Respuesta :
The velocity of the block use this equation.
v = sqrt((2PE_initial - 2PE_spring)/m) = sqrt((238304 lbft - 2*(1/2)k(5 ft)^2)/(240 lb))
Potential energy is the energy possessed by an object because of its position relative to other objects, or because of its internal structure. Potential energy is often associated with the forces acting on an object, such as the gravitational force or the elastic force in a spring.
To solve this problem, we need to apply the principles of conservation of energy.
The initial potential energy of the block is given by:
PEₐ = mgh = (240 lb)(32.2 ft/s^2)(5 ft) = 38304 lb*ft
The final kinetic energy of the block is given by:
KEₓ = 1/2 * m * v^2
The total energy of the system is conserved, so the initial potential energy of the block must equal the final kinetic energy of the block plus the potential energy of the spring:
PEₐ= KEₓ + PE_spring
The potential energy of the spring is given by:
PE_spring = 1/2 * k * x^2
where k is the spring constant and x is the displacement of the spring from its equilibrium position. The displacement of the spring is equal to the distance the block has traveled, which is 5 ft.
Substituting these expressions into the equation for conservation of energy and solving for the velocity of the block gives:
v = sqrt((2PE_initial - 2PE_spring)/m) = sqrt((238304 lbft - 2*(1/2)k(5 ft)^2)/(240 lb))
Since the weight of the drum and the radius of gyration are not needed to solve this problem, we can ignore them.
To find the velocity of the block, we need to know the value of the spring constant k. Without this information, it is not possible to determine the velocity of the block
The missing part in the question is shown below.
If the 240-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 & weight of 70 Ib and a radius of (gyration of ko 0.5 ft about its center of mass 0. Express your answer to three significant fligures and include the appropriate units.
Learn more about potential energy, here https://brainly.com/question/24284560
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