A block of mass m_1 is attached to a cord of length L_1, which is fixed at one e

Question

A block of mass m_1 is attached to a cord of length L_1, which is fixed at one end. The block moves in a horizontal circle on a frictionless tabletop. A second block of mass m_2 is attached to the first by a cord of length L_2 and also moves in a circle on the same frictionless tabletop, as shown below. If the period of the motion is T, find the tension in each cord in terms of the given symbols. (Use any variable or symbol stated above as necessary. Ignore the width of the blocks.) T_1 = 69.1 (cord of length L_1) T_2 = (cord of length Z_2) Draw free-body diagrams showing the four forces acting on the inner block and the three forces acting on the outer block. Use Newton's second law and the definition of centripetal acceleration to relate these forces to each other and to the masses and accelerations of the blocks.

Explanation / Answer

Here ,

angular speed of the motion ,

w = 2pi/T

for the mass m2

T2 = m2 * w^2 * (L1 + L2)

T2 = m2 * (2pi/T)^2 * (L1 + L2)

the tension T2 is m2 * (2pi/T)^2 * (L1 + L2)

for the mass m1

T1 - T2 = m1 * (2pi/T)^2 * L1

T1 = m2 * (2pi/T)^2 * (L1 + L2) + m1 * (2pi/T)^2 * L1

the tension T1 is m2 * (2pi/T)^2 * (L1 + L2) + m1 * (2pi/T)^2 * L1

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