(Use energy conservation to answer the following question.) A mass is attached t

Question

(Use energy conservation to answer the following question.)

A mass is attached to one end of a massless string, the other end of which is attached to a xed support. The

mass swings around in a vertical circle as shown in the gure. Assuming that the mass has the minimum speed

necessary at the top of the circle to keep the string from going slack, at what location should you cut the string

so that the resulting projectile motion of the mass has its maximum height located directly above the center of the circle?

Please show work, thank you!

A mass is attached to one end of a massless string, the other end of which is attached to a xed support. The mass swings around in a vertical circle as shown in the gure. Assuming that the mass has the mini mu m speed necessary at the top of the circle to keep the string from going slack, at what location should you cut the string so that the resulting projectile motion of the mass has its maxi mu m height located directly above the center of the circle?

Explanation / Answer

Vmin = sqrt(gl)

at theta speed = V1

mg(l-lcos(theta)) = 0.5*m*(v1^2-gl)

3gl- 2glcos(theta) = v1^2

Range = v1^2sin(2theta)/2g = 2lsin(theta)

v1^2*cos(theta)/2g = l

3gl-2glcos(thea) = 2gl

cos(theta) = 1/2

theta + 60deg

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