1.  Energy, Work and Simple Machines  Chapter 10  Physics I

2.  Energy  Energy is the property that describes an object’s ability to change itself or the environment around it.  Energy can be found in many forms.  Kinetic Energy (KE) – energy of motion.  Potential Energy (PE) – energy gained by a change in position or structure

3.  Kinetic Energy (KE)  Moving objects possess Kinetic Energy.  KE = ½ mv 2  Energy is a scalar quantity and has the unit of Joule (J) (1 J = 1 Nm)

4.  Work  Work has its own meaning in physics.  Work is done on an object when an applied force acting on the object moves the object over a distance.  Work depends on two factors.  Force (F)  Displacement (d)

5.  Work  Work = Force x Displacement  W = Fd  Unit for Work = Newton Meter (Nm)  1 Nm = 1 Joule (J) (Same as Energy)  Work is a scalar quantity (no direction)  In doing Work the Displacement has to be in the same direction as the Force!

6.  Work-Energy Theorem  Work and Energy are closely related.  Work and Kinetic Energy can be connected with the kinematics equations and Newton’s 2 nd Law  W =  KE (Work-Energy Theorem)  W = KE f – KE i = ½ mv f 2 – ½ mv i 2

7.  Work, Force and Direction  W = Fd  In doing Work the Displacement has to be in the same direction as the Force!  If the Force is at an angle, then the component of the Force (F x ) produces Work  W = F x d = Fdcos 

8.  Work  Work can be Zero (W NET = 0) in three ways;  d = 0 (does not move or finishes where it starts)  F NET = 0 (v = 0 or v = constant)  F NET is perpendicular to d (F | d)

9.  Work  If F ll d, then W = Fd or W = -Fd  W = Fd, Force in same direction as displacement (  = 0 o : cos  = 1, Positive Work)  W = -Fd, Force is in the opposite direction as the displacement (  = 180 o : cos  = -1, Negative Work)

10.  Work From a Force vs Displacement Graph  If you have a Force vs Displacement Graph, where the Force is in Newtons (N) and the Displacement is in Meters (m), you can find the Work by finding the Area Under the Curve!  W = Area under F vs d graph

11.  Work From a Force vs Displacement Graph  W = Area under F vs d graph  For a Constant Force:  The Area is a rectangle use W = A = lw  For a Force Varying at a Constant Rate:  The Area is a triangle use W = A = ½ bh

12.  Power  Power – The time rate of doing Work  If you do the same Work faster, you have more Power!  Power = Work/Time  P = W/  t  Unit for Power = J/s  1 J/s = 1Watt (W)

13.  Power  Power is a scalar quantity (no direction)  Another way to find Power:  P = W/t = (Fd)/t  Since v = d/t  P = Fv = Force x Velocity = Power  Since a Watt is small, Power often uses kilowatt (kW) megawatt (MW) or Horsepower (hp)

14.  Energy From Power  We can use the Power Equation to find Energy.  P = W/t (Work is similar to Energy)  Therefore; P = E/t  E = Pt (Solve for Energy)  A Unit for Energy = W s or kW-hr (kilowatt-hour)

15.  Machines  Machines can do any of the following;  Machines can Multiply the Force (Lever)  Change the Direction of the Force (Pulley)  Change the speed in which the force acts (Gears)

16.  Machines  Most machines make work easier by multiplying the Force!  Machines never Multiply the Work!  When using a machine there is always a Work put into the machine (W IN ) and a Work the machine puts out (W OUT ).  Ideally, the W IN = W OUT in an ideal machine (no friction).

17.  Machines  How Does a Machine multiply the force without multiplying the Work?  Answer: If a machine multiplies the Input Force (F IN ), then the machine must act over a larger Displacement (d IN )!  Remember, W = Fd

18.  Machines  W IN = W OUT  F IN d IN = F OUT d OUT  F IN will be small so d IN will be large!  F OUT will be large so d OUT will be small!

19.  Types of Simple Machines  Simple Machine (SM) – a machine with one or two moving parts.  There are six types of Simple Machines:  1. Lever4. Inclined Plane  2. Pulley5. Wedge  3. Wheel and 6. Screw Axle

20.  Mechanical Advantage  Mechanical Advantage (MA) – is the number of times a machine multiplies the Input Force (F IN )  Example:  MA = 2 Means the machine doubles the force you put into it.  MA = 10 Means the machine multiplies the force put into it by 10.

21.  Mechanical Advantage  MA >1 (Machine multiplies the force)  MA < 1(Machine multiplies the distance)  MA = 1(Machine does not multiply either force or distance. Probably only changes the direction to the force.)

22.  Mechanical Advantage  To find the Mechanical Advantage (MA) of a machine, we take the ratio of the Resistance Force (F r ) to the Effort Force (F e )  Effort Force (F e ) – is the force applied to the machine  Resistance Force (F r ) – is the force the machine applies to the object

23.  Ideal Mechanical Advantage (IMA)  The Ideal Mechanical Advantage (IMA) is the largest possible MA a machine can have if the machine operated without friction.  To find the Ideal Mechanical Advantage (IMA) of a machine you take the ratio of the Effort Distance (d e ) over the Resistance Distance (d r )

24.  Calculating MA and IMA  To calculate MA we use the Forces (F r and F e ). Since Friction is a force, Friction affects MA. MA = F r /F e  To calculate IMA we use the distances (d r and d e ). Friction does not affect IMA. IMA = d e /d r  MA has No Unit!! It’s a number telling how many times the force is multiplied!

25.  Ideal Mechanical Advantage and Actual Mechanical Advantage  The Actual Mechanical Advantage (MA) is always less than the IMA (MA < IMA) because of Friction.  Machines are designed with an IMA  Machines are tested to find Actual MA

26.  Input/Effort and Output/Resistance  Note from this point on:  Effort = Input  (F IN = F e and d IN = d e )  Resistance = Output  (F OUT = F r and d OUT = d r )  W IN = W OUT (Ideal Machine)  F e d e = F r d r

27.  Compound Machines  Compound Machine – any combination of two or more simple machines  Examples: Axe, Shovel, Scissors  Compound Machines have a higher Mechanical Advantage (MA) because they are made up of multiple machines

28.  Mechanical Advantage of Compound Machines  To calculate the Mechanical Advantage (MA) of a Compound Machine (CM), you multiply the Mechanical Advantages of all the Simple Machines in the Compound Machine  MA CM = MA SM#1 x MA SM#2 x MA SM#3 x …

29.  Efficiency  Efficiency is the ratio of the useful work you get out of a machine (W OUT ) over the work you put into a machine (W IN )  In an ideal world (no friction);  W OUT = W IN therefore;  W OUT /W IN = 1

30.  Efficiency  In the real world (with friction);  W OUT < W IN therefore;  W OUT /W IN < 1  We express Efficiency as a Percentage by multiplying the ratio by 100%  Ideal World Efficiency = 100%  Real World Efficiency < 100%

31.  Efficiency  We can use different equations for Efficiency  Eff = (W OUT /W IN ) x 100%  Eff = (F r d r /F e d e ) x 100%  Eff = (MA/IMA) x 100%

32.  Efficiency and Machines  Simple Machines have a small MA but work with a high Efficiency.  Compound Machines have a high MA but work with a lower Efficiency.  The more complicated the machines the greater the MA but the lower the Efficiency!

33.  The Human Machine  Levers – Muscles and Tendons  Wedges – Teeth and Finger Nails  Your Body uses many Simple and Compound machines to create Mechanical Advantage  Human Walking Machine Page 273