Question

# Imagine you are trying to make a ramp to move your trash cans. The 1830-NN trash...

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. 