A force acting over a distance to move something is the definition of work. In
order for any work to be done there must be movement.
Work= force x distance
The formula for work is:
Work=N∙M or Joule (J)
Power is the rate at which work is done, or the amount of work per unit of time.
The formula for power is:
Power = work
OR power=force x distance
Power is measured in watts and they are named after James Watt (inventor of the first
steam engine).
One thousand watts is equal to one kilowatt (kw). The electric company measures the
electric power used in your home in kwh. Horsepower is the power that one horse could
do = 745.56 w, originally it was the power necessary for a strong horse to move a 750N
object one meter in one second. Horsepower is commonly used to measure the power of
engines and motors.
Machines are devices that help us to do work easier! Some examples of early
machines are stones (used for tools), tree branches (pry up heavy objects), carts with
wheels (carry objects). Machines make work easier because they change the size or the
direction of the applied force. So, in other words, machines either lessen the amount of
force you have to apply and/or they change the direction and distance an object has to
move. There are always two forces involved when using machines to do work.
Effort force (FE) and Resistance force (FR)
(FE) effort force is force that is applied to a machine.
(FR) resistance force is force applied by a machine.
(DE) effort distance is the distance through which a machine moves or distance through
which the effort force is applied to a machine.
(DR) resistance distance is the distance through which the resistance force is applied or
the distance through which the object moves.
(WI) work input is work done on a machine equal to the effort force times the distance
through which the force is applied.
(WO) work output is work that is done by a machine equals resistance force
times the distance through which the force is applied.
Formula for work input
Formula for work output
Work output (WO) can never be greater than the work input (WI). Although machines
make work easier, they do not multiply work.
Mechanical Advantage is the number of times a machine multiplies the force.
Formula for mechanical advantage is:
Mechanical Advantage = Force of resistance \ Force of effort
Sample Problems: If a crowbar allows you to exert only 20 newtons of force to raise a
200 newton object, what would its mechanical advantage be?
MA = 200N / 20 N
MA = 10.0 (There is NO Unit for MA)
The mechanical advantage of a machine can be greater than one, equal to one, or less
than one. It depends on how it changes the force you apply.
Efficiency is the comparison of work output to work input and is always expressed as a
Efficiency = (Work output/ Work input) x 100
E= (WO x WI) x 100
The efficiency of a machine can NEVER be greater than 100! Machines always have
parts that rub on something, so you always loose some effort to overcome FRICTION.
Due to this, no matter how much effort force you put into a machine you can never get a
greater work output from the machine!
A slanted surface used to raise an object is called an inclined plane. When an
inclined plane is used a smaller effort force is required to move the object but the object
is moved over a greater distance.
The formula for finding the mechanical advantage of an inclined plane is:
MA= length of the plane / height
The length of an inclined plane can never be shorter than its height! Therefore,
the mechanical advantage of an inclined plane is always more than one.
The threads of a screw are like an incline plane wrapped around a cylinder to
form a spiral. The closer the threads of a screw are the greater the mechanical advantage
of the screw, because the longer the incline plane.
A wedge is an inclined plane that moves. The longer and thinner the wedge is,
the effort force is required to do work.
A kind of wedge is an inclined plane, double wedge and single wedge. The use
for these wedges are to cut, split or fasten. (a tack, a nail, a knife, an axe and a chisel).
The formula for levers is: MA = effort arm force / resistance arm length
Resistance is the object moved and effort is the force placed.
SYMBOLS: F=fulcrum R=resistance E=effort
Resistance = object moved
Fulcrum = pivoting point
Effort = force is placed
Some examples of levers are a bottle opener, a fishing pole, a seesaw, a broom, a
pair of pliers, and a wheelbarrow.
A lever that rotates in a circle is a wheel and axle. A wheel and axle is made of
two wheels of different sizes. The axle is the smaller wheel. The effort force is applied
to the wheel. Some examples of wheels and axles used everyday are a ferris wheel,
wheel chair and the wheels of a car.
The formula for the mechanical advantage of a wheel and axle is:
MA= radius of wheel
radius of axle
A small force on the wheel produces a larger force on the axle. A large
movement of the wheel edge produces a small movement of the axle.
A pulley is a chain, belt or rope wrapped around a wheel. Pulleys can change
either the direction and/or amount of effort force.
FIXED PULLEY: a fixed pulley is a pulley that is attached to a stationary object
(wall, ceiling, etc.). A fixed pulley can not multiply effort force, but it can change the
direction of the force which might make life easier.
The mechanical advantage of a fixed pulley is one.
Effort force = resistance force
MOVEABLE PULLEYS: a moveable pulley is suspended from a rope and can
move with the effort force. Moveable pulleys can multiply effort force but they cannot
change direction of effort force.
The mechanical advantage of a moveable pulley is greater than one. To
find the mechanical advantage of a pulley system you would count the number of
supporting sections of rope.
The two parts of a pulley are the rope and the grooved wheel. Some examples of
everyday pulleys are an elevator, a crane, or window shades.