聆听和学习科学/力
< 聆听和学习科学
Everyday, we experience, a number of forces, around us. They are so common, we do not even pause, to think about them. Let us discuss, a few examples, of common, everyday forces. Do you feel that, your school bag, is little heavy? Blame it on gravity. Gravity is ever present, everywhere, near earth. It is a force, by which, the earth attracts, all bodies, towards it. We should be thankful, to gravity though. Without gravity, all of us, and many other things, including the chair and table, will be flying around. This force by which, earth attracts bodies, towards it, is called, gravitational force. When something is too heavy, for us to lift, like in a railway station, we take the help, of the porter. The weight of the entire luggage, on the porters head, is a force, acting down upon him. He uses his muscle power, to carry the luggage, for you. Our muscles can also, exert force. A weight lifter spends, a lot of effort, to strengthen his muscles. The weight lifter, uses his muscles, to lift a heavy weight. Let us take an example, of sitting in the chair. Our weight exerts, a downward force, via the chairs legs, to the ground. The ground fortunately, is able to resist, this force. So, we are able, to comfortably sit. If we try standing, in a wet paddy field, we might sink, a few inches. This is because, the wet soil, is not able to fully resist, our body force. Of course, if we try, standing on water, we will immediately, sink. Water is unable to resist, our body force. On the other hand, a log of wood, floats on water. An ice cube, in a glass of water, floats on top. Here, in these examples, the log of wood, and the ice cube, are lighter than, water. The water is able, to resist the force, and hold up the log of wood, and the ice cube. Though, we are heavier than water, we can design a boat, which can carry us. We can even design ships, which can carry, a lot of passengers. Upward force exerted by water, on the log of wood, ice cube, boat, ship, is called buoyancy. The design of boats, and ships, involves working with, forces.
A tree is able to stand, because its roots, give its strength. Sometimes, when there is a strong wind, the wind force overcomes, the force of the roots, the tree topples over. The roots of a tree, is like a foundation, for the tree. In cities, when we build roads, and buildings, we tend to cut, the roots of the tree. In cities, when there is a strong wind, some trees succumb, to the wind force, and fall down.
A building to stand, also requires a foundation. The larger the building, the stronger the foundation, needs to be. Engineers, work on these forces, when they design buildings. They are called, structural engineers.
In fact, our body itself has a structure. It is called, the Skeleton. Without a skeleton, we will tend to flop down, on the floor.
Many things that we use normally, needs to be, structurally designed. Structural engineers, work on designing cars, aircrafts, and machineries.
When the forces, acting on the body are balanced, the body does not move. The forces are very much there, but it is not obvious. When a body is under a balanced force, it is said to be, in "equilibrium". It is good to remember, that engineers do a lot of calculations, to keep a mechanism, in equilibrium.
When we eat an apple, we can easily bite, into it. The apple is unable to resist, the force exerted by our teeth. If we try to eat a coconut, you will find it very difficult, to get through the shell. The coconut shell, is able to resist, the force applied by our teeth.
If we take a piece of paper, we can easily tear it, into two. The paper is unable to resist, the force we apply on it. If we try to tear our handkerchief, into two, you will find it difficult. The cloth, in the handkerchief, is able to resist the force, we apply on it. This is called, the shearing force.
If we take a thin cotton string, and pull it on both sides, we can easily snap it into two. If we take a rope, and try the same thing, we will find it very difficult to do so. If we take a metal wire, and pull it, it will be very difficult, to break it. These forces are called, tensile forces. A tensile force can sometimes, cause a body, to compress, or elongate. If we sit, on a bicycle seat, the spring will compress a little, before it settles down. Your weight is causing, the spring to compress. When we pull, a rubber band, it elongates, or stretches. The force we apply, causes this elongation.
There is another force, which is almost everywhere. It is a force, of friction. When we walk, it is the force of friction, which helps us to get a grip, on the ground. When we walk on a floor, wet with soap water, we tend to slip. This is because, the soap water, has very little friction, to resist the force, applied by us. This is also, why it is difficult, to walk on solid ice. Ice offers, much less, frictional resistance. It is also, why skaters can almost effortlessly, skate on solid ice.
A Parachutist , who is coming down, from an aircraft, in a parachute, is able to land gently. This is because, the wind resistance, is able to counter act, his body weight.
Let us think of some examples, in our experiences, where a force, causes objects to move. If we kick a football, which is at rest, it tends to shoot forward. The force that we applied, is causing, the football to move. If we throw a tennis ball, it travels some distance. So, greater the force, more the movement. When we pedal our bicycle, we are applying our force, which causes, the wheels to turn. The force that we applied, results in forward motion, of the bicycle. A car engine generates, the force required to propel, the car forward. A jet engine generates, the force required to propel, the jet forward.
We had discussed earlier that, when the forces are balanced, the body remains at rest. We now can visualise that, when an unbalanced force, acts on the body, it causes it to move. The example of the football, cricket ball, bicycle, car, and jet, are cases, where an unbalanced force, is in action. In simple terms, an unbalanced force, causes the body at rest, to move.
Newton, was a 17th century, English physicist, and mathematician. He published the book, "mathematical principles of natural philosophy". These principles stated, the 3 universal laws of motion. The 3 laws of Newton, laid the foundation, for most of, classical mechanics. Newton also, conceived the concept, of gravity. He defined the law, of universal gravitation. Newton also contributed, to the field of optics, and calculus.
The first law, of Newton states that, An object remains at rest, or moves at constant velocity, unless acted upon, by an external force. We can state this law, in two parts, as follows. 1. An object, which is at rest, will stay at rest, unless an external force, acts upon it. 2. An object, which is in motion, will not change its velocity, unless an external force, acts on it.
In a simple language, we can say all objects, resists changes to their state. Objects tend to keep, on doing what they are doing. This can also stated as, an object, has "inertia". The English meaning of "inertia", is tendency to do nothing, or remain unchanged. Interestingly, the mass of an object represents, its inertia. The larger the mass, the greater the inertia. It is easy to throw, a tennis ball. It is difficult, to move, a huge piece of rock. So, more the mass, more the inertia.
We can easily understand, the first part, of Newtons first law, in a simple way. A foot ball, in the field, will stay at rest, unless you kick it. We can easily appreciate, objects will not move, unless you apply, a force on it.
The second part of Newtons law states, An object, that is in motion, will not change its velocity, unless an external force, acts on it.
A body of mass "m", moving with a velocity, of "v", Will continue to, move with a velocity, of "v", When there is no external force, acting on it. When a body is moving, with the same, or uniform velocity, It is called, uniform motion.
The second part of Newtons law, is not so obvious, on earth. This is because, many other forces, are acting on the object, on earth. The examples, of the forces are, Gravity, Friction, Wind resistance, etc. The foot ball you kicked, will not keep on moving. Gravity, Friction and wind resistance, will act on it. It will slow down the foot ball, and ultimately bring it to a stop.
But let us remember, that Newtons first law, holds good, only if there is no external force, acting on it. This is almost true, in outer space. In outer space, there is no significant, gravity, friction, or wind resistance. In the space station, astronauts float freely. A space craft, moving towards mars, in outer space, with constant velocity, will continue to move, with the same constant velocity.
If an object is moving, it is said to have momentum. If an object, with mass "m", is moving with a velocity of "v", its momentum is =, "m", multiplied by "v". So, momentum, is =, "m, v". The S I unit for mass, is kg. The S I unit for velocity, is metre per second. The S I unit for momentum is kg, metre per second.
One way to state this law, is the force applied, on an object, is equal to the rate of change, of its momentum. A Mass "m", has an initial velocity, of "u". Its initial momentum, is "m, u". It has a final velocity, of "v". Its final momentum, is "m, v". It takes "t" seconds to increase, the velocity from, "u" to "v". So, the rate of change of momentum, is "m, v" minus "m, u", whole divided by "t". According to Newtons second law, force is =, rate of change of momentum. Force is =, "m, v" minus "m, u", whole divided by "t". Force is =, "m" multiplied by "v" minus "u" whole divided by "t". We know that, acceleration =, rate of change of velocity. "v" minus "u", whole divided by "t", is =, acceleration. Substituting, Force =, Mass multiplied by, acceleration. Force is usually represented, as capital "F". Mass is represented, by lower case "m". Acceleration is represented, by lower case "a". So, Force is =, "m, a". "F" =, "m, a". This is the most popular way, adopted to represent, Newtons second law. We just say, "F" =, "m, a".
In fact, the unit of force, is defined, using the equation, “F” =, "m, a". The S I unit of acceleration, is metre per second squared. The unit of force is kg, metre per second squared. This formula is widely used, in engineering and science.
A Force is required to increase the velocity, of an object, with mass of 20 kg, From an initial velocity, of 2 m/sec, To a final velocity, of 10 m/sec, In a time, of 4 sec. This requires the object, to be accelerated, from, 2 m/sec to 10 m/sec, in 4 seconds. The required acceleration is 10 minus 2, divided by 4, Which is 2 metre per second squared. Force = Mass into acceleration. Force = 20 multiplied by 2. = 40 Newtons. So, force required is =, 40 Newtons.
We will review, some of the examples discussed earlier, When we kick a foot ball, the force gives acceleration, to the ball. When we hit a six in cricket, the force gives acceleration, to the cricket ball. If we pedal a bicycle, it gives the force, required to accelerate. When a car accelerates, to a higher speed, the engine gives, the force required.
We can review Newtons first law, in light of Newtons second law. Force is equal to, Rate of change of momentum. "F" =, "m, v" minus "m, u", divided by "t". Transposing, "FT" =, "m, v" minus "m, u". When there is no force, "F" =, "0", Then, "m, v" minus, "m, u" is =, "0". That is, "m, v" =, "m, u". That is, "v" =, "u". There is no change in velocity. The first law of Newton, is consistent with, the second law. When there is no external force, there is no change of velocity. The body moves with, uniform velocity.
Gravity is ever present, everywhere near Earth. It is the force, by which earth attracts, all bodies to it. The gravity of the Earth, is denoted by lower case, "g". It is equal to, 9.81 m/sec squared. All objects are attracted, by gravity with an acceleration, of 9.81 m/sec squared. A mass of 1 kg, will apply a force, of 1 multiplied by 9.81, = 9.81 Newtons, on Earth. On the moon, this will be one sixth, of what it is on earth. You will weigh only, one sixth on the moon, of what you weigh on earth. This is because, the gravitational pull of the moon, is one sixth, that of earth. If you are able to do a high jump, of 3 feet on earth, you can jump, 18 feet on the moon.
One way to state this law is For every action, there is an equal, and opposite reaction. This means that, When a body exerts a force, on a second body, The second body, simultaneously, exerts a force, Equal in magnitude, and opposite in direction, On the first body.
Let us experiment with, what is meant by Equal and opposite reaction. Let us try, to lightly bang the table, with our bare hand, We feel, a sense of discomfort. This is because, when we exert a force, on the table, with our hand, It exerts, an equal and opposite force, on our hand. Let us try, banging the table, a little harder. This causes, our hand to hurt. The harder, we bang the table, with our bare hand, The more, our hand hurts. This means, the more force, we exert on the table, The same force, is exerted by the table, on the hand.
We will find a lot of examples, of Newtons third law, around us. Our mother breaks a coconut, by banging it, on a hard stone. In this case, the stone exerts, a reverse force, which is enough, to crack the coconut.
When we swim, we push the water back, with our palms. This propels us, forward in the water.
When we row a boat, The oars push, the water back. The boat gets, propelled forward.
A jet engine expels air, at high velocity. This propels the jet aircraft, forward.
There is one more law, which can be derived, from Newtons laws. This is the law, of conservation of momentum. Momentum of a body =, mass multiplied, by velocity. Momentum =, "m, v". The law of conservation of momentum, says, When two bodies interact, the total momentum, is conserved. That is, the total momentum, before the interaction, Is the same as the total momentum, after the interaction.
Let us consider, two balls with mass, "m1" and "m2". Ball with Mass "m1," is moving with, a velocity of "u1". Ball with Mass "m2", is moving with, a velocity of "u2". Momentum of ball, with mass "m1", is "m1, u1". Momentum of ball, with mass "m2", is "m2, u2". Total momentum =, "m1, u1", + "m2, u2". These two balls collide. After the collision Ball with Mass "m1", moves with, a velocity of "v1". Ball with mass "m2", moves with, a velocity of "v2". After the collision, Momentum of ball, with mass "m1", is "m1, v1". Momentum of ball, with mass, "m2", is "m2, v2". Total momentum =, "m1, v1", + "m2, v2". According to the law, of conservation of momentum, Momentum before collision =, Momentum after collision. "m1, u1", + "m2, u2" =, "m1, v1", + "m2, v2".
Let us take, a simple example, of a pistol, firing a bullet. Mass of the pistol, "m1" =, 2 kg, Which is =, 2000 grams. Mass of the bullet, "m2" =, 20 grams. Before firing the bullet, Initial velocity of pistol, "u1" =, 0. Initial velocity of bullet, "u2" =, 0. Initial momentum, = "m1, u1", +"m2, u2", =, 0. After firing the bullet, it reaches a final velocity of "v2", of 150 m/sec. What will be, the velocity, of the pistol?
Final momentum =, "m1, v1", + "m2, v2". = 2000, multiplied by "v1", + 20, multiplied by 150. Since, initial momentum is 0, Final momentum, is also = 0. So 2000, multiplied by "v1", + 20, multiplied by 150, = 0. Transposing, 2000 "v1" =, minus 3000. "v1" =, minus 3000 divided by, 2000. "v1" =, minus 1.5 m/sec. What it means, is after firing the bullet, The gun will recoil, In the opposite direction, At a speed, of 1.5 m/sec.