A peg is located a distance h directly below the point of attachment of the cord. If h = 0.760 L, what will be the speed of the ball when it reaches the top of its circular path about the peg?

Respuesta :

Answer:

Explanation:

Given

Pivot is at h=0.76 L

Where L is the length of String

Conserving Energy at A and B

[tex]mgL=\frac{1}{2}mu^2[/tex]

where u=velocity at bottom

[tex]u=\sqrt{2gL}[/tex]

After coming at bottom the ball completes the circle with radius r=L-0.76 L

Suppose v is the velocity at the top

Conserving Energy at B and C

[tex]\frac{1}{2}mu^2=mg(2r)+\frac{1}{2}mv^2[/tex]

Eliminating m

[tex]u^2=4r+v^2[/tex]

[tex]v^2=u^2-4\cdot gr[/tex]

[tex]v^2=2gL-4g(L-0.76L)[/tex]

[tex]v^2=1.04gL[/tex]

[tex]v=\sqrt{1.04gL}[/tex]          

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