What is a machine?
Ali:- Some device like a key of a door lock.
Nelly:- How can a key be a machine?
Ali:- Key is the simplest ‘simple machine’ that we can think of.
Bert:- What about a stick or just a needle?
Ali:- Quite so; they also can be used as simple machines.
As we go through the chapter we will realise why a key, a stick or even a needle can be considered as a machine.
Simple machines include 3 basic devices. They are Levers, ramp (inclined plane} and wheels and pulleys.
LEVER
Lever is a rigid bar that can change the direction of a force. Man pushes down as the load goes up.
| 2. RAMP
The car has to go up. It is much easier to take it on a slope than taking it vertically up. | 3. PULLEY
The pulley wheel and the load requires only half the weight to lift it up. |
Levers.
This diagram shows that the pushing hand has to move a greater distance than the load moves.
As work done by hand should be equal to work on load.
∴ effort x effort displacement =load x load displacement.
When the effort displacement is greater that load displacement, effort becomes less than load.
As effort displacement : load displacement = effort arm : load arm
We can use this formula for calculations.
Effort x effort arm = Load x load arm |
When using this formula, we assume that the weight of the lever is negligible or it is at the fixed point.
Velocity Ratio and Mechanical advantage.
These are two useful ratios with regard to simple machines.
Velocity ratio
= Distance Effort moves / Distance load moves. | Mechanical advantage. = Load / Effort |
In the case of an ideal machine . Velocity ratio = Mechanical advantage. |
Class of Lever
Class 1. Levers
order:- Load : Fulcrum : Effort More examples:- Pair of scissors. See saw, Garden fork, Advantage:- Whenever the effort arm is longer, the weight or any other force is opposing, there will be a mechanical advantage, That means effort will be less than the load. | Class 2. Lever
Order:- Effort: Load : Fulcrum
More examples:- Wheel barrow,
Advantage:- As the effort arm is always longer than the load arm, there will be a mechanical advantage. The weight of the lever will always oppose the effort. | Class 3 levers.
Order:- Fulcrum; Effort: Load. More examples:- Fishing rod, Advantage:- As the load arm is always longer than the effort arm the effort will be always greater than the load. The benefit of the system is that you can gain distance though force is sacrificed. |
An Experiment
Aim;-
To find the force necessary to pull a toy car along an inclined plane.
A string is tied to the car which is kept parallel to the slope. The string goes above a pulley and a pan is fixed at the other end. You have to add the weights to the pan until the car is about to move. This will give the effort. The load is the weight of the car.
Calculations
I. Amount of useful work to be done. Let the mass of car be =0.5 kg. Then the weight of car = 5N The work to be done in lifting the car up to 0. 25m. = 0.25 m x 5 N =1.25 J. (Useful work or OUTPUT)
| II. Minimum force necessary to pull the car. Let 'F' be the force. Work done by effort will be = F x 1 m. Work done by Effort = Work done by Load. ( Assuming no loss of energy) F x 1 m. = 0.25 m x 5 N Therefore F = 0.25 x 5/1 =1.25 N |
III. Velocity Ratio of the Machine. Velocity Ratio = Displacement of Effort Displacement of Load = 100/ 25 = 4.
Highest possible Mechanical advantage = Load ÷ Effort = 5 N / 1.25 = 4 Also called the Ideal mechanical advantage. | IV, Real Mechanical advantage. If there was a frictional force of 0.25 N
The force necessary to pull would be = 1.5 N In order to find the real Mechanical advantage it is necessary to determine the real Effort. Ideal MA = Load / Effort. 5N / 1.5 N = 3.3 |
Efficiency percentage
Percentage efficiency = Mechanical advantage / Velocity ratio x 100
= (3.3 / 4) x 100
= 82.5 %
2. Ramp.- Inclined plane.
There are 3 methods for a man to reach the top. The shortest distance is to climb the ladder. In this mode, he has to use a force equal to his weight to lift himself up. After climbing, the work done will be equal to weight (in newtons) x height.
Man’s weight = 65 N. The height = 4m. ∴ Work done = 260 Joules.(Nm)
In climbing up man has converted 260 J of kinetic energy to 260 Nm or J of gravitational potential energy.
If mhe man takes the green path he has to cover a longer distance, 4.5 m. yet he will climb the same height. So he will accumulate the same amount of potential energy. Potential energy = Force x distance. Force = potential energy/ distance. F = 260 Nm / 4.5 m ………...F = 57.8 N. | If the man takes the blue path he has to go 5 m. Yet he will climb the same height, 4m. So he too will accumulate the same amount of energy. Potential energy = Force x Distance. Force = potential energy / distance. F = 260 Nm / 5 m………..F = 52 N. |
Variations of Ramp
The Screw.
What has a screw in common with a slope ?
The slope or the inclined plane in a threaded nut or a screw nail can be clearly understood by a simple activity. Take a string and tie it at the lowermost point. It should be tight enough to prevent turning. Then wind the string along the groove upward. Tie the top end of the string to a post as shown here. Then unwind the string slowly. The string will stretch as an incline.
Velocity ratio The velocity ratio of the screw can easily be calculated by finding the height of the nail and the distance of the string that was wound round the threads.
Velocity Ratio = Length of the groove / Height of screw |
The screw may be used to get an enormous mechanical advantage. For this reason the velocity ratio has to be much higher as the friction in these machines is considerable. The Motor car mechanical jack is a very good example of this. The figure shows the use of screw in a clamp where an object can be subjected to a very high force.
Calculating the Velocity Ratio. Length of the handle = 20 cm Pitch (gap between threads) = 0.5cm. The load is the vertical force used to crush the object. Effort is given by the handle. Distance effort moves =2x 3.14 x 20 Distance load moves = 0.5 cm ( pitch) Velocity ratio would be = / 0.5 = 251.2 As the friction is high the mechanical advantage will be less than this value. |
The Wedge.
Fig. Ali is hammering a wedge.
A wedge is something like a double inclined plane. In Fig.4 Ali is hammering a wedge. The bottom end of this is almost a pint. This can easily enter a small crack in the timber. As Ali hammers the wedge it will go down widening the gap. By pressing a distance equal to the height we can get the two parts to widen by the length equal to the maximum width of the wedge.
The effort is used down while the load is sideways, pushing the two planks apart..
The velocity ratio = Height of wedge / width
Knives are wedges
All knives and cutting instruments have blades. Blades are nothing but wedges. As you press a knife on an apple the wedge (blade) separates the object into two portions.
Now you will know why a needle is a simple machine.
If a device can change the direction of a force or the magnitude , it becomes a machine. |
Pulleys and wheels are taken in a separate chapter.
Please click Pulleys.
Multiple choice
Questions 1 - 4
What type of a machine could these be:
A - Class 1 lever B Class 2 lever C- Class 3 lever D- Inclined plane (ramp)
- .
Q.5.and 6.
Son making an attempt to lift dad.
Substitute the correct values for this formula.
Effort x effort arm = Load x load arm. |
Q.5.
A- 500 x 3 = Dad x 1
B- Dad x 3 = 500 x 4
C- Dad x1 = 500 x 1
D- 500 x 2 = Dad x 1
A- E x 30 = 20 x 10
B- (Ex 20 + 2 x 5) = 20 x 10
C- E x 15 + 2x5 = 20 x10
D - E x 20 = 20 x 10
Q 7. And 8
Use the law:- Clockwise moments = Anticlockwise moments
A- 16 x 1 = w x 50 B- (W +5) x 50 = 16 x 50
C- (w+5) x 50 = 16 x 100 D - w x 50 = 16 x 100 + 5
Q.8.
Take A as pivot and use the law of moments. Take N as the reaction at N.
A- 24 x 1 +25x 0.8 = 2 x N. B- 25 x 1.2 = N x 2
C- (24 x 1) + ( 25 x 1.2) = N x 2 D- (24 x 2) + 25 x 0.8 = 2x N
Q.9. A machine must:-
A- have mechanical moving parts. B - reduce the required effort.
C- provide a force to work. D - change a force.
Q, 10.
Consider the work that has to be done in order to put the car at the higher level and calculate the minimum force necessary for the process.
A - 10 x 5 / 20.N. B- 10 x 20 /5 N
C- 10 x 20 N D- 10 / 20 N.
Answers highlight to get the answers.
1. C , 2- A. 3-B, 4- D. 5- D, 6- B ,7- C, 8- C, 9-D, 10- A,