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

grav potential energy

the minimum amperage that the current in this wire would have to have so that its weight is completely supported by the magnetic force due to earth's field, assuming that no other forces except gravity act on it