Simple Machines

In a simple machine, input work is done by a person applying a single force, and the machine does output work also by means of a single force.

Conservation of energy demands that the work input be equal to the sum of the work output and the heat lost to friction.

Energy: Ability to do work

Work= Force x Distance

Force: A Push or a Pull

Definitions:

The 6 Simple Machines

Lever

Pulley Wheel and Axle

WedgeScrewInclined Plane

Inclined Plane

Inclined Plane The Egyptians used simple machines to build the

pyramids. One method was to build a very long incline out of dirt that rose upward to the top of the pyramid very gently. The blocks of stone were placed on large logs and pushed slowly up the long, gentle inclined plane to the top of the pyramid.

Inclined Planes An inclined plane is

a flat surface that is higher on one end.

Inclined planes make the work of moving things easier – less force is required.

Inclined PlanesAn inclined plane can be used to

alter the force and distance involved in doing work, such as lifting loads.

The trade-off is that an object must be moved a longer distance than if it were lifted straight up, but less force is needed.

Work input and output Work input is the amount of work done on

a machine. (What work you did using it.) Input force x input distance

Work output is the amount of work done by a machine. (What did the machine accomplish?) Output force x output distance

Wout = Win

Fout x Dout = Fin x Din

Din

Dout

Work input and outputExample: If you lift an object that weighs 10 N straight up 3 meters, the work required will be

W = F x d = 10 N x 3 m = 30 J

If you push it up this ramp, the work has to be the same amount. (Why?) But the force you have to exert will be less:

15 m

3 m

Wout = Win

Fout x Dout = Fin x Din

10N x 3m = 2N x 15m 10 N Fin

DinDout

Mechanical Advantageof any simple machine:

The mechanical advantage, MA, is the ratio of Fout to Fin.

o

Ai

Foutput forceM

input force F

Mechanical Advantageof any simple machine:

The mechanical advantage, MA, is the ratio of Fout to Fin.

o

Ai

Foutput forceM

input force F

The mechanical advantage is also:

MA = input distanceoutput distance

Can you see why?

Mechanical AdvantageIn our previous example, the output force is 10 N, the input force is 2 N.

What is the mechanical advantage of this inclined plane?

15 m

3 m

10 N2 N

Mechanical AdvantageSo…

The advantage of using this inclined plane is that your force is multiplied by five.

15 m

3 m

Wout = Win

Fout x Dout = Fin x Din

10N x 3m = 2N x 15m 10 N 2 N

DinDout

So far, we’ve been talking about imaginary machines.

In real life,

Win will never equal Wout.

(Why not?)

Remember Mechanical Advantage?

What is the mechanical advantage of this inclined plane?

The mechanical advantage you calculate using the distances is the ideal mechanical advantage.

That’s what themechanical advantagewould be if there wereno friction.

15 m

3 m

Remember Mechanical Advantage?

The ideal mechanical advantage of this inclined plane is 5.

In real life, it will be less than 5. To findthe actual mechanical advantage, you need to try out the machine.

AMA = Force out Force in 15 m

3 m

The Lever

Once again, the input work Fidi is equal to the output work Fodo.

A lever shown here consists of input and output forces at different distances from a fulcrum.

Fin

Fout

dout din

Fulcrum

3 Classes of Levers

Ideal Mechanical AdvantageWhat is the ideal mechanical advantage

if the rock is 2 meters from the fulcrum, and you push down 3 meters from the fulcrum?

Ideal Mechanical Advantage What is the ideal mechanical advantage if the

rock is 2 meters from the fulcrum, and you push down 3 meters from the fulcrum? 1.5

How much force should be required if the rock weighs 30 N?

Actual Mechanical AdvantageWhat is the actual mechanical

advantage if the rock weighs 30 N, and you have to push down with 25 N of force?

In real-life Simple Machines… Input work = output work + work against frictionInput work = output work + work against friction

Efficiency is defined as the ratio of work output to work input.

Efficiency = Work outputWork input

Example The efficiency of a simple machine is 80%, and a 400-N weight is lifted a vertical height of 2 m. If an input force of 20 N is required, what distance must be covered by the input force?

The efficiency is 80% or e = 0.80, therefore:

0.80 = Fout x dout

Fin x din

0.80 = 400 N x 2 m 20 N x din

Practice Problem: Clyde, a stubborn 3500-N mule,

refuses to walk into the barn, so Farmer McDonald must drag him up a 5.0 m ramp to his stall, which stand 0.50 m above ground level.

a. What is the ideal MA of the ramp?

b. If Farmer McDonald needs to exert a 450-N force on the mule to drag him up the ramp, what is the actual mechanical advantage?

c. What is the efficiency of the ramp?

Example A 1-m metal lever is used to lift a 800-N rock. What force is required at the left end if the fulcrum is placed 20 cm from the rock?

d1d2

800 N

F = ?

1. Draw and label sketch:2. List given info:

Fo = 800 N; d2 = 20 cm

d1 = 100 cm - 20 cm = 80 cm

3. To find Fi we recall that Win = Wout

F x d = F x dF x 80 = 800 x 20 F = 200 N

Example A 1-m metal lever is used to lift a 800-N rock. What force is required at the left end if the fulcrum is placed 20 cm from the rock?

d1d2

800 N

F = ?

What is the mechanical advantage of the lever?

Screw A screw is an inclined plane wrapped

around a pin. A screw “lifts” objects by pulling them together.

The longer the incline plane, the tighter the screw’s threads.

The Mechanical Advantage of a screw is the length of thread (length of the inclined plane) over height of screw (hight of the inclined plane).

MA = Distance In

Distance Out

MA = Thread Length

Pin Length

Wheel & Axel

A simple machine consisting of an axle that is attached to a wheel. The torque (force) that is applied to the wheel is increased in the axel – which does the work on larger loads.

Mechanical Advantage of a wheel and axle radius of wheel over radius of axle.

MA = Wheel RadiusAxle Radius

Everyday Wheel & Axles

Pulley

Mechanical Advantage of a pulley is equal to the number of supporting strands

The pulley is a wheel & axle designed to support a load with a cord about it’s circumference.

Wedge A wedge is a simple machine used to separate two objects, or portions of

objects, through the application of force. A wedge is made up of two inclined planes. These planes meet and form a sharp edge. This edge can split things apart. Wedges are used as either separating or holding devices. There are two major differences between inclined planes and wedges. First, in use, an inclined plane remains stationary while the wedge moves. Second, the effort force is applied parallel to the slope of an inclined plane, while the effort force is applied to the vertical edge (height) of the wedge.

Ideal Mechanical Advantage of a wedge; sloping side over thickness