Jill of the Jungle swings on a vine 5.00m plusminus 0.01m long. What is the tens

Question

Jill of the Jungle swings on a vine 5.00m plusminus 0.01m long. What is the tension in the vine at the bottom of her swing if Jill, whose mass is 60.0kg. plusminus 1.00kg is moving at 3.00m/s plusminus 0.05m/s when the vine is vertical. (The vine is vertical at the lowest point in the swing!) A free body diagram will be useful here! Show work. A conical pendulum mass is attached to a 2.00m long string. The mass moves in a circle of radius 40.0cm. You measure the period to be 2.83 s. Use the information to determine the speed of the mass and also the angle as shown in the figure. Then develop a formula (starting with Newton's 2^nd law) to determine the acceleration due to gravity at the location of this experiment. We will do uncertainty analysis in the lab. but not at the present. Your result should solve "g" in terms of radius, speed, and the tangent of the angle. Determine g. Formula for g: g = Your numerical result for g = _______

Explanation / Answer

speed = distance / time

v = 2*pi*r/T = 2*pi*0.4/2.83 = 0.888 m/s

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from the figure

sintheta = r/L

r = radius

L = lenght of the string

sintheta = 0.4/2

theta = 11.5 degrees

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along vertical

T*costheta = m*g

along horizontal

T*sintheta = m*v^2/r

tantheta = v^2/rg

g= v^2/(r*tantheta)

g = 0.888^2/(0.4*tan11.5)

g = 9.68 m/s^2

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