Work, Power, and Simple Machines

Work Work = Force x Distance The force must be in the direction No Work Work = Force x Distance The force must be in the direction of the motion, or no work is done. Work

The unit of work is the Joule Force x Distance = Work 1 Newton x 1 meter = 1 Newton meter 1 Newton meter = 1 Joule James Prescott Joule

Example 1: A high jumper weighs 700 newtons. What work does the jumper perform in jumping over a bar 2.0 meters high? Answer: W = F x d W = 700N x 2.0 m = 1400 nm = 1400 Joules

No work is done if there is no distance! The statue of liberty has been holding up her torch for an awfully long time. How much work has she done? Answer: 0! Although it takes a force to hold the torch against the force of gravity, there is no motion so no work is done.

Which does more work? Frictionless The net work is the force (weight) of the cart x the vertical distance. This is the same in all three cases. In the first, the force is less, but distance is greater to reach the same vertical height.

Example 2 A force of 200N is required to push a lawn mower. If 4000 J of work is performed on the lawnmower, how far does it move? Answer: W__ F d 4000J__ 200N d 4000Nm ÷ 200N = 20m

Power = Force x distance Work done per unit of time Power = Work Time Power = Force x distance

The unit of power is the watt Power = Work Time 1 watt = 1 Joule Second

Example 3 A crane lifts a car into a junk pile in 10 seconds. What is the crane’s power if 120,000 J of work are performed? Answer: Power = Work Time 120,000J = 10 sec 12,000 Watts

Power = Force x distance Example 4 A 750 N diver does a somersault off a 10m platform. It takes her 1.5 seconds to hit the water. What is her power? Since work is Force x distance, the power formula can be written as Power = Force x distance Time

Answer: Power = 750N x 10m Power = 7500N m Time 1.5 sec = 5000 Watts Power = Force x distance Time Power = 750N x 10m 1.5 sec Power = 7500N m = 5000 Watts

Other units of power 1 kilowatt = 1000 watts 1 horsepower = 750 watts In the previous example, how many kilowatts power was generated? How much horsepower?

Answer: 5000 watts ÷ 1000 kw/w = 5 kilowatts 5000 watts ÷ 750 hp/w = 6.7 horsepower

Work, mechanical advantage, and efficiency Machines Work, mechanical advantage, and efficiency

Machines make work easier Machines change the size or direction of the applied force.

2 forces are involved in machines FE = effort force The force applied to the object FR = resistance force The force that opposes effort. Often equal to the weight of the object. FE FR

Machines move a force through a distance Effort distance The distance through which the force is applied Resistance distance The distance the object moves DE DR

Work in = work out (neglecting friction) WI = work input The work done on a machine Wo = Work output The work done by the machine

DE = 5ft DR = 5ft For a lever, the effort distance and resistance distance can be measured from the fulcrum. In this case, we call them the effort arm and resistance arm. DE = 5ft DR = 5ft

What is the work input and work output? DE = 5ft DR = 5ft 10 lbs x 5 feet = 50 ft lbs DR = 5ft

Find FE, the force required to balance the seesaw: DE = 2ft DR = 8ft

Answer: FE =40 lbs Work output = work input FR • dR = FE • dE 10 lbs • 8ft = x lbs • 2ft 80 = 2x x = 40 lbs FE =40 lbs FR DE = 2ft DR = 8ft

Find the effort force: 6.7 lbs Work output = work input DE = 6ft 4(10) = 6x 40 = 6x x = 6.7 lbs DE = 6ft DR = 4ft

Mechanical = Resistance force_ MA = FR_ Mechanical Advantage Number of times a machine multiplies effort Mechanical = Resistance force_ Advantage Effort force MA = FR_ FE

1 What is the mechanical advantage? DE = 5ft DR = 5ft 10 lbs ÷ 10 lbs = 1 DR = 5ft

What is the mechanical advantage? MA = FR_ FE 40 lbs = 10lbs ÷ 40 lbs = 0.25 DE = 2ft DR = 8ft

Find the mechanical advantage: 6.7 lbs MA = FR_ FE = 10 lbs ÷ 6.7 lbs = 1.5 DE = 6ft DR = 4ft

What does mechanical advantage mean? A mechanical advantage of one has no effect on the force required A mechanical advantage of less than one makes it harder for you to do the work A mechanical advantage greater than one makes the work easier.

Efficiency Compares work output to work input Can never be greater than 100% Machines can never give out more work than is put in Friction reduces efficiency

Efficiency FE = 50N Work output Work input Expressed as a percent Example: A box is slid up an incline with a force of 50N. The length of the incline is 7 meters, and its height is 5 meters. The box weighs 70N. What is the efficiency? FR = 70N dR = 5m FE = 50N dE = 7m

Answer: FE = 50N Work output = FR x dR Work input FE x dE = 70N x 5m = 350 350 = 1 = 100% FE = 50N FR = 70N dR = 5m dE = 7m

Describe the friction from the last example FRICTIONLESS!! 100% efficient

Efficiency with friction Example: A box is slid up an incline with a force of 100N. The length of the incline is 7 meters, and its height is 5 meters. The box weighs 70N. What is the efficiency? FR = 70N dR = 5m FE = 100N dE = 7m

Answer: FE = 100N Work output = FR x dR Work input FE x dE = 70N x 5m = 350 700 = 0.5 = 50% FE = 100N FR = 70N dR = 5m dE = 7m

Simple machines

Levers The resistance and effort move about the fulcrum.

Levers: 3 types First class Third class Second class

E First class lever R F Resistance Effort Fulcrum : Fulcrum is between effort and resistance F Resistance Effort Fulcrum

R F E resistance effort Fulcrum 2nd Class Levers The resistance is located between the effort force and the fulcrum. E   resistance effort Fulcrum

R E F Second class lever

The effort force is located between 3rd Class Levers The effort force is located between the resistance force and the fulcrum. E F   Effort Resistance Fulcrum

R F Third class lever E

What class lever? Second class Resistance in the middle

What class lever? First class Fulcrum in the middle

What class lever? First class Fulcrum in the middle

What class lever? Second class Resistance in the middle

What class lever? Third class Effort in the middle

What class lever? Third class Effort in the middle

What class lever? Effort in the middle Third class

What class lever? Second class Resistance in the middle

How are the force and distance related in a machine? Less force requires a greater distance to do the same amount of work.

If the 20kg frog sits 8 meters from the fulcrum, where should the 5kg frog sit to balance? 20(8) = 5(x) 32 m = x 32 m from the fulcrum

WHEEL AND AXLE: a lever rotating in a circle

Wheel and axle examples

Inclined Plane: any sloping surface used to raise objects, such as a ramp

Inclined plane

Inclined plane

The ideal mechanical advantage of an inclined plane is length ÷ height. What is the ideal mechanical advantage? 10m ÷ 2m = 5 Length = 10m Height = 2m

The actual mechanical advantage of an inclined plane is resistance ÷ effort. What is the actual mechanical advantage? 24N ÷ 6N = 4 Why is AMA<IMA? Effort = 6N  FRICTION! Resistance (the weight of the cart) = 24N

What is the efficiency of this inclined plane? Work output ÷ work input FR x dR = 24N x 2m FE x dE 6N x 10m = 48 = .8 60 80% Effort force = 6 N  Resistance force (the weight of the cart) = 24N Height = 2m Length = 10m

SCREW: an inclined plane wrapped around a cylinder to form a spiral A screw multiplies effort by acting through a long effort distance.

WEDGE: an inclined plane that moves.

PULLEY: a rope, belt, or chain wrapped around a wheel

Fixed pulley No mechanical advantage Changes the direction of the force.

Moveable pulley Pulley is not connected to anything. This pulley has an ideal mechanical advantage of 2.

Combined pulleys A single fixed and a single moveable. This pulley system has an ideal mechanical advantage of 2.

The ideal mechanical advantage of a pulley system is found by counting the number of ropes that pull up. MA = 2 MA = 3 MA = 4

What is the ideal mechanical advantage of this system? 3

Effort equals resistance! The ideal mechanical advantage of a pulley system is found by counting the number of ropes that pull up. What is the ideal mechanical advantage of this pulley? 1 Effort equals resistance!

To Review: 6 simple machines are: lever wheel and axle inclined plane wedge screw pulley

To review: Work = force x distance power = work ÷ time mechanical advantage = resistance force ÷ effort force efficiency = work output ÷ work input

That's All Folks!!