Fig.1. Dad being lifted by a son. How come?
1. Levers
A lever is a rod or a plank used for any of the following purposes.
i. To change the direction or size of a force..
ii. To exaggerate or diminish a movement.
.It is generally believed that , a uniform stick supported at the middle will balance when the weights on the two sides are equal. A simple experiment may show that this can be a fallacy.
A demonstration
As the candle wax drops the paper cat and dog will go up and down, but not to London town.
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6. A slope , inclined plane, or ramp.
A car can be driven up only by using a sloping road. The force necessary to drive on a slope is much less than the force necessary to go up vertically. So a sloping road, , becomes a machine of the category called an Inclined Plane or a ramp.
Fig.2 The road becomes a simple machine,
Let us study the basics of the Machine called the Inclined plane or ramp. There has to be a difference in height which has to be conquered. The force has to be applied parallel to the slope
Fig.3 An experiment to find the effort .
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
(For only those who are clever in Mathematics.)
Calculations
Let the mass of car be = 500 g
Then the weight of car = 5N
Neglecting Friction we can calculate this Force
The work to be done in lifting the car 25cm = 25cm x 5 N (Useful work or OUTPUT)
= 125 (This is not Joule as distance is in cm)
Let F be the force necessary to move the car on the slope, which is the Effort.
Work done by effort will be = F x 100 cm
Work done by Effort = Work done by Load
F x 100 cm = 25cm x 5 N
Therefore F = 25 x 5/100
=1.25 N
( This will be the minimum force necessary to pull neglecting fricton)
Now let us work out the 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
This is sometimes called the Ideal mechanical advantage.
Real Mechanical advantage
In order to find the real Mechanical advantage it is necessary to determine the real Effort.
Let us assume the real effort necessary determined by experiment was 1.5 N
Then the real Mechanical advantage = 5N / 1.5 N = 3.3
Efficiency percentage
Percentage efficiency = Mechanical advantage / Velocity ratio x 100
= (3.3 / 4) x 100
= 82.5 %
Variations of slope
What has a screw in common with a slope ?
Fig 4 A Screw.
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'
st
ring slowly. The string will stretch as an incline.
Fig. The slope of a screw.
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 sub
jected to a very high force.
Fig.5 A clamp has a high velocity ratio.
Calculations
If the length of the handle is 20cm and the pitch(gap between threads) is 0.5cm let us find the Velocity ratio which is also equal to the highest mechanical advantage possible.
Effort is given by the handle. The load is the vertical force used to crush the object.
Distance effort moves is the circumference of the circle the hand makes with the handle
This would be = 2xpie x 20 cm (pie= 3.14)
Distance load moves = 0.5 cm (pitch)
Therefore Velocity ratio would be = 2x 3.14 x 20 / 0.5
= 251.2
As the friction is high the mechanical advantage will be less than this value.
WEDGE
Fig. 6 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.
The velocity ratio of this will be as follows;
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.
Which of these cannot be considered as a slope or a ramp?
a. A nut and bolt. b. a knife blade c. Escalator d. Lift.
2.0 Which is the correct SI unit to measure work?
a. Newton b. Calorie c. Joule. d. Watt.
3.0 Which is the correct formula to determine the amount of work done.
a. W= weight x horizontal displacement.
b. W = Weight x height moved.
c. W. = Mass x height moved.
d. W = Mass x displacement
4.0 Efficiency of a machine gives an idea of which of the following:
a. Amount of energy wasted.
b. Amount of energy used.
c. The power of machine.
d. How easy to perform a task.
5.0 Which two quantities are measured by the same units.
a. Weight and mass. B. Mechanical advantage and velocity ratio.
c. Energy and efficiency d. Energy and work. ( 10 x 5 =50 marks)
6.0 Jim says it is easier to cycle than to walk. But when he goes home, which is on a hill he has to get down and push the bike. Why is it so? (10 marks)
7.0
Henry has a mass of 70kg and he has to take concrete on a slope as shown. The weight of the cart and load is 1000 N. (1kg. = 10 N )
7.1 What is the work done on the load when he takes it to the top?
7.2 What is the work done by walking up to the top?
7.3 What is the force he has to give to push the cart along the slope?
7.4 What is the efficiency of the system.? (10 x 4 = 40 marks)
For answers visit answer page and go down alphabetical order
Fig. 2 Nelly’s balancing trick.
Nelly is trying to balance a 20cm long ruler . A coin is placed at one end 8cm away from the fixed point and two similar coins are placed 4 cm away. Do you think she can balance a heavy weight and a light weight? You can try this out for yourself.
Turning Effects of a Force (torque) We can solve this kind of problems by considering turning effects. The turning ability of a force does not depend merely on the magnitude and the direction of the force. The point where the force is applied also becomes crucial. Greater the distance from the fixed point to the point of force , greater will be the turning ability. Therefore in order to find the turning effect, which is called the MOMENTUM or TORQUE, we consider the product of force and the distance to fixed point. The fixed point is also called the Pivotor fulcrum.
Moment (Torque) = Force X Perpendicular Distance from Force to Pivot.
For an object to balance, that is to achieve equilibrium, the sum of the clockwise moments has to become equal to the sum of anti clockwise moments. This is known as the ;Law of Moments or the Principle of Moments.
What is the difference between a moment of a force and Torque?
Especially when we talk of forces that can maintain equilibrium of a lever the product of force and perpendicular distance to pivot is termed as a moment. When a force is used to create circular motion it is generally called a torque.
The Law of Moments
At Equilibrium,The sum of Clockwise Moments = Sum of Anti clockwise moments.
Fig.3. One hand pushes while the other pulls. This forms a couple.
Turning is a very common exercise we have to do in everyday life. There are often two parallel forces used either clockwise or anti clockwise. The torque of a couole is equal to the product of force and diameter of the circle.
Torque of a couple = Force x diameter.
Class of Lever
Class 1. Levers
order:- LOAD FULCRUM EFFORT
or EFFORT FULCRUM LOAD
Fig. 4 A garden fork being used as a Class 1 Lever.
EA - Effort arm, LA - Load arm.
Class 2. Levers
Order:- EFFORT LOAD FULCRUM
Fig.5 In lifting a wheelbarrow, we use it as a Class II lever.
Class 3 levers.
Order:- LOAD EFFORT FULCRUM
Fig.6 Fishing rod is often used as a Class III lever.
Weight of a Lever
Sometimes the weight of a lever also can help the lift. It is important to know where the weight of a certain body acts. The point through which the weight acts is called the ‘Centre of Mass’ or ‘Centre of Gravity’ and is usually denoted by the letter G. If you have a stick, which is not uniform, G has to be determined by an experiment. Shift the stick on a support until the two sides balance. The balancing point will be the Centre of Gravity.
Fig.7 Finding the Centre of Gravity of an un-even stick
An Experiment
Aim: To find the weight of a stick using some given weights,
First we must determine the Centre of Gravity of the stick. Attach a pan to the other end of the balance . You will be able to balance the stick at a point between it’s G and the added weight
Fig.8 Given weight balances the stick.
Formula to be used;
The sum of ACW moments = the sum of CW moments. ACW = Anti clockwise
CW = clockwise
That is
W1 x d1 = W2 x d2
Therefore W1 = (W2 x d2) ÷ d1
= (10 x 24) ÷ 16
= 15 N
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Wt. given W 2
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D 2
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D 1
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Weight of stick W 1
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10 N
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24cm
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16cm
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(10 x 24) ÷ 16
= 15 N
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Fig. 9. Acrobatics.
This is an acrobatic show. The weights of Nelly and the lever are pushing the heads of the two boys. Some weights and distances are given. You have to find the Reaction forces the boys have to give to maintain the equilibrium.
Data Sheet
Total length of the board = 3m
Weight of the board. = 120N
Weight of Nelly = 550N
Distance from Ali to Nelly = 0.75m
G is in the middle.
In this case the Fixed point or the Pivot is not given We may assume Ali or Bunty as the pivot and work out the CW and ACW moments.
Let A be the reaction force of Ali and B be the reaction force of Bunty.
The sum of ACW moments = The sum of CW moments.
B x 3 = (550x 0.75) + (120 x 1.5)
Therefore B = 592.5 ÷ 3
= 197.5
Similarly if you take B as the pivot we can get the Reaction force of Ali.
CW moments = ACW moments
A x 3 = (550 x 2.25 ) + (120 x 1.5)
A = 1417.5 ÷ 3
= 472.5
Verification
If your answers are correct R at A and R at B must be equal to the Weight of Nelly + Weight of Board.
Sum of Weights 120 + 550 ……….. = 670
Sum of R forces 197.5 + 472 .5 = 670
This shows that our answers are correct.
1.0
Nelly wants to post a parcel. In order to find the weight, he is using a steel meter ruler having a weight of 5 N. If the parcel can hang as shown find the weight of the parcel.
2.0 A man who found the balance he had could not measure a parcel used the following device using the same spring ba;ance. According to the readings in the diagram, what is the weight of the parcel?
3.0
The wooden bridge is 6 m long and has a weight of 300kg. Johnny standing 2m away from the right end is 40kg. Find the force acting at the two ends. The centre of mass (G) is in the middle.
3.1 Right end.
3.2 at the left end.
4.0
The Captain is steering a ship. He pushes the wheel with one hand and lifts with the other. There are two parallel forces acting on the wheel.
4.1What is the name of such a pair of forces, equal but opposite acting slightly apart ?
4.2 If the diameter of the wheel is 0.6 m and the Captain gives a force of 100 N with each hand in opposite directions what is the torque?
5.0
A spanner of 0.4 m hass a weight of 10 N . You have to unscrew a bolt on the wall,
5.1 What is the maximum useful force you can get on the bolt, using a 40 N force pushing up? (10 marks)
5.2 If you use the force in the opposite direction, from the same position of spanner, what is the maximum force you can get on the bolt? (10 marks)
5.3 Explain why there is a difference between the two above answers.
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What is a Machine?
A machine is a device that can transmit or change a force. There are three categories of simple machines.
They are .............1. levers, 2. Wheels, 3. Inclined plane
Pulleys come under Wheels while the Screws and the Wedge are variations of inclined plane.
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