NASA-Threads
Work and Mechanics
Lesson 17: Simple Machines
Simple Machines
Machines consist of an arrangement of parts designed to perform a task, such as amplifying
a force, providing motion, or changing energy from one form to another. Complex machines
such as automobiles, bicycles and copy machines are made up of a collection of simple
machines. The most commonly accepted list of simple machines is provided below. We will
examine the mechanical advantage and efficiency of simple machines using Newton’s Laws.
An inclined plane is a sloped flat
surface that facilitates moving
objects from one elevation to
another. Here, the crawlertransporter slowly carries Space
Shuttle Atlantis up an inclined
plane with a 5% grade to Launch
Pad 39A which is 12 meters
above ground level. The inclined
plane here is a practical way to
elevate the shuttle.
A wedge is a moving, doubleinclined plane. Wedges create
large forces perpendicular to
their direction of travel. For
example, when a wedge is driven
into the end of a wooden log,
large forces are induced
perpendicular to the direction of
travel of the wedge, thus splitting
the wood. A door stop is a simple
example of a wedge; the small
force that pushes the wedge
under the door results in a larger
vertical force between the wedge
and the floor and the wedge and
the door, keeping the door in
place.
NASA-Threads
Work and Mechanics
Lesson 17: Simple Machines
A screw is an inclined plane that
winds around an axis. Screws
convert rotational motion into
linear motion. Closing a c-clamp
by rotating its handle causes
linear motion of the clamping
surfaces. The clamping force that
is induced is much larger than the
force applied to the handle.
A lever is a rigid bar that rotates
about a fixed point (the fulcrum)
and often generally used to
amplify force. A seesaw or teetertotter that you would find on a
playground is an example of a
lever. The curling iron shown
here incorporates a lever to lift
the spring-loaded hair clamp. A
longer lever would make it easier
to overcome the spring force that
keeps the hair clamp closed.
A wheel and axle involves a
wheel that is rigidly attached to a
smaller cylinder called an axle.
Examples include a screwdriver, a
doorknob and a steering wheel
on a car. The classic example
shown here uses a larger outer
wheel to turn a shaft thereby
lifting a water bucket; the force P
applied to the larger wheel is
smaller than the weight W of the
bucket resulting in a mechanical
advantage of W/P.
A natural philosophy: embracing the most recent discoveries in the
various branches of physics, and exhibiting the application of scientific
principles in every-day life. George Payn Quackenbos, 1860.
NASA-Threads
Work and Mechanics
Lesson 17: Simple Machines
A pulley is a wheel that carries a
rope, belt, cable or chain along its
rim while rotating freely about its
axis. Pulleys can be used in a
variety of mechanical
applications, including changing
the direction of a force and
amplifying a force. The pulley
shown to the right is part of a
system that raises and lowers the
forks on a fork lift. If the chain
wrapped around the pulley were
removed, the pulley would spin
freely on its bearing;
consequently, the tension of the
chain on both sides of the pulley
is equal.
Inclined Planes
An inclined plane allows an object to be moved from a lower elevation to a higher elevation
using a force that is less than the weight of the object itself. The mechanical advantage of an
inclined plane is determined as follows:
𝑀𝑒𝑐ℎ𝑎𝑛𝑖𝑐𝑎𝑙 𝐴𝑑𝑣𝑎𝑛𝑡𝑎𝑔𝑒 = 𝑀. 𝐴. =
𝑓𝑜𝑟𝑐𝑒 𝑡𝑜 𝑒𝑙𝑒𝑣𝑎𝑡𝑒 𝑏𝑜𝑑𝑦 𝑤𝑖𝑡ℎ𝑜𝑢𝑡 𝑎𝑛 𝑖𝑛𝑐𝑙𝑖𝑛𝑒𝑑 𝑝𝑙𝑎𝑛𝑒
𝑓𝑜𝑟𝑐𝑒 𝑡𝑜 𝑒𝑙𝑒𝑣𝑎𝑡𝑒 𝑏𝑜𝑑𝑦 𝑤𝑖𝑡ℎ 𝑎𝑛 𝑖𝑛𝑐𝑙𝑖𝑛𝑑𝑒𝑑 𝑝𝑙𝑎𝑛𝑒
Since the force to elevate a body without an inclined plane is just the weight of the body
itself, the above expression can be written as follows:
𝑀. 𝐴. =
𝑤𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑏𝑜𝑑𝑦 𝑡𝑜 𝑏𝑒 𝑒𝑙𝑒𝑣𝑎𝑡𝑒𝑑
𝑓𝑜𝑟𝑐𝑒 𝑡𝑜 𝑒𝑙𝑒𝑣𝑎𝑡𝑒 𝑏𝑜𝑑𝑦 𝑤𝑖𝑡ℎ 𝑎𝑛 𝑖𝑛𝑐𝑙𝑖𝑛𝑒𝑑 𝑝𝑙𝑎𝑛𝑒
One primary consideration when examining inclined planes or ramps is the friction
between the ramp and the object being slid up or down the ramp. Friction will increase the
force required to push an object up a ramp, thus decreasing the efficiency of the process as
we will see later. First, let’s examine an object being slid up an ideal or “frictionless” ramp.
NASA-Threads
Work and Mechanics
Lesson 17: Simple Machines
CLASS PROBLEM: A 200 lb box is slid into a moving truck using a ramp that makes a 30˚ angle with
the level ground. The ramp is equipped with a series of small rollers to reduce frictional effects.
(a) Assuming that a uniform normal force (call this force N) acts between the box and the
ramp, draw a diagram showing the forces acting on the box. This is called a Free Body
Diagram (FBD).
(b) Estimate the minimum force F required to push the box up the ramp.
(c) Determine the mechanical advantage for this ramp.
30˚
(Friction
Friction is a force that resists the relative motion between two contacting bodies. Friction
can be good or bad depending on the situation. Friction between our shoes and the floor
allow us to walk without slipping; this is a case where friction is absolutely necessary in
everyday life. When parts rub together inside the engine of a car, the frictional forces that
result decrease the efficiency of the engine and lead to wear; this is a case where friction is
not desirable. There are many types of friction:
 Friction between dry solid surfaces
 Friction between lubricated solid surfaces
 Friction that occurs when fluid particles rub past one another
 Friction that occurs when fluid passes over a solid surface
NASA-Threads
Work and Mechanics
Lesson 17: Simple Machines
DRY FRICTION: Even apparently smooth objects have some level of
waviness and roughness when examined under a microscope. This
variation in surface geometry causes contacting objects to physically
touch on a small fraction of their apparent contact areas. In
reality, the “contact” forces between objects are due to
electromagnetic forces between atoms and molecules. The energy
lost to friction is converted to heat.
Static Friction applies to the contact between bodies with no relative
motion. For static friction, the stationary points of contact can become cold welded together,
and these tiny welds must be broken for sliding to occur. The friction force (Ff) and the normal
force (N) are related as shown below:
𝐹𝑓 ≤ 𝜇𝑠 𝑁
where µs is the coefficient of static friction and usually falls between 0 and 1. The static friction
force assumes whatever value is required to prevent motion as long as it does not exceed µ sN.
Kinetic Friction: Once sliding starts, the coefficient of friction changes from µs to µk, where the
subscript k stands for kinetic and implies motion. The value of µk is usually smaller than µs since
it generally takes more force to break the surfaces apart to get them moving than it does to
sustain motion. The following relation applies for kinetic friction:
𝐹𝑓 = 𝜇𝑘 𝑁
The diagrams below illustrate the frictional forces on bodies under static and kinetic
conditions.
stationary body on flat surface; no external loads
There is no frictional force between the block and
W
the floor (nothing is trying to make the block slide
across the floor).
N
F
W
N
Ff
stationary body on flat surface with external
load
Summing forces in the horizontal direction shows
that the externally applied force F is equal and
opposite to the friction force Ff. The block will not
move as long as F ≤ µsN.
When F exceeds µsN, the body will begin to slide.
NASA-Threads
Work and Mechanics
ax
F
W
N
Ff
y
x
Lesson 17: Simple Machines
accelerating body on flat surface with external
load
The external load is greater than the frictional
resistance. Here, F must initially exceed µsN in
order to induce movement; after motion starts, F
must exceed µkN for movement to continue. The
difference between F and Ff causes the body to
accelerate.
Σ𝐹𝑥 = 𝐹 − 𝐹𝑓 = 𝑚𝑎𝑥
𝐹 − 𝜇𝑘 𝑁 = 𝑚𝑎𝑥
Notice in the above analysis that Ff=µkN and
m=W/g.
CLASS PROBLEM: A 200 lb box is slid into a moving truck using a ramp that makes a 30˚ angle
with the level ground. The coefficient of static friction (µs) is 0.45, and the coefficient of kinetic
friction (µk) is 0.35. Assume the box starts from a stationary position at the bottom of the ramp
and, once started, does not stop moving until it reaches the truck.
(a)
(b)
(c)
(d)
Draw a Free Body Diagram (FBD) showing the forces on the box just before moving.
Estimate the minimum force F required to make the box start moving.
Estimate the force to keep the box moving.
Determine the mechanical advantage for this ramp.
NASA-Threads
Work and Mechanics
Lesson 17: Simple Machines
Efficiency of an Inclined Plane
Friction increases the force required to move a body up an inclined plane, thereby
decreasing the efficiency of this simple machine. The energy required to overcome
frictional forces is converted into heat and generally cannot be recovered for a useful
purpose; this energy is lost. The efficiency of an inclined plane can be computed as follows.
𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 =
𝑀. 𝐴. 𝑤𝑖𝑡ℎ 𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛 𝑝𝑟𝑒𝑠𝑒𝑛𝑡
∙ 100%
𝑀. 𝐴. 𝑤𝑖𝑡ℎ 𝑛𝑜 𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛 (𝑖𝑑𝑒𝑎𝑙 𝑐𝑎𝑠𝑒)
CLASS PROBLEM: Consider the two class problems above, one WITH friction and on WITHOUT
friction. What is the efficiency of the inclined plane that includes the effect of friction?
This efficiency is equivalent to the ratio of the energy (or work) required to move a body up
an ideal inclined plane to the energy required to move a body up an inclined plane with
friction present. We will learn how to solve problems using conservation of energy later.