object when 100 J of force are applied? ■ 50%

Practice #1 ■ You do 100 J or work. If the output work is 20 J, what is the efficiency of the machine? ■ 20%

Practice #2 ■ A machine is 50% efficient. If you input 40 J of work, what will be the machine’s output work? ■ 20 J

Practice #3 ■ An electric motor is used to life a 0. 412 kg mass 1 meter off of the floor. If the machine requires an input of 10 J of energy, what is the efficiency of the machine? ■ 40%

Mechanical Advantage ■ How much a machine increases force. ■ Machines change the way that work is done. – Ideally, the machine will trade a certain amount one aspect of movement in order to achieve more force ■ 3 types of mechanical advantage: – Force mechanical advantage – Distance mechanical advantage – Speed mechanical advantage

Force MA ■

Speed and Distance MA ■ Similar concept to force MA – Trade off one aspect of movement in order to achieve an increase in the desired movement

What Mechanical Advantage Means ■ Mechanical Advantage can be any positive number – IF MA=1, force is not increased ■ Direction or speed can be changed though – If MA>1, force is increased by the machine – If MA<1, the machine requires more force than it outputs ■ The machine is still useful, but increases distance at the expense of force

Example Problem-Mechanical Advantage ■ After months of your parents asking you to do so, you finally sweep the floor. To move the broom, you input 3 N of force. The broom moves with a force of 1 N on the floor. What is the mechanical advantage of the broom? ■. 3 – Less than one, so it decreases the force. ■ However, the broom moves a greater distance than you move your hand.

Practice #1 ■ You apply a force of 10 N to a crowbar to pry open a door that has a resistance force of 600 N. What is the mechanical advantage of the crowbar? ■ 60 – Greatly increases the force.

Practice #2 ■ You do 150 J of work to move the handle of a car jack a total distance of 10 m. The jack lifts the 2000 kg car with an acceleration of. 1 m/s 2. What is the mechanical advantage of the jack? ■ 13. 3

Energy ■ The ability to do work or cause a change to the system ■ Can be transferred, or changed to different forms ■ Several forms: – Mechanical energy-The sum of the kinetic and potential energy of a system – Electrical energy – Chemical energy – Radiant energy – And more

Kinetic Energy ■

Example Problem-Kinetic Energy ■ What is the kinetic energy of a 1000 kg car moving at 100 m/s? ■ 5 x 106 J

Practice #1 ■ What you throw a 5 kg ball at 10 m/s to your friend. What is its kinetic energy? ■ 250 J

Practice #2 ■ A student with a mass of 60 kg walks down the hall at 3 m/s. What is their kinetic energy? ■ 270 J

Practice #3 ■ An object moving north has a mass of 10 kg. If it has kinetic energy of 10, 000 J, what is its velocity? ■ 44. 7 m/s north

Potential Energy ■ Stored energy ■ Energy that has the ability (potential) to change forms ■ Due to interactions between objects ■ Different Types: – Elastic Potential Energy ■ Energy stored by stretching or squeezing (rubber band, stress ball) – Chemical Potential Energy ■ ■ Energy stored in chemical bonds Energy is released when the bonds are broken, and become available for other activities – Gravitational Potential Energy ■ Energy due to gravitational attraction between objects – Ex. Apple on tree and ground

Gravitational Potential Energy (GPE) ■

Example Problem: GPE ■ A 4 kg textbook rests on a shelf 2 meters from the floor. What is the book’s GPE relative to the floor? What is the GPE relative to the shelf? ■ 78. 4 J relative to the floor ■ 0 J relative to the shelf

Practice #1 ■ What is the GPE of a 10 kg object 40 m from the floor, relative to the floor? ■ 3920 J

Practice #2 ■ What is the GPE of a ceiling fan with a mass of 12 kg that is handing ½ meter from the ceiling if the room is 4 meters tall? ■ 411. 6 J

The Law of Conservation of Energy ■ Energy cannot be created or destroyed ■ It can, however, change forms – And does often ■ Example: Roller coaster – At the top of the high hill, GPE is high and KE is low – As the car moves over the hill and begins to speed up, KE increases because velocity increases ■ At the same time, height is decreasing so GPE decreases – At the end of the ride, the cart stops, transforming KE (movement) to thermal energy (heat) due to friction

Mechanical Energy ■ The sum of the kinetic and potential energy of a system ■ It is the energy related to the motion and position of an object – Includes KE, GPE, and elastic potential energy – Does not include nuclear energy, thermal energy, or chemical potential energy ■ The mechanical energy and total energy are not necessarily the same – Therefore, mechanical energy is not necessarily conserved ■ Total energy is though – Always

Transformations of Energy ■ Objects in motion lose energy to their surroundings as heat – This lost energy is called thermal energy (the energy of heat) ■ Electric energy can also be transformed to thermal energy (heat) and radiant energy (light) – Light bulb ■ Fuel (chemical energy) can be transformed into mechanical energy ■ Radiant energy (sunlight) can be transformed into chemical potential energy (sugars in food) and that can be transformed into the energy needed to do everyday tasks – Breathing, heart beating, etc.

Power ■

Example Problem: Power ■ A lightbulb transforms 600 J of energy from electricity to radiant and thermal energy in 10 seconds. What is its power? ■ 60 W

Practice #1 ■ How much energy does a 100 W bulb convert to other forms in 10 minutes? ■ 1000 J

Practice #2 ■ You do 100 J of work in 10 seconds. What is your power> ■ 10 W

Practice #3 ■ You accelerate a 10 kg object at a rate of 2 m/s 2 over a distance of 300 m. It takes you 60 seconds. What is your power? ■ 100 W