You are designing a delivery ramp for crates containing exercise equipment. the 1470 n crates will move at 1.8 m/s at the top of a ramp that slopes downward at 22.0°. the ramp exerts a 515 n kinetic friction force on each crate, and the maximum static friction force also has this value. each crate will compress a spring at the bottom of the ramp and will come to rest after traveling a total distance of 5.0 m along the ramp. once stopped, a crate must not rebound back up the ramp. calculate the largest force constant of the spring that will be needed to meet the design criteria.

K = 25351. 69 N / m

Explanation:

Given : Fk = 515 N , v = 1.8 m /s  , d = 5.0 m , β = 22.0 ° , m = 150 kg

Using the work done by all forces at initial and the end can determine the constant of the spring

Ws + We - Fk = Em - Ef

- ¹/₂ * K * x²  + m*g*h - F*d = 0 - ¹/₂ * m * v²

Also the round motion part

K* x = F + We

K * x = F + m*g*h

Replacing numeric to equal the equations and find the constant

¹/₂ * K * x² = 150*9.8* 5* sin (22°) - 5150* 5 + ¹/₂*150*(1.8m/s)²

K * x² = 421.358

Now use the other equation

K * x = 515 + 150*9.8* sin(22°)

K * x = 3268.35

Both equation give x' as a

x = 0.1289 m now using in any equation can find K

K = 25351. 69 N / m

the order for strong to weak forces such as

strong nuclear force → electromegnetic force → weak nuclear force → gravitational force

the fundamental forces are those forces that act between to objects or element to make interactions. there are four types of fundamental forces such as strong and weak nuclear forces (due to protons and electrons), electromagnetic force (due to the motion of electrons) and gravitational force (due to orbital movement of the planet). if these forces are arranged on the basis of their maximum strength then the order is

strong nuclear force → electromegnetic force → weak nuclear force → gravitational force

i would say