Question

The 5-lb cylinder is falling from A with a speed vA = 10 ft/sonto the platform. Determine the maximum displacementof the platform, caused by the collision. The spring has anunstretched length of 1.75 ft and is originally kept incompression by the 1-ft long cables attached to the platform. Neglect the mass of the platform and spring and any energy lost during the collision.

Answer 1

Answer: hello some pictorial details related to your question is missing attached below is the missing detail

answer : 0.0735 ft

Step-by-step 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