Question
10. A yo-yo is made by wrapping a 2-m long string around a 500-g 10-cm diameter uniform disk. The string is fastened to the ceiling, and the yo-yo is released. What is the tension in the string as the yo-yo falls?
A.9.8N
B.1.6N
C.4.9N
D. 0.49N
E.3.3N
The answer is B. How do I get this answer? I'm having trouble figuring out why tension would be less than (mg). Thank you in advance.
A.9.8N
B.1.6N
C.4.9N
D. 0.49N
E.3.3N
The answer is B. How do I get this answer? I'm having trouble figuring out why tension would be less than (mg). Thank you in advance.
Answers
Tension = T
force up = T
force down = m g
m g - T = m a
torque = I * angular acceleration
T * R = I alpha = I a/R
but I for disk = (1/2) m R^2
so
T R = (1/2) m R a
T = (1/2) m a interesting :)
so
m g - (1/2) m a = m a
g = (3/2) a
a = (2/3) g
so
T = (1/2) m (2/3) g = (1/3) m g
= (1/3)(0.5)(9.81)
= 1.63 N or B
force up = T
force down = m g
m g - T = m a
torque = I * angular acceleration
T * R = I alpha = I a/R
but I for disk = (1/2) m R^2
so
T R = (1/2) m R a
T = (1/2) m a interesting :)
so
m g - (1/2) m a = m a
g = (3/2) a
a = (2/3) g
so
T = (1/2) m (2/3) g = (1/3) m g
= (1/3)(0.5)(9.81)
= 1.63 N or B
T-tension, M –torque,
I = mR²/2 -moment of inertia of disc
ε-angular acceleration
T•R= M
I•ε =M
ε =a/R
I•a/R = T•R,
a=TR²/I= 2TR²/mR²=2T/m,
ma=mg-T
m•2T/m = mg-T,
T=mg/3 =0.5•9.8/3 = 1.63
ANS: B
I = mR²/2 -moment of inertia of disc
ε-angular acceleration
T•R= M
I•ε =M
ε =a/R
I•a/R = T•R,
a=TR²/I= 2TR²/mR²=2T/m,
ma=mg-T
m•2T/m = mg-T,
T=mg/3 =0.5•9.8/3 = 1.63
ANS: B
Related Questions
A long string is wrapped around a 6.2cm diameter cylinder, initially at rest, that is free to rotate...
A toy top consists of a rod with a diameter of 13.00 mm and a disk of mass 0.0160 kg and a diameter...
A student uses a 2.00-m-long steel string with a diameter of 0.90 mm for a standing wave experiment....