The inclined plane is a simple machine, and that reduces the force necessary to perform to raise a load. Is a flat surface at an angle of 90 degrees to the ground. Bodies were used to raise a certain height. Suppose we want to drag
weight from a height G 1 to a height 2, being in position 1 and 2 to which we refer, the center of gravity of the block represented in Fig.
The weight of the block, (which we know is a vertical vector quantity and down), can be decomposed into two components F1 and F2 ', parallel and perpendicular inclined plane respectively: F1 = G
· sin (α) = G ·
F2 cos (α)
As well, the surface of the incline, there generally a friction force FR that also need to overcome to move. This force is:
FR = F2 = μ μ · · G · cos (α) / μ being the coefficient of friction.
Analyzing the figure, it is clear that moving the block to get the force (F) that we make, is:
F = F1 + FR = G · sin (α) + μ · G · cos (α) = [sin (α) + μ · cos (α)] · G
Obviously, if instead of a slope, we tried to lift the block without more help than our own muscles, strength (G) that would have to do is simply the weight of the block due to the action of gravity, ie G
= P
The Inclined Plane is the starting point for a large group of operators and technology is undeniable cuya.utilidad mechanisms . Its main uses are three:
· The commonly used as a ramp to reduce the effort required to mass increase (roads, up cattle trucks, access to underground garages, stairs ...).
• In a helix to convert a rotary motion into linear (Archimedes screw, bolt, screw, boat propeller, nozzle ...) • In
wedge to tighten (holding doors not to close, assemble ...), cut wood pieces (knife, scissors, saw, saw ...) and remove or open (ax, plow, chisel opener .. .).
The ramp is a flat surface forms an acute angle to the horizontal.
The ramp is defined by its inclination, which can be expressed by the angle to the horizontal or percentage (ratio between the height reached about what moves horizontally, multiplied by 100). The latter is what is usually used to indicate the inclination of the road.
A bit of history.
Although the slope is an operator present in nature (as a ramp or slope) and had already been made wedge-shaped (arrowheads and spear axes ...) by prehistoric cultures, are not supposed to build ramps began consciously to the birth of the megalithic cultures (4000 BC) and the consequent need to move and use large blocks of stone.
With the advent of cars began to build roads that had to overcome significant geographical features (about 3000 BC)
Around 2800 BC, in Mesopotamia, began to be used in the form of stairs (ramp adaptation to the face human) in housing and social constructions. After the Romans
widespread use for the delineation of roads and water conveyance to the cities (aqueducts).
The ramp is an inclined plane whose utility is focused on two aspects: reducing the effort required to lift weights and run the drop objects or liquids.
reduction effort. The ramp can lift heavy objects more easily than doing it vertically. The route is longer (as the board of the ramp is always longer than the height to save), but the effort is less.
ramps can find this utility on roads, railways, garage access ramps, stairs, wheelchair access, fishing ports, pools ... Direct
falling objects or liquids. When you want to channel the downward movement of an object is also used the ramp, then adding a few simple guidelines (or using slants) can make the path taken is the one we want, avoiding unwanted deviations.
With this utility is used on roofs, gutters, water slides, water, bowling, water parks, vending machines, public telephones (guide for coins) ...
incline Formula motherboard
P = F = N
L hb
Here we describe a simulated practice that studies the motion of a body that slides along an inclined plane down and upward. From displacement measurements and times, is to determine the kinetic coefficient of friction μ and the acceleration of gravity g.
Assuming the incline angle θ is frictionless μ = 0
forces on the body are:
- The
mg weight reaction plane - N
As there is balance in the direction perpendicular to the incline
N = mgcosθ
Applying Newton's second law of motion along the plane
Ma = mgsenθ , a = gsenθ,
If the body starts from rest at position A, the equations of motion are: v = gsenθ
· gsenθ · tx = t2 / 2 Famous
angle θ which is the incline with the horizontal displacement x of the mobile between A and B and time t that used to travel, solve for the acceleration of gravity g
When there is friction Normally
frictionless inclined plane, so it is necessary to take measurements when the body slides down, and when slides up.
- Moving Down
forces on the body are: Weight mg
reaction plane N
Fr friction force that opposes the movement of the body
assume that the friction coefficient μ is small so that is always true that tanθ> μ
apply Newton's second law of motion of the body in the direction of the inclined plane down.
ma1 = mgsenθ-Fr, Fr = μN = μmgcosθ
acceleration a1, a1 = g
worth (senθ-μcosθ)
x1del Measured body displacement from A to B and the time t1 used to travel based on A resting. From these two facts, we obtain the acceleration a1
apply Newton's second law of motion of the body in the direction of the inclined plane above.
ma2 = mgsenθ + Fr, Fr = μN = μmgcosθ
acceleration a2, voucher
a2 = g (senθ + μcosθ)
body is thrown in A with initial velocity v0, x2 displacement is measured from A to that for B, and the time you spend on travel t2. From these two facts, we obtain the acceleration a2. Given that the velocity v0 and the acceleration a2 are of opposite sign.
known accelerations a1 and a2 and the angle θ which is the slope to the horizontal world is a system of two equations with two unknowns which clears g μ.
a1 = g (senθ-μcosθ) a2 = g (senθ + μcosθ)
Measuring coefficient of kinetic friction and the acceleration of gravity
One of the difficulties pilot is to establish with precision the initial position and initial velocity of a body. It starts timing when the body initially at rest in a determined position, is released. It is also difficult to measure accurately the final position of the body when its velocity is zero, then stop the stopwatch.
These difficulties are avoided if we have along the inclined plane of three detectors that start and stop both timers.
PULLEY
A pulley, also called pulley, carrucha, trochlear, sheaves or cheek is a simple machine. This is a wheel, usually solid and grooved edge, which, with the help of a rope or cable that passes through the channel, is used as a transmission in machines and mechanisms for changing the direction of movement or joint-speed forming equipment or hoists, to also reduce the amount of force necessary to move a weight.
Pulleys are wheels with the outer perimeter specially designed to facilitate contact with ropes or straps. Throughout pulley
are three parts: body, hub and throat.
• The body is the element that connects the hub to the throat. In some types of pulleys are formed by spokes or blades to reduce weight and provide the ventilation of the machines they are installed.
• The hub is the central part covering the hole, increases the thickness of the pulley to increase their stability on the shaft. Usually includes a keyway that facilitates the binding of the pulley shaft or tree (for both spin solidarity).
The throat (or channel) is the part that comes into contact with the rope or strap and is specially designed to achieve the best possible grip. The deepest part is called a rim. You can take different forms (flat, semicircular, triangular ...) but the most used today is the keystone. Basically
pulley is used for two purposes: to change the direction of a force with ropes or transmit rotary motion from one shaft to another by straps.
In the first case we have a cable pulley that can be used in the form of fixed pulley, moveable pulley or hoist. Its usefulness is focused on lifting (snatch blocks, cranes, elevators ...), closing curtains, moving automatic doors, etc..
In the second case we have a belt pulley which is very useful to connect to other machines, electric motors (compressors, drills, fans, electric generators, chain saws ...) it allows to transfer rotary motion from one shaft to another. With this type of pulley mechanisms such as built-up gear, the gearbox and the gear wheels.
cable pulley is a type of pulley having a groove (channel) has been designed specifically for ease of contact rope therefore usually semicircular. The mission of the rope (cable) is to transmit a power (a movement or a force) between its ends.
The mechanism resulting from the union of a cable pulley with a rope is called a block and tackle.
This pulley can be found in two basic forms: as a simple pulley and a pulley hook.
A simple pulley is basically a pulley that is attached to another operator through the axis. Always accompanied by at least a bracket and a shaft.
support that holds the entire set and keeps it in a fixed position in space. It is part of another operator who is to hold together the pulley (wall, car door, housing the video ...).
The shaft has a double function: the axis of rotation of the pulley and locking system of the pulley to the support (usually a lag bolt, screw or rivet).
The hook block is a simple pulley change by replacing the media by an armature to which is added a hook, the rest of the basic elements (shaft, pulley and other accessories) are similar to the previous.
The hook is an element that facilitates the connection of the "hook block" with other operators through a fast and reliable connection. In some cases the hook is replaced by a screw or lag.
The block and tackle (a combination of pulleys and rope) is used in the form of fixed pulley, pulley or hoist Cell:
• The fixed pulley cable is characterized by its shaft is held in a fixed position in space preventing their movement. Because it is not the only mechanical gain focuses on practical use:
or reduce the friction of the cable changes direction (thus increasing its lifetime and reducing energy losses by friction) or change the direction
application of a force.
is located in the drive mechanisms of automatic doors, lift systems, car windows, elevators, awnings, lifting pulleys ... and combined with running blocks forming hoists. Cell
• The pulley cable is one that is attached to the load and moves with it. Because it is a mechanism with mechanical gain (to overcome a resistance "R" is necessary to apply only a power "P" slightly more than half of its value "P> R / 2") is used in moving cargo, but not in isolation but as part of hoists.
The hoist is a combination of fixed and movable pulleys. Because it is the main use of mechanical gain focuses on the lifting or moving loads. Can be found in cranes, lifts, tie rods.
