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Fera09
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Homework Statement
You are designing a delivery ramp for crates containing exercise equipment. The crates of weight 1480 N will move with speed 2.1 m/s at the top of a ramp that slopes downward at an angle 23.0 degrees. The ramp will exert a 578 N 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 8.0 m along the ramp; this distance includes x. 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.
Homework Equations
hinital= (sin23=h/8) = 3.126
hfinal= 0
(spring)xinitial= 0
(spring)xfinal= ?
vfinal= 0
vinitial= 2.1
Wfriction = Ffriction * Distance
Change in gravitational potential energy = mghfinal-mghinitial
Change in elastic potential energy = (1/2)kxfinal2 - (1/2)kxinitial2
Change in Kinetic Energy = (1/2)mvfinal2-(1/2)mvinitial
The Attempt at a Solution
Since the final velocity, final height, and initial x for the spring are all equal to zero I got the equation..
Wfriction + mghinital + (1/2)mvinital2 = (1/2)kxfinal2
And then I solved for k..
k= (2(Wfriction+mghinital+(1/2)mvinitial2))/x2I don't know if what I did it's right, but if it is.. I can't solve for k since I don't know x, the distance that the spring compressed, and I don't know how to find it =[[
Help pleaseee