# Chapter 4 Work and Energy

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Chapter 4 Work and Energy
Section 1: Work and Machines Section 2: Describing Energy Section 3: Conservation of Energy

Section 1: Work and Machines
Work – the transfer of energy that occurs when a force makes an object move no movement, no work direction of the net force indicates where or on what work is being done calculating work: equation for work: work = force x distance, or: 𝑾=𝑭𝒅 Example: How much work is done if Reggie lifts a box, m = 50-kg, 1.75 meters? Solution: Where: W = Work F = force (N) d = distance (m) Units for Work: W =Fd W = (N)(m) = Nm 1Nm = 1 Joule (J) The unit for work is Joules (J) m = 50.0kg d = 1.75m Because Reggie is lifting the box he must exert a force greater than the weight of the box 𝑊=𝑚𝑔 𝑊=50.0 𝑘𝑔 𝑚 𝑠 2 𝑊=490 𝑘𝑔𝑚 𝑠 2 =490.0 𝑁 Solve for work: 𝑊=𝐹𝑑 𝑊=490.0 𝑁 1.75𝑚 𝑊=857.5 𝑁𝑚 𝑾=𝟖𝟓𝟕.𝟓 𝑱

Section 1: Work and Machines
Machine – a device that makes doing work easier Machines make doing work easier in three ways: Increasing the force applied to the object example: a car jack to lift a car to change a flat tire Increasing the distance over which the force is applied example: using a ramp to raise objects to a height Changing the direction of the applied force example: a wedge – the vertical force is changed to a horizontal force Work done by machines Two forces are involved when a machine is used to do work: Effort force – the force applied to the machine Resistance force – the force applied by the machine to overcome resistance Conservation of Energy You transfer energy to a machine, the machine transfers that energy to the object Energy is neither created nor destroyed, so the work done by the machine is never greater than the work done to the machine Because of energy losses due to friction, the work done by the machine is always less than the work done to the machine

Section 1: Work and Machines
Mechanical Advantage – the number of times a machine multiplies the effort force Equation for Mechanical Advantage : Example: A claw hammer is used to pull a nail from a board. If the claw exerts a resistance force of 2500-N to the applied force of 125-N, what is the mechanical advantage of the hammer? Solution: Notice that the force units (N) cancel; mechanical advantage has no units, it is just a number. 𝑴𝑨= 𝒇 𝒐 𝒇 𝒊 Where: MA = mechanical advantage fo = force out (force applied by the machine) fi = force in (force applied to the machine) fo = 2,500.0N fi = 125.0N MA =? 𝑀𝐴= 𝑓 𝑜 𝑓 𝑖 𝑀𝐴= 2,500𝑁 125𝑁 𝑴𝑨=𝟐𝟎

Section 1: Work and Machines
Simple machine – a machine that does work with only one movement There are six (6) simple machines divided into two types: Compound machine – a machine that consists of two or more simple machines used together The lever type The inclined plane type Includes: Lever Pulley Wheel and axle Ramp Wedge Screw

Section 1: Work and Machines
Lever – a bar that is free to pivot, or turn, about a fixed point. There are three classes of levers: 1st class lever – the fulcrum is between the effort and the resistance Multiplies effort force and changes its direction Examples: crow bars, teeter-totters 2nd class lever – the resistance force is between the effort force and the fulcrum Multiplies force without changing direction Examples: wheel barrows, doors 3rd class lever – the effort force is between the fulcrum and the resistance force The effort force is always greater than the resistance force. MA < 1 Examples: the fore-arm, fishing poles If the 3rd class lever has no mechanical advantage, why use one?

Section 1: Work and Machines
Calculating the mechanical advantage of levers Equation: 𝑴𝑨= 𝒅𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝒐𝒇 𝒆𝒇𝒇𝒐𝒓𝒕 𝒂𝒓𝒎 𝒅𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝒐𝒇 𝒓𝒆𝒔𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝒂𝒓𝒎 , or: 𝑴𝑨= 𝒅 𝒆 𝒅 𝒓 the distances are measured from the fulcrum to the point where the forces are acting Example: If the distance of the effort force is 3-m, and the distance of the resistance arm is 1-m, what is the mechanical advantage of the lever? Solution: Notice the distance units cancel. Remember, mechanical advantage is just a number. de = 3.0m dr = 1.0m MA = ? 𝑀𝐴= 𝑑 𝑒 𝑑 𝑟 𝑀𝐴= 3.0𝑚 1.0𝑚 𝑴𝑨=𝟑.𝟎

Section 1: Work and Machines
Pulleys The two sides of the pulley are the effort arm and the resistance arm. A fixed pulley changes the direction of the force only, it does not increase force A moveable pulley will increase the effort Block-and-tackle – a system of pulleys consisting of fixed and moveable pulleys. The block-and-tackle will multiply the effort force Wheel-and-axle – a machine consisting of two wheels of different sizes that rotate together Inclined plane (ramp) – a sloping surface that reduces the amount of force required to do work The same amount of work is done by lifting a box straight up or by sliding it up a ramp. However, the ramp reduces the amount of force required by increasing the distance Mechanical advantage of a ramp: 𝑴𝑨= 𝒍𝒆𝒏𝒈𝒕𝒉 𝒐𝒇𝒊𝒏𝒄𝒍𝒊𝒏𝒆 𝒉𝒆𝒊𝒈𝒉𝒕 𝒐𝒇 𝒓𝒂𝒎𝒑 , or: 𝑴𝑨= 𝒍 𝒉 Example: Jessica uses a ramp 5-m long to raise a box to a height of 1-m. What is the mechanical advantage of the ramp? Solution Length =5.0m Height = 1.0m MA = ? 𝑀𝐴= 𝑙 ℎ 𝑀𝐴= 5.0𝑚 1.0𝑚 𝑴𝑨=𝟓.𝟎

Section 1: Work and Machines
Screw – an inclined plane wrapped around a cylinder Wedge – an inclined plane with one or two sloping sides Mechanical Efficiency (ME) Recall that the amount of work done by the machine (work output) is always less than the work done on the machine (work input) Mechanical Efficiency is the measure of how much of the work put into a machine is changed into useful output work by the machine Because of friction no machine is 100% efficient. ME will always be less than 100% Equation: 𝑴𝑬= 𝒘𝒐𝒓𝒌 𝒐𝒖𝒕𝒑𝒖𝒕 𝒘𝒐𝒓𝒌 𝒊𝒏𝒑𝒖𝒕 𝐱𝟏𝟎𝟎%, or: 𝑴𝑬= 𝒘 𝒐 𝒘 𝒊 𝒙𝟏𝟎𝟎% Example: John is changing a flat tire on his truck. He does 2,500J of work on the jack, while the jack does 2,100J of work on the car. How efficient is the jack? Solution wi = 2,500J wo = 2,100J ME = ? 𝑀𝐸= 𝑤 𝑜 𝑤 𝑖 𝑥100% 𝑀𝐸= 2,100𝐽 2,500𝐽 𝑥100% 𝑀𝐸=0.84𝑥100% 𝑴𝑬=𝟖𝟒%

Section 2: Describing Energy
Energy – the ability to cause change Energy comes in different forms  chemical, electrical, thermal, etc. We will be looking at three (3) types of energy: kinetic, potential, and mechanical. Kinetic Energy (KE) KE is energy in a moving object Anything that moves has kinetic energy Kinetic energy depends of two things: 1. the mass of the moving object 2. the velocity of at which the object is moving Equation for kinetic energy: Unit for energy: 𝐾𝐸=𝑘𝑔( 𝑚 𝑠 ) 2 𝐾𝐸=𝑘𝑔 𝑚 2 𝑠 2 𝐊𝐄= kg m 2 s 2 =Nm=𝐉 𝑲𝑬= 𝟏 𝟐 𝒎 𝒗 𝟐 Where: KE = kinetic energy M = mass (kg) V = velocity (m/s)

Section 2: Describing Energy
Example: A ball, m = 1.5-kg, is rolling across the floor towards the door at 2 m/s. What is the KE of the rolling ball? Solution Important: Always square the velocity before you do any multiplication Potential Energy Potential energy – energy stored due to an object’s position Three types of potential energy: Elastic – PE stored by things that stretch or compress Ex.: rubber bands, springs, pole vault poles Chemical – PE stored in chemicals bonds Ex.: nuclear weapons and fuels Gravitational – PE stored by things that are elevated Ex.: fruit on trees, bouncing balls m = 1.5-kg v = 2.0-m/s KE = ? 𝐾𝐸= 1 2 𝑚 𝑣 2 𝐾𝐸=( 1 2 )(1.5𝑘𝑔)( 2.0 𝑚 𝑠 ) 2 𝐾𝐸= 𝑘𝑔 𝑚 2 𝑠 2 𝑲𝑬=𝟑.𝟎 𝒌𝒈 𝒎 𝟐 𝒔 𝟐 =𝟑.𝟎 𝑱

Section 2: Describing Energy
The amount of potential energy can be determined mathematically. We will focus on gravitational PE Equation for gravitational PE: Example: An apple, mass = 0.5-kg, is hanging from a branch 4.0-m above the ground. What is its gravitational PE? Solution 𝑷𝑬=𝒎𝒈𝒉 PE = Potential Energy (J) M = mass (kg) g = 9.8 m/s2 H = height (m) m = 0.5 kg h = 4.0 m PE = ? 𝑃𝐸=𝑚𝑔ℎ 𝑃𝐸=0.5𝑘𝑔 9.8 𝑚 𝑠 𝑚 𝑃𝐸=19.6 𝑘𝑔 𝑚 2 𝑠 2 𝑷𝑬=𝟏𝟗,𝟔 𝑱

Section 3: Conservation of Energy
Mechanical Energy – the total amount of potential and kinetic energy in a system Equation: mechanical energy = potential energy + kinetic energy, or: Example: An object held in the air has a gravitational PE of 480.0J. What is its kinetic energy if it has fallen two-thirds of the way to the ground? Law of Conservation of Energy: Energy is neither created nor destroyed On a large scale: total energy in the universe is constant Consequence: energy can change form: potential  kinetic kinetic  thermal chemical  mechanical Solution Before the object started falling ME = PE, so ME = 480.0J. As the object is falling PE is being converted to KE. At anytime during the fall ME = PE + KE. When the object is two-thirds of the way down ME = 1/3PE + 2/3KE. So: KE = 2/3(480.0 J), or KE = 320.0J

Section 3: Conservation of Energy
Power – the amount of work done in a certain amount of time Power is a rate Equation for calculating power: Units for Power: the Watt (W) 1 watt is about equal to the power required to lift a glass of water from a table to your mouth Example 1: It took 20 seconds to move a refrigerator, You did 3,150 J of work in the process. How much power was required to move the refrigerator? Solution Example 2: It took you 1.5 s to lift a 10-kg box of the floor to a height of 1.0-m. How much work did you do on the box, and how much power was required to do this? Solution