DOM JSON App TeX Focus Test Problem 7.54 Part A Submit Hints My Answers Give Up

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DOMJSONAppTeXFocusTest Problem 7.54 Part A SubmitHintsMy AnswersGive UpReview Part Incorrect; Try Again; 9 attempts remaining Incorrect; Try Again; 9 attempts remaining Incorrect; Try Again; 9 attempts remaining Provide FeedbackContinue of 0 of 0           Phys2325 F13

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                      m8 energy              Problem 7.54              ResourceseTextConstantsStudy Area                 Phys2325 F13

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                      m8 energy              Problem 7.54              ResourceseTextConstantsStudy Area                 Phys2325 F13

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          m8 energy              Problem 7.54              ResourceseTextConstantsStudy Area       m8 energy              Problem 7.54    m8 energy              Problem 7.54    ResourceseTextConstantsStudy Area ResourceseTextConstantsStudy Area Problem 7.54 You are designing a delivery ramp for crates containing exercise equipment. The crates of weight 1490N   will move with speed 1.9m/s   at the top of a ramp that slopes downward at an angle 23.0 ? . The ramp will exert a  582N   force of kinetic friction on each crate, and the maximum force of static friction also has this value. At the bottom of the ramp, each crate will come to rest after compressing a spring a distance x .  Each crate will move a total distance of 7.9m   along the ramp ; this distance includes x . Once stopped, a crate must not rebound back up the ramp. Part A Calculate the maximum force constant of the spring k max that can be used in order to meet the design criteria. SubmitHintsMy AnswersGive UpReview Part Incorrect; Try Again; 9 attempts remaining Provide FeedbackContinue k max = N/m of 0              Phys2325 F13

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                      m8 energy              Problem 7.54              ResourceseTextConstantsStudy Area       You are designing a delivery ramp for crates containing exercise equipment. The crates of weight 1490N will move with speed 1.9m/s at the top of a ramp that slopes downward at an angle 23.0? The ramp will exert a 582N force of kinetic friction on each crate, and the maximum force of static friction also has this value. At the bottom of the ramp, each crate will come to rest after compressing a spring a distance x. Each crate will move total distance of 7.9m along the ramp this distance includes Once stopped, a crate must not rebound back up the ramp Calculate the maximum force constant of the spring k max that can be used in order to meet the design criteria.

Explanation / Answer

the distance x compressed by the block should be such that the force exerted by the spring balances the frictional and gravitational forces.so,

spring force=kx

frictional force=582 N

gravitational force along the incline=1490 sin(23)

=582.189 N

so kx=582+582.189

also we need to conserve energy,

inital energy=final energy+energy lost due to friction

or 0.5*(1490/9.81)*1.9^2 + 3.08*9.81*(1490/9.81) = 0.5*k*x^2+ 582*7.9

so K=2551.9 N/m

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