How Does a Spring System Work on an Inclined Plane?

AI Thread Summary
A spring mounted at a 29-degree angle on a frictionless incline is compressed to 15 cm to propel a 4.6 kg mass. The spring constant is given as 560 N/m, and the discussion focuses on calculating the mass's velocity as it leaves the spring and the maximum distance it will travel up the incline. Key concepts include using the spring potential energy formula W=1/2kx² and applying conservation of energy principles, considering spring potential energy, kinetic energy, and gravitational potential energy. Participants emphasize the importance of establishing a coordinate system along the incline and recognizing how the incline angle affects gravitational potential energy. The discussion seeks guidance on solving these physics problems effectively.
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Homework Statement



A spring is mounted at an angle of 29 degrees on a frictionless incline as illustrated in the figure below. The spring is compressed to 15 cm where it is allowed to propel a mass of 4.6 kg up the incline.

https://chip.physics.purdue.edu/protected/GiordanoMimg/chapter6/06P94.jpg

Homework Equations



All I am really aware of is W=1/2kx2

But i do not know where to go from there

The Attempt at a Solution



Idk..i really need some guidance..THANKS!
 
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Sorry i forgot the questions!

(a) If the spring constant is 560 N/m, how fast is the mass moving when leaves the spring?

(b) To what maximum distance from the starting point will the mass rise up the incline?
 
loosk like a good one for conservation of energy

at each point teh energy can be in 3 forms

spring potential energy, kinetic energy & gravitation potential energy

should know the formulas for each of these think about where they apply
 
i tried that and I am not getting the right answer..i figured i would have to find the velocity in x and y before i find THE velocity..but i don't know where to start with that
 
show your working then...

this should be a 1D problem, set up your coordinate system at the incline

the Grav Potential will be the only place the angle enters into
 
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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