An object of 51.5 N is attached to thefree end of a light string wrapped around

Question

An object of 51.5 N is attached to thefree end of a light string wrapped around a reel with a radius of0.250 m and mass of 3.00 kg. The reel is a solid disk, free torotate in a vertical plane about the horizontal axis passingthrough its center. The suspended object is released 5.50 m above the floor. (a) Determine the tension in the string, theacceleration of the object, and the speed with which the objecthits the floor. tension 1 N acceleration 2 m/s2 speed 3 m/s
(b) Verify your answer by using the principle of conservation ofenergy to find the speed with which the object hits the floor.
4 m/s (a) Determine the tension in the string, theacceleration of the object, and the speed with which the objecthits the floor. tension 1 N acceleration 2 m/s2 speed 3 m/s
(b) Verify your answer by using the principle of conservation ofenergy to find the speed with which the object hits the floor.
4 m/s tension 1 N acceleration 2 m/s2 speed 3 m/s

Explanation / Answer

(a)    in the given problem we can see that for thecounter weight we get     Fy = m ay    51.5 - T = (51.5 / 9.8) a    for the reel we get     = I    T R = I           =I (a / R)    where I = (1 / 2) M R2                = ......... kg . m2    substitute to eliminate theacceleration    solve for a and T    vf2 =vf2 + 2 a (xf -xi)    vf = [2 (a) (5.50)]        = ........ m / s (b)    here we use the conservation of energy forthe system of object, reel and the earth so that we get    (K + U)i = (K + U)f    m g h = (1 / 2) m v2 + (1 / 2) I2    2 m g h = m v2 + I(v2 / R2)                = v2 [m + (I / R2)]    so that the speed will be    v = [2 m g h / (m + (I /R2))]       = ......... m / s    m g h = (1 / 2) m v2 + (1 / 2) I2    2 m g h = m v2 + I(v2 / R2)                = v2 [m + (I / R2)]    so that the speed will be    v = [2 m g h / (m + (I /R2))]       = ......... m / s    2 m g h = m v2 + I(v2 / R2)                = v2 [m + (I / R2)]    so that the speed will be    v = [2 m g h / (m + (I /R2))]       = ......... m / s

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