(a) A physics experiment you may have performed involves threading a light strin

Question

(a) A physics experiment you may have performed involves threading a light string through a soda straw and then attaching a mass to each end of the string. The straw is then held vertical in one hand over your head and one mass is set into circular motion around your head while the other mass hangs straight down. If the straw edge is flared slightly at the top, the string slides almost without friction so that the tension is the same in both segments of the string. If L = 30.0 cm, the hanging mass m_A = 0.5 kg, and the orbiting mass m_B = 0.25 kg, find the angle theta the string makes with the vertical and the rotation rate (in radians per second) of the circling mass, (b) Explain why the experiment cannot be performed with two equal masses.[Answer: theta = 60 degree]

Explanation / Answer

resolving tension T into two components

one component is Horizontal component and one component is vertical component

Vertical component is balanced by weight of block B

T*cos(theta) = mB*g = 0.25*9.8

T*sin(theta) = mB*r*w^2

and aloso wrting equations of motion for mass A

T = mA*g = 0.5*9.8 = 4.9 N

then

4.9*cos(theta) = 0.25*9.8

cos(tehta) = 0.25*9.8/4.9

theta = cos^(-1)(0.5) = 60 deg

T*sin(theta) = m*r*w^2

4.9*sin(60) = 0.25*0.3*w^2

w = 7.52 rad/sec

b) if ma = mb = m

then

T*cos(theta) = mB*g

T*sin(theta) = mB*r*w^2

and T = mA*g

mA*g*cos(theta) = mB*g

cos(theta) = 1 = cos(0)

theta = 0 deg

the mass B and mass A along vertical line ,so we cannot perform teh experiment

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