Imagine you are trying to make a ramp to move your trash cans. The 1830-NN trash cans travels with velocity of 1.8 m/sm/s at the top of a ramp which slopes downward at 22.0∘∘. The ramp applies a 515-NN kinetic friction force on each trash can, consider that the maximum static friction force would also be this number. Each trash can can compress a spring at the bottom of the ramp and will stop after traveling 5.0 mm along the ramp. When stopped, a trash can can not move back. Calculate the maximum spring force constant (k) that obey the buiding criteria.
As can stops, work done on can is equal to -ve of its initial Kinetic energy (work done = change in kinetic energy). Work done on can
By gravitational force = mgLsin(theta)
By friction = - fLcos(theta)
By spring force = - kx^2/2
mg is weight of trash cans
L is distance travelled along ramp before stopping
f is force of friction
k is spring constant
x is spring compression.
As trash does not move up, after stopping, upward spring force must be less than or equal to component of force of gravity along ramp + maximum force of static friction.
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