Answer to Question #3694 in Mechanics | Relativity for Syed Salik Ali
a) Calculate the angular velocity of the sphere when it swings through the vertical position.
b) Calculate the tension in the string at this instant.
Q-2 Two automobiles both of 1200kg and both trvelling at 30km/h collide on a frictionless icy road.They were initially moving on parallel paths in opposite directions, with a center -to -center distance of 1.0m. In the collision, the moment of inertia of this body about its center of mass is 2.5*10 power 3 kgm power 2.
a)Calculate the angular velocity of yhe wreck.
b) Calculate the kinetic energy before and after the collision. What is the change in Kinetic Energy?
(mv2)/2 = mgh
Where h is the difference of heights. Angular velocity is:
ω = v/r
Where r is the radius of a circle. In our case:
r = R/2
h=R/2 - R/2×cos45° = R/2(1-√2/2)
ω=√(8gh/R)=√(8g(R/2 (1-√2/2))/R^2) = √(4g(1-√2/2)/R)
b) Tension is the force that makes ball move downwards:
T = (mv2)/2+mg
From the a) we have v2 = 2gh
T = 2mgh/R+mg = mg(1+2h/R)
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