I\'m working some practice problems given by my teacher so I can study for a tes
ID: 2294464 • Letter: I
Question
I'm working some practice problems given by my teacher so I can study for a test and am having some problems coming up with complete answers, I'll show what answers i've come up with so far:
8 Year old Ermentrude is amusing herself by twirling her new yo-yo in a circle. The yo-yo has mass m, and the string (which is much lighter than the yo-yo) has length L. Ermentrude keeps the yo-yo goin at a constant speed v. As shown in the picture below, she tries to keep the string nearly parallel to the ground, so that the yo-yo moves in a horizontal circle at the same height as her hand. The tension in the string in this situation has magnitude T
Explanation / Answer
a) to spin in a circle
T = m v^2/L = m (1.63 v)^2/L = 1.63^2 m v^2/L
but m v^2/L = T0
T = 2.66 T0
b) T = m v^2/L = 1.63^2/0.72 mv^2/L = 3.69 T0
c) since the vertical component of tension is needed to cancel out the weight of hte yoyo
d)
sum in the x
T sin theta = mv^2/r
but r = L sin theta
T sin theta = mv^2/(L sin theta)
T = mv^2/L 1/sin(60)^2
T = T0*4/3
e) at the top of the circle
T + mg = mv^2/r
min T = 0
so m g = m v^2/r
v = sqrt( g r) = sqrt(g L)
v = sqrt(9.81*1)=3.13 m/s