## 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

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.

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?