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.

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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