Law of conservation of linear momentum
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Now let us look at Example 3.2 (page 91) ,which is an application of the Law of conservation of linear momentum principle.
A 1000 kg automobile (car 1) runs into the rear of a stopped car that has a mass of 1500 kg (car 2). Immediately after the collision, the cars are hooked together and their subsequent speed is estimated to be 4 m/sec. What was the speed of car 1 just before the collision?
By the conservation law,
the sum of the momentum of car 1 and car 2 before collision is EQUAL to sum of the momentum of car 1 and car 2 after the collision.
sum of the momentum of car 1 and car 2 before collision
= (mass of car 1)(speed of car 1 before it collides) + (mass of car 2)(0 m/s)
sum of the momentum of car 1 and car 2 after the collision
= (mass of car 1 + mass of car2) (speed of both the cars hooked together)
The two linear momenta are equal ,
(plug in the numbers);
Speed of car 1 before it collides = 10 m/s.
A bullet becomes embedded in a block of wood. If the speed of the block and the masses of the block and the bullet are measured, the initial speed of the bullet can be computed using the conservation of linear momentum. As a rocket gives momentum to the exhaust gases, it gains momentum in the opposite direction.
The law of conservation of energy is arguably the most important of the conservation laws. The concept of energy is very vital in trying to understand many physical phenomenon. The concept of energy is a bit difficult to understand because there is no simple way to define it. As an aid,we first introduce another physical quantity WORK .
Work is defined to be the product of a force that acts and the distance moved in the direction of the force. It is a scalar and its S.I unit is Joule (Symbol J).
Whenever an object moves and there is a force acting on the object in the same or opposite direction that it moves, work is done. When the force and the motion are in the same direction, the work is positive. When they are in opposite directions, the work is negative. It is important to note that work is not done if the force is perpendicular to the displacement. When you carry a box across a room, your force on the box is vertical, where as the displacement of the box is horizontal. Hence you do no work on the box.
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Let us look at Example 3.4 (Page 96) :
The barrel has a mass of 30 kg and that the height of the dock is 1.2 meters. How much work would you do when lifting the barrel?
Work = (Force)(distance moved in the direction of the force).
For a constant lift speed, the force is just the weight of the barrel ( = mg; where m is the mass and g is the acceleration due to gravity).
F = (30 kg) ( 9.8 m/s2) = 294 N.
Hence, work = Fd = (294 N) (1.2 m) = 353 J.
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Uniform circular motion is another situation in which a force acts on a moving body but no work is done.
Energy is the measure of a system’s capacity to do work. That which is transferred when work is done. Abbreviated E. The units of energy are the same as the units of work. Like work, energy is a scalar.
In mechanics, there are two main forms of energy, which we can classify under the single heading of mechanical energy. Anything that has energy because of its motion is referred to kinetic energy or because of its position or configuration has potential energy.
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