Q. Two particles of mass m are connected by a light rope on a sphere shown in figure.It can move within the guide after a quarter circular shape .Find the speed of the masses when the upper mass...

Q. Two particles of mass m are connected by a light rope on a sphere shown in figure.It can move within the guide after a quarter circular shape .Find the speed of the masses when the upper mass just leaves the guid.

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steveschoen | College Teacher | (Level 1) Associate Educator

Posted on

Hi, 8235,

For the top ball to leave the sphere, it has to overcome its weight, m*g.  To do that, the necessary force would come from the balls spinning.  That force would be:

Fc = mass * acceleration = m * (v^2  /R)

But, then, with these balls being connected by a string a quarter of a sphere apart, it means the balls will always be 45 degrees apart.  Or, the Fc would be acting in a 45 degree angle.  Thus:

Fc = mass * acceleration = m * (v^2  /R) * cos 45

Fc = centripetal force

v = linear speed

So, now, this needs to be equal to the weight of the ball:

Fc = m*g

m*g = m * (v^2  /R) cos 45

The masses cancel out.  We can multiply by r/cos 45.

g*R/cos 45 = v^2

Then, take the square root:

sqrt (g*R/cos 45) = v

So, that would be the velocity of the balls just before the top ball comes off the sphere.

Good luck, 8235.  I hope this helps.

Till Then,

Steve

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