MACHINES

MACHINES

A machine is a device or tool which allows a force (or effort) applied at one point to overcome a resisting force (or load) at another point.

Mechanical  Advantage =  =

Velocity Ratio is defined as the ratio of the distances moved by the effort and load, in the same interval.

Velocity Ratio =

Efficiency of a machine is defined as the ratio of useful work done by the machine and work put into the machine.

Efficiency  =  x 100%  = x 100%

Total work done = Work done in raising the Load + work done against Friction.

TYPES OF MACHINE

1.        LEVER: This is one of simplest machines know. With it we can overcome a large resistance by the application of a small force. It consist of pivot or fulcrum, effort  and load.

Types of Lever

There are three classes of levers: first lever; second lever and third order.

First class of lever- The pivot is between the load and the effort. Examples are the crowbar, a pair of scissors or pincers, claw hammer and pliers.

Second class of lever: - The load is between the effort and the fulcrum. Examples are wheelbarrow and nut crackers.

Third order of lever: Effort is between load and fulcrum. Examples are the forceps, tongs, forarm.

2.        PULLEY: A simple pulley is a fixed wheel with a rope passing round a groove in its rim. A load, L,  is attached at one end of the rope and an effort, E, is applied at other end. If the friction and weight of the rope is negligible then , Effort, E, = Load, L, and also distance moved by the effort = distance moved by load. M.A = V.R = 1.

3.        BLOCK AND TACKLE SYSTEM OF PULLEYS: This is continuous passing of rope to move pulley. The Effort, E, is applied on one end of the pulley and round in moveable and non-moveable pulleys. If the effort moves through a distance, d, the load, L, move at d/4. If there are four pulley and four ropes then , V.R =  = 4.

In general, in block and tackle, with a string support the load, then V.R = n also M.A increase as n increases.

4.        THE INCLINED PLANE: This is when a rigid plane is kept inclined at an angle Ф to the horizontal.

 

 

 

 

Effort along AC and load through BC.

V.R =  =  ;  ;   =

V.R = , without friction, M.A = V.R. with friction, M.A < V.R and also affect efficiency.

5. WEDGE: This is machine like chisel, axes, knife etc used to separate materials e.g steel. The effort E is applied at the top through x2 and overcome a load L through x1.

M.A =  =  =  .    Also, V.R =  

6. THE SCREW JACK: This is simply a kind of machine like an inclined plane wrapped round a cylinder to form a thread. Eg bolt and nut, the distance between successive screw thread is called pitch, P. the input effort act through a distance equal to circumference of a circle of radius, r,

So,  V.R=   =

M.A = V.R, if there is no friction.

7. THE WHEEL AND AXLE: It consists of round cylindrical drum (wheel) and a smaller drum (axle) of different radius. If effort is applied, the wheel and axle rotate through one complete revolution equal to their circumference respectively.

So, V.R = = =

8. THE HYDRAULIC PRESS: A machine that small effort could lift a large load, the main part of it is called piston.

Effort = P x A1 = pressure in small piston x area of small piston

Load = P x A2 = pressure in large piston  x area of large piston

M.A = = ; where R and r are radii of large and small piston respectively.

9. GEAR WHEEL: It works with the principle of wheel and axle, commonly used in cars, bicycle and cranes. The wheel is of different radius. V.R = =

Examples

1.        A machine with a velocity ratio of 30 moves a load of 3000N when an effort of 200N is applied. The efficiency of the machine is.

Solution

V.R= 30; L= 3000N; E= 200N; Eff =?.

Mechanical  Advantage =  = = 15

Efficiency =   x 100% =   x 100% = 50%

2.        A screw jack whose pitch is 2mm is used to raise a motor car of mass 900 kg through a height of 20.0 cm. The length of the tommy bar of the jack is 40cm. if the jack is 60% efficient, calculate the : a. velocity ratio

 b. mechanical advantage of the jack           c. effort required.     d. work done by the effort.

Solution

P= 2mm = 2x10-3 m; m= 900kg; h= 20cm =0.2m; h= 40cm = 0.4m; Eff = 60%.

a.        V.R=   = 2x3.142x0.4/2x10-3 = 1256.8

b.        Efficiency  = x 100%;  M.A = Eff. X V.R/100 = 60x 1256.8/ 100 = 754.08

c.        Mechanical  Advantage =   ; Effort = load/M.A = 900 x 10 N/ 754.08 = 11.94N

d.        Efficiency =  x100%; work input = x 100% ; work output = 900x10N x 0.2m x100/60= 3000N

Workdone by effort = work out put = 3000N

Assignment

1.        A man uses a rope to haul a box of weight 600N up an inclined wooden plank of effective length 3.0m and onto a platform 1.0m high. If in doing so, he exerts a force of 400N on the rope, calculate:

a.        The frictional force between the case and the plank               b. The velocity ratio of the machine

c.     The mechanical advantage                                                     d. The useful work done in joules. 

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