Question

How do I solve this problem? I cannot figure it out for the life of me.

If you could, please put the steps! I'd like to be able to use this as a reference if possible.

Thanks in advance!

Answer 1

See below

Step-by-step explanation:

There is no friction so we will not need to calculate the Fn

we only need the Fdp = Force downplane = mgsin 36 = 69.19 N

F = ma

69.19 = 12 a a = 5.766 m/s^2

df = 3 = do + vo t + 1/2 at^2

3 = 0 + 0 + 1/2 (5.766) t^2 t = 1.02 s

vf = vo + at

vf = 0 + 5.766 ( 1.02) = 5.88 m/s

KE when it hits the spring = 1/2 (12)(5.88)^2= 207.58 J

The work of compressing the spring must equal this

Ws = 1/2 kx^2 207.58 = 1/2 (1 x10^4) x^2 shows x = .204 m

(Check my math !)