9) A 0.101 kg yo-yo has an outer radius R that is 5.60 times greater than the ra

Question

9) A 0.101 kg yo-yo has an outer radius R that is 5.60 times greater than the radius r of its axle. The yo-yo is in equilibrium if a mass m is suspended from its outer edge, as shown. Find the tension in the two strings and the mass in. 10) a) If you roll a sphere and a disc. both 10 cm in diameter and 200 g in aims, down a 2m long inclined plane that makes an angle of 10 degrees with the horizontal, which one finishes first? WHY? b) Calculate the speed of the sphere and of the disc at the bottom of the incline.

Explanation / Answer

??=0

summing torque about the center of the yo-yo
T1*r=T2*R

a fbd of the hanging weight yields
T2=m*g

T1=m*g*R/r
note that R/r=5.6
T1=m*g*5.6

sum of forces in the y=0
M*g+T2=T1

M*g+m*g=m*g*5.6
solve for m

M/(5.6-1)=m

m = 0.101/4.6
m = 0.02195 kg

T1=m*g*5.6

T1=0.0219*9.8*5.6

T1 = 1.205 N

T2 = m*g

T2 = 0.0219*9.8
T2 = 0.215 N

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