Ask Question
21 August, 10:46

If the 250-lb block is released from rest when the spring is unstretched, determine the velocity of the block after it has descended 5 ft. The drum has a weight of 50 lb and a radius of gyration of k0 =.5 ft about its center of mass 0

+1
Answers (1)
  1. 21 August, 14:10
    0
    1080 rpm

    Explanation:

    The drum will follow a constant acceleration for a given time and then maintain its speed.

    The constant acceleration will follow:

    w (t) = w0 + γ * t

    Where

    w0 = initial angular speed (zero in this case)

    γ = angular acceleration

    The angular acceleration will depend on the torque applied and the inertia moment of the drum

    T = γ * J

    The block will apply a torque of:

    T = P * r

    T = 250 * 0.5 = 125 lb*ft

    The drum weights 50lb, so it has a mass of

    m = P/g = 50/32.2 = 1.55 lb*s^2/ft

    The drum has a moment of inertia of

    J = 1/2 * m * r^2

    J = 1/2 * 1.55 * 0.5^2 = 0.194 lb*s^2*ft

    (remember that lb is a unit of force not mass, but lb*s^2/ft is an indirect unit of mass)

    So, the angular acceleration is

    γ = T/J

    γ = 125/0.194 = 644 rad/s^2

    Now we need to know how long will it take the block to fall 5 ft.

    Since wee know the drum has radius r = 0.5 f, we need to find how much it needs to spin to release 5 ft of rope.

    The circumference is 2π*r = 3.14 feet, it will take it 5/3.14 = 1.59 turns to release 5 feet of rope. 1.59 turns is 2π*1.59 = 10 radians.

    The equation for the rotation is:

    a (t) = a0 + w0 * t + 1/2 * γ * t^2

    a0 and w0 are zero

    10 = 1/2 * 644 * t^2

    t^2 = 0.031

    t = 0.176 s

    Then, the angular speed is:

    w (0.176) = 644 * 0.176 = 113.3 rad/s

    Which is 113.3/2π = 18 turns per second or

    18 * 60 = 1080 rpm
Know the Answer?
Not Sure About the Answer?
Find an answer to your question ✅ “If the 250-lb block is released from rest when the spring is unstretched, determine the velocity of the block after it has descended 5 ft. ...” in 📘 Engineering if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions.
Search for Other Answers