Jill of the Jungle swings on a vine 500m PlusMinus 0.01m long. What is the tensi

Question

Jill of the Jungle swings on a vine 500m 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 F_Tension= ______ PlusMinus ______N 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

1] Applying newtons second law,

T - mg = mv^2/r

T = mg + mv^2/r

= 60*9.8+60*3^2/5 = 696 N

dT = g*dm + dm*v^2/r + m*[[2vr dv - v^2 dr]/r^2]

= 9.8*1 + 1*3^2/5 + 60*[[2*3*0.05 + 3^2*0.01]/5^2]

= 12.5 N

T =  696 +/- 12.5 N

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