Arturo O. answered • 03/23/18

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Use energy conservation. When it is released from rest, all of its energy is gravitational potential energy. At the bottom, it is all kinetic energy. Equate the two energies, and solve for the angle.

L = length of string

θ = angle from vertical at moment of release from rest

h = height where it is released from rest

mgh = mv

^{2}/2h = L - Lcosθ = L(1 - cosθ)

gL(1 - cosθ) = v

^{2}/21 - cosθ = v

^{2}/(2gL)θ = cos

^{-1}[1 - v^{2}/(2gL)] = cos^{-1}{1 - 3.0^{2}/[2(9.8)0.8]} ≅ 64.78°Gnarls B.

Could you explain why this is the case? Gravity also supplying the centripetal force isn't making sense for me

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03/24/18

Arturo O.

Draw a free body diagram showing the forces acting on the mass when it is revolving in a vertical plane. You will see that both the tension and a component of the weight act in the radial direction, and both have to be accounted for when calculating the centripetal force. For example, at the top, both the tension and weight point down toward the center, so they both add up to the centripetal force. At the bottom, the tension and weight point in opposite directions, so their difference is the centripetal force. In between the top and bottom, you have to do a vector addition of tension and weight, accounting for the changing direction of the radius vectors.

Report

03/24/18

Arturo O.

03/23/18