A rubber stopper of mass m is connected by two light strings of length l to a ve
ID: 2281202 • Letter: A
Question
A rubber stopper of mass m is connected by two light strings of length l to a vertical revolving
axle. The axle is set to rotate at an angular velocity ?? causing each
string to make an angle of 45o
with the axle. Take gravity to be
directed downwards.
A) Draw a clear freebody diagram for the stopper.
B) Find the tensions T1 in the upper string and T2
in the lower
string.
A rubber stopper of mass m is connected by two light strings of length l to a vertical revolving axle. The axle is set to rotate at an angular velocity omega causing each string to make an angle of 45degree with the axle. Take gravity to be directed downwards. Draw a clear freebody diagram for the stopper. Find the tensions T1 in the upper string and T2 in the lower string.Explanation / Answer
mg + T1*cos45 = T2*cos45
T1*sin45 + T2*sin45 = mrw^2
r = L*cos45
Thus,
T2 + T1 = mL*w^2
T2 - T1 = (sqrt 2)*mg
T2 = m*[(sqrt 2)*g + Lw^2] / 2
T1 = m*[Lw^2 - (sqrt 2)*g] / 2