Need physics help to find the displacement in the following figure.

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Nov 16th, 2015

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First, we can find the speed of the first ball at its bottom through conservation of energy

mgh = .5mv^2 (mass cancels)

(9.8)(.1) = (.5)v^2

v = 1.4 m/s

Then through conservation of momentum we can find the speed the two will have after the collision

(2)(1.4) = (5)(v)

v = .56 m/s

That is the preliminary information we need...

Part A)

To find the frequency, apply  \(T = 2\pi\sqrt{l/g}\)

T = (2pi)(.5/9/8)^.5

T = 1.42 sec

The frequency is the inverse of that. 1/1.42 = .705 Hz

Part B)

Now we can find how high the two masses travel after the collision

mgh = .5mv^2 (again mass cancels)

(9.8)(h) = (.5)(.56)^2

h = .016 m (1.6 cm)

From that, we can find the angular displacement

The hypotenuse is 50 cm

The opposite side from by the triangle made is 50 -1.6 = 48.4 cm

cos(angle) = 48.4/50

angle = 14.53 degrees

Please let me know if you need any clarification. I'm always happy to answer your questions.
Nov 16th, 2015

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