
Gravitational Force
Gravitation simply refers to the force of attraction between all object that tends to pull them toward one another. it is a universal force affecting the largest and smallest objects, all forms of matter and energy. Gravitational force governs the motion of astronomical bodies. It keeps the moon in orbit planets of the solar system in orbit around the sun. The gravitational attraction of objects for one another is the easiest fundamental force to be observed and was the first fundamental force to be described with a complete mathematical theory by the English physicist and mathematician sir Isaac Newton.
Gravitational force plays an important role in most processes on the earth. The gravitational pull of the earth on all objects holds the object to the surface of the earth. Without it, the spin of the earth would send them floating off into space.
The gravitational attraction of every bit of matter in the earth for every other bit of matter amount to an inward pull that holds the earth together against the pressure forces tending to push it outward. If an object near the surface of the earth is released, it will fall and accelerate or pick up speed, as it descends. This acceleration is caused by gravity, the force of attraction between the objects and the earth.
The force of gravity in the object is also called the object’s weight. This force depends on the object’s mass, or the amount of matter in the object. The weight of an object is equal to the mass of the object multiplied by the acceleration due to gravity.
Momentum
Momentum is an important property of a moving object. It explains its tendency to continue to move a straight line. Momentum of a body is the product of its mass and its velocity.
i.e momentum =mv
Since the unit of mass (m) is the kilogramme (kg) and the unit of velocity (v) is ms’, then the S.I unit of momentum is kgms, it is a vector quantity, it has both magnitude and direction. Its direction is the same as that of the velocity.
Thus a boy of mass 50kg moving with a velocity of Im/s has a momentum of 50 x
A body of mass 3kg with velocity of 10m/s has the same momentum as body of mass 6kg moving with a velocity of 5m/s.
However, the concept of momentum can be applied to various bodies. It will be observed that when thrown with the same velocities, a table tennis ball will have a lower momentum than a stone, because the mass of the stone is much more greater than that of the tennis ball. Also, when a bullet is fired by a gun, the gun jerks backwards and recoil, because the mass of the gun is much larger than that of the bullet, the velocity and the kinetic energy of the gun are much smaller than those of the bullet, the propulsive force (action) acting on the bullet must be equal and opposite to the recoil force (reaction) acting on the gun.
Newton’s Law of Motion
First Law: it states that a body will continue in its present state of rest or if it is in motion, will continue to move with uniform speed in a straight line unless it is acted upon by a force. This tendency of a body to remain in its state of rest or uniform motion is called the inertia of the body. For this reason the first law is sometimes referred to as the law of inertia. It is important to realize that once a body is moving with uniform speed in a straight line it needs no force to keep it in motion provided there are no external or accelerating forces. For example a rocket thrust into space. In general however, from common experience it does not appear that Newton’s 1st law is obeyed, because it is known that a body moving in a straight line with uniform speed does not move forever, but come to rest after a time. It does not mean that the law is not obeyed or valid.
The body will come to rest because opposing force such as air resistance and friction can gradually reduce its speed. For example, a body thrown into the air is opposed by air resistance and the pull of gravity. Sooner or later it returns to the earth. If air resistance and gravitation could be removed, the body will continue to move in a straight line forever.
Second Law: It states that the rate of change of momentum of a body is directly proportional to the applied force and takes place in the direction in which the forces act.
i.e force a change in momentum
F=Kma where K is Constant
The impulse of a force which is the measure of the time for which a force acts on a body can be deduced from Newton’s second law.
Ft = mv-mu
The quantity Ft is called the impulse of the force (I). The S.I unit of impulse is Newton second (Ns) and since it as equal to change in momentum, it means that momentum can also be expressed in Ns.
Third Law of Motion: It states that “to every action there is an equal and opposite reaction”. This implies that when a body A exerts a force FA on a body B, the body B always exerts a force FB on the body A. The force FA and FB are equal in magnitude but opposite in direction.
FA = -FB. For example when you hit your hand on the wall, the force exerted by your hand acts on the wall, at the same time the wall exerts an equal and opposite force on your hand. You then feel this reaction in your hand as pain.
Worked examples:
A force of 10N acts for 20s. What is the change in momentum of the body?
Impulse = Ft= change in momentum
F =10N, t =20s
Change in momentum =F x t
= 10 x 20 = 200 Ns
A body of mass 5kg moving with a speed of 30m/s is suddenly hit by another body moving in the same direction, thereby changing the speed of the former body to 60m/s. What is the impulse received by the first body.