Block on slop compressing spring.

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A block with a mass of 20.0 kg is released from rest on a frictionless incline at a 30.0° angle and compresses a spring by 5.5 cm after moving down the incline. The spring can be compressed by 2.0 cm with a force of 271 N, leading to a spring constant of 13550 N/m. The block's acceleration down the incline is calculated to be 3.59 m/s², but the user is unsure how to find the initial velocity or the distance moved before touching the spring. A suggestion is made to use energy conservation principles instead of force calculations for a more straightforward solution. The discussion highlights the challenges of applying kinematic equations without initial velocity information.
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Homework Statement


A spring can be compressed 2.0 cm by a force of 271 N. A block whose mass is 20.0 kg is released from rest at the top of a frictionless incline as shown, the angle of the incline being 30.0°. The block comes to rest momentarily after it has compressed the spring by 5.5 cm. How far has the block moved down the incline at this moment? What is the speed of the block just as it touches the spring?

m = 20kg
\Theta=30

Homework Equations



K = 1/2mv^2
vf^2 = vi^2 -2a(xf-xi)

The Attempt at a Solution



How far has the block moved down the incline at this moment?
First I found K to be 271N/2cm =13550 N/m, but I'm not sure if that matters for anything

ax = mgcos(\Theta - mgsin\Theta)/m
(20*9.81cos30 - 20*9.81*sin30)/20kg = 3.59 m/s^2

I tried plugging this into vf^2 =vi^2 -2a(xf-xi) but then I realized that I don't have the initial velocity.

I'm very confused, can someone please give me a tip or some advice on what to try. I would try to find the distance to just before the spring, but I don't even know what to do since the only thing i have is the acceleration.

I would greatly appreciate some tips or advice for what I should try. Thanks
 
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Try using energy conservation. That's usually more straightforward than using forces.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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