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Equilibrium – Numerical Problem

SOLID HEMISPHERE OF RADII R EACH, are placed in contact with each other with each other with their flat faces on a rough horizontal surface. A sphere of mass m and radius R is placed symmetrically on top of them. The normal reaction between the top sphere and any hemisphere assuming the system to be in state equilibrium is

Time Dilation problem – Special Relativity

With what speed will a clock have to be moving in order to run at a rate that is one half the rate of a clock at rest?

Posted by Mona

Answer:

Using the formula for Relativistic Time (according to Special Theory of Relativity)

T=\frac{T_{0}}{\sqrt{1-\frac{v^{2}}{c^{2}}}}

√[1 – (v²/c²)] = ½ → v² = (3/4)c²

v = [√3/2]*c = .866c

 

Question from Special Relativity

A spacecraft starts from earth moving at constant speed to planet A which is 20 light-hour away from Earth.

Edit 1 of :Image:Soyuz_TMA-7_spacecraft2.jpg b...

It takes 25 hour (according to an earth observer) for a spacecraft to reach this planet. Assuming that clocks are synchronized at the beginning of the journey, compare the time elapsed in the spacecraft frame for this one-way journey with the time elapsed as measured by an earth-based clock?

Posted by Mona

Angle between acceleration and velocity in projectile motion

What is the angle between the directions of  acceleration and velocity at the highest point of projectile?

Answer:

At the highest point of a projectile, the vertical component of velocity is zero and the velocity is entirely horizontal. The direction of acceleration (due to gravity) is vertically downwards throughout the motion of the projectile.

Therefore, the angle between the direction of acceleration and velocity at the highest point of a projectile is 90 °

Displacement – A Numerical Problem

A fly is sitting in the middle of a wall of a cubic room of side ’a’.If it flies and sit to one of opposite corner of the wall. Find its displacement?

(Harmeet Singh asked)
Answer:
If the fly sit on the same wall on the horizontal, (from A to B in the diagram) the displacement is “a
If the fly sits on the diagonally opposite corner on the same wall, (from A to C in the diagram) the displacement is “√2 a
If the fly sits on the corner on the longest diagonal of the room,  (from A to H in the diagram) the displacement is “√3 a

A problem from Dynamics

The coefficient of kinetic friction between the 2.00-kg and 3.00-kg blocks
is 0.300. The horizontal surface and the pulleys are frictionless, and the masses are released from rest.
a) Draw a free-body diagram for each block.
b) Determine the acceleration of each block.
c) Find the tension in the strings.

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