Answer: hello some pictorial details related to your question is missing attached below is the missing detail
answer : 0.0735 ft
Explanation:
weight of cylinder = 5 IB
speed ( v ) = 10 ft/s
Calculate the maximum displacement of platform
Express the initial energy of the system as
potential energy of cylinder + potential energy of spring + Kinetic energy of cylinder
= mgh + 1/2 ky^2 + 1/2 mv^2
y = initial spring compression = 1.75 - 1 = 0.75
hence the initial energy can be expressed as
= 5 ( 3 + x ) + 1/2 (400)(0.75)^2 + 1/2 ( 5/32.2) (10)^2 ------------ ( 1 )
Next : determine the Final energy of the system
Final energy of the system = potential energy of the system
= 1/2 k ( x + 0.75 )^2 ----- ( 2 )
Equating equations ( 1 ) and ( 2 ) to determine the value of x
5 ( 3 + x ) + 1/2 (400)(0.75)^2 + 1/2 ( 5/32.2) (10)^2 = 1/2 k ( x + 0.75 )^2
solve for x
x ( max displace of platform ) = 0.0735 ft
