Back end - KP Physics

^Sun appears red at Sun rise & sun set

January 13, 2022/in Back end /by kp-web-admin

^Sun appears red at Sun rise & sun set

This is because at Sun rise & sun set light passes through greater thickness of atmosphere, as a result more scattering takes place & blue colour & low wavelengths are scattered away by the scattering caused by the atmosphere & the colour which reaches us is unscattered red.

General scattering

When size of obstacles encountered by the light is much greater than the wavelength of light used, all wavelengths of light are scattered equally.

^Dangers signals are made red

January 13, 2022/in Back end /by kp-web-admin

^Dangers signals are made red

Danger signals, traffic lights etc. are made red. Red light being longest wavelength is scattered least & hence can go to large distance without any appreciable loss due to scattering.

^Sky appears blue

January 13, 2022/in Back end /by kp-web-admin

^Sky appears blue

As blue colour has least wavelength, hence when white light encounters obstacles of size a << λ, blue colour is scattered max. Due to this reason sky appears blue.

^Scattering of light

January 13, 2022/in Back end /by kp-web-admin

^Scattering of light

When unpolarized light falls on a gas or air molecules light falling on air molecules. The electric field of light polarises the air molecule makes it an electric dipole, which starts oscillating under the influence of oscillatory electric field of light & these dipoles radiate electromagnetic waves in all directions. This process is called scattering of light & the radiated light is called scattered light, it is unpolarized & intensity is found to be strongest along a line perpendicular to the oscillation, & drops to zero along the line of oscillation. The amount of scattering depends on the obstacle size coming in its way e.g. dust particles, rain drops, ice particles etc. We have divided scattering in two type.

1. Rayleigh scattering

When size of obstacles encountered by the light is much smaller than the wavelength (a << λ) of light used, the amount of scattering is inversally proportional to the fourth power of the wavelength of light.

^Problem solving tips

January 12, 2022/in Back end /by kp-web-admin

^Problem solving tips

If a particle is moving on a circular path with angular speed w about the center, then its angular speed about a point on the opposite side of the diameter passing through it is w/2.
If uniform speed remains constant then the motion is called uniform circular motion. Magnitude of v, a_t & a_n respectively are
On a rigid body all points undergo same angular displacement (θ) in same time interval thus all the points on a rigid body rotate at same angular speed (ω) & have angular acceleration (α), thus v, a_t & a_n ∝ r. Thus a point situated farthest from center circle will have maximum value of speed, tangential acceleration & normal acceleration. Also a point at center will have zero values of v, a_t & a_n.
is a unit vector directed radially or normally outwards.

^Kinematics of circular motion

January 12, 2022/in Back end /by kp-web-admin

^Kinematics of circular motion

Suppose a particle is rotating anticlockwise in a circular path in xy plane. Its angular velocity vector at any point on circular path w.r.t. center is

^Inclined plane projectiles

January 12, 2022/in Back end /by kp-web-admin

^Inclined plane projectiles

^Horizontal range

January 12, 2022/in Back end /by kp-web-admin

^Horizontal range

Horizontal distance in the plane of projection is called horizontal range, it is

Horizontal range is same for complementary angles.

The product of time of flights of two projectiles fired from same point with same speeds at complementary angles is

Vertical range

Diagram above shows a situation a projectile is fired at a speed u = 25 m/s. On changing the angle of projection its range and height changes. Note horizontal range is same for complimentary angles. Also vertical range is maxi if projection angle is maxi.

Facts

In going from O to A the following changes take place

Change in speed = zero
Change in velocity = 2u sinθ
Change in momentum 2 mu sinθ
in kinetic energy = zero
Change in potential energy = zero
Change in the direction of motion = ∠ 2θ

Facts

Three particles A, B and C are thrown from the top of a tower with the same speed. A is thrown straight up, B is thrown straight down and C is thrown horizontally, then the speeds & time on hitting the ground are given as:

v_A = v_B = v_Cand t_A> t_C > t_B

2. Suppose a body projected vertically upwards from the top of tower of height ‘h’ reaches the ground in t₁ second. If it is projected vertically downwards from the same top with same velocity, it reaches the ground in t₂ seconds. If it is just dropped from the top, it reaches the ground in t second, then

^Time of flight

January 12, 2022/in Back end /by kp-web-admin

^Time of flight

From point F.5. b (ii) we know v_y = zero at

projectile reaches its maximum height from point of projection. In the absence of air friction, wind & upthrust (actually all forces other than gravity) projectile takes same time to return back from maximum height to level plane of projection i.e. to travel path OPMA will be twice of this time, the total time to travel path OPMA is called time of flight (T), thus