Gurumuda Networks
Diffraction grating – problems and solutions
1. A grating containing 4000 slits per centimeter is illuminated with a monochromatic light and produces the second-order bright line at a 30° angle. What is the wavelength of the light used? (1 Å = 10-10 m)
Known :
The distance between slits (d) = 1 / (4000 slits / cm) = 0.00025 cm = 2.5 x 10-4 cm = 2.5 x 10-6 meters
Order (n) = 2
Sin 30o = 0.5
1 Å = 10-10 m
Inelastic Collisions
The conservation of kinetic energy law is not applicable in inelastic collisions. The conservation of momentum law is applicable in inelastic collisions if only no external force acts on the two colliding objects. In an inelastic collision, two objects stick together or are attached to each other after the collision.
Example question 1.
Two objects are of the same mass, namely 1 kg. Object 1 moves on a flat plane at a speed of 10 m/s and collides with object two which is at rest. After the collision, the two objects stick together. What is the speed of the two objects after the collision?
Partially elastic collisions
In partially elastic collisions, the law of conservation of momentum is applicable, while the conservation of kinetic energy law is not applicable. At the time a collision takes place, some kinetic energy is converted to sound energy, heat energy, and internal energy. The use of the word elastic signifies that after the collision, the two objects do not stick together but bounce off.
An example of partially elastic collision is the one-dimensional collision of two marbles or two pool balls.
Conservation of linear momentum
Law of conservation of linear momentum states that if there is no external force acting on two colliding objects, the momentum of the objects before the collision is equal to the momentum of the objects after the collision.
p1 + p2 = p1 ’ + p2 ’ ………………….. Equation 1.4
m1 v1 + m2 v2 = m1 v1 ’ + m2 v2 ’
If after collision both objects stick together,
m1 v1 + m2 v2 = (m1 + m2 ) v’
Perfectly elastic collisions
A collision of two objects is called a perfectly elastic collision if the momentum or kinetic energy of each object before the collision is equal to the momentum and kinetic energy of each object after the collision. In other words, the conservation of momentum law and conservation of kinetic energy law are applicable in perfectly elastic collisions. The use of the word elastic signifies that after the collision, the two objects do not stick together or are not attached to each other but bounce off. The momentum of each object is conserved.
The momentum of each object is conserved.
Work-mechanical energy principle
The work-kinetic energy theorem states that the net work or the work done by the net force is equal to the change in kinetic energy.
Wnet = KEt – KEo = 1⁄2 m(vt2 – vo2)
Wnet = There are two types of forces, namely conservative force, and non-conservative force. Thus, net work can be considered to be comprised of the work done by a conservative force and the work done by a non-conservative force.
Wc + Wnc = ΔKE
Work done by conservative forces Potential energy
Observe an object which moves vertically upwards and then return to its initial position after reaching a maximum height. When the object is moving vertically upwards, weight does negative work on the object. When the object is moving upwards, the object’s height increases. Therefore, the object’s gravitational potential energy increases as well. It can be concluded that the negative work done by weight is equal to the increase in the object’s gravitational potential energy (PE).
Conservative force and nonconservative force
1. Conservative Force
1.1 Weight (w)
Observe an object which moves vertically upwards until reaching a maximum height before moving downwards towards its initial position. When moving vertically upwards by h, the weight is opposite in direction from displacement. Thus, the weight does negative work on the object.
W = w h (cos 180o) = – w h = – m g h
After reaching a maximum height, the object moves downwards towards its initial position by h. When moving downwards, the weight is in the same direction as the displacement. Because it is in the same direction as displacement, the weight does positive work.
Work-Kinetic Energy principle
If net force works on an object, the object experiences acceleration (the object experiences displacement). When the object experiences acceleration, the speed of the object changes. In other words, the work done by the net force is related to the object’s initial and final speed.
The work done on an object by constant net force is:
Wnet = ΣF s
Newton’s second law states that if there is a net force working on an object, the object experiences acceleration.
Work done by force
1.1 Definition of Work
If you push a book on the surface of a table until the book is displaced, you are said to have done work on the book. If an object falls to the ground due to the pull of gravitational force, the gravitational force is said to have done work on the object. On the contrary, if you push an object with all your might to the point that you sweat profusely, but the object does not move at all, you are said to have done no work on the object. In everyday life, people might say that you have done hard work by pushing the object but in Physics, you did not do work on the object because there has been no displacement of the object.