Mechanics | Relativity Answers

A ball of mass 50 g tied to the end of a 50 cm inextensible string is whirled around in a vertical circle. Find the tension in the string when the ball is at the top of the circle. Take
g=10m=s2

7 Given that the mass and radius of Jupiter are respectively
1:90×1027
kg and
7:15×104
km, calculate the escape velocity from the surface of the planet

What is the orbital radius and speed of a synchronous satellite which orbits the earth once every 24h? Take
G=6:67×10−11Nm2=kg2
, Mass of the earth is
5:98×1024
kg

A 2000 kg satellite orbits the earth at a height of 300 km. What is the speed of the satellite and its period? Take
G=6:67×10−11Nm2=kg2
, Mass of the earth is
5:98×1024

A cyclist and cycle have a combined mass of 78 kg as they accelerate along a race track at 2.5 m/s2. Calculate the fore exerted as they accelerate. ( F= 195 N ) I solved this , but I do not know other one, which is :
A lift of mass 400 kg is accelerated upwards at 2 m/s2. calculate the force in the rope pulling.

Please help me. Many thanks

Explain the cause of the components accelerating from rest down the conveyor.

Establish the differential equation for damped harmonic oscillator and obtain its solution.
Show that the damped oscillator will exhibit non-oscillatory behaviour if the damping is
heavy.

Consider a system of three equal mass particles moving in a plane; their positions are given by
ˆi ˆj
i i a + b .
For particle 1, 3 4, 1 0
2
a1 = t + b =
For particle 2, a2 = 7t + 5, b2 = 2
For particle 3, a3 = 2t, b3 = 3t + 4
Determine the position and velocity of the centre of mass as functions of time.

A light thread with a mass m tied to its end is wound over a uniform solid cylinder of radius R
and mass M and the system is set into motion at t = 0. Obtain the angular velocity of the cylinder.

A body of mass 0.5 kg travels in a straight line with velocity V = ax3/2 where a = 5 m1/2s1. Find the work done by the net force during its displacement from x = 0 to x = 2 m is :-
(1)1.5 J
(2)50 J
(3)10 J
(4)100 J