An object with a mass of m = 5.4 kg is attached to the free end of a light strin

Question

An object with a mass of  m = 5.4 kg is attached to the free end of a light string wrapped around a reel of radius R = 0.235 m and mass of M = 3.00 kg.The reel is a solid disk, free to rotate in a vertical plane about the horizontal axis passing through its center as shown in the figure below. The suspended object is released from rest 5.00 m above the floor.

(a) Determine the tension in the string.
N

(b) Determine the magnitude of the acceleration of the object.
m/s2

(c) Determine the speed with which the object hits the floor.
m/s

An object with a mass of m = 5.4 kg is attached to the free end of a light string wrapped around a reel of radius R = 0.235 m and mass of M = 3.00 kg.The reel is a solid disk, free to rotate in a vertical plane about the horizontal axis passing through its center as shown in the figure below. The suspended object is released from rest 5.00 m above the floor. (a) Determine the tension in the string. N (b) Determine the magnitude of the acceleration of the object. m/s2 (c) Determine the speed with which the object hits the floor. m/s

Explanation / Answer

Tension T = m g - m a

Torque T = T * R = (m g - m a) * R = I * alpha = I * (a / R)

I = 1/2 m R2 = 1/2 * 3* 0.2352 = 0.0828 N.m2

a = m g / (I / R2 + m)

a = 5.4 * 9.81 / (0.0828 / 02352 + 5.4)

a = 7.68 m/s2

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Tension = 5.4 *( 9.81 - 7.68)

= 11.5 N

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v = sqrt(2 a s) = sqrt (2 * 5.0 * 7.68)

v = 8.76 m/s

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