Can a Spring-Propelled Mass Clear the Gap on a Frictionless Ramp?

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The discussion focuses on a physics problem involving a 5.22 kg mass on a frictionless ramp, compressed by a spring and launched to clear a gap. Participants are calculating the spring constant based on the mass's speed as it leaves the spring and determining the ramp's length required for the mass to reach a specific speed at the top. Key concepts include the conservation of energy, where potential energy in the spring converts to kinetic and gravitational potential energy as the mass ascends the ramp. The calculations involve setting up equations that account for the energy transformations, emphasizing that no work is done due to the absence of friction. The goal is to ascertain whether the mass can successfully jump the gap to the landing area.
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The picture below shows a block of mass 5.22kg held against a spring of spring constant compressed by a distance d = 28.3cm on a frictionless ramp of length . The ramp has an angle of 20°. A distance x = 1.16m separates the ramp from a landing area that is at the same height as the top of the ramp.

http://session.masteringphysics.com/problemAsset/1000182266/40/114-24-1.png

1.If the mass leaves the end of the spring at a speed of 4.43 , what is the spring constant of the spring?
2.If the mass reaches the top of the ramp moving at speed 2.81 , what is the length of the ramp?
Measure the length of the ramp from the starting point (compressed spring) as shown in the picture.
3. Does the mass successfully jump the gap and land on the other side?
I thought I could use W(work) = PEg+KE
but that is as far as I got if someone could walk me through this I would greatly appreciate it I have a final next week on this and I want to make sure I'm doing it right.
 
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What changes in energy (kinetic, potential) occur as the spring goes from compressed to uncompressed? btw, I don't see a value for L. I assume all speeds are in m/s.
 
L is the frictionless ramp of length and yes the speeds will be in m/s.

the energy in this are well Spring, Kinetic and work. Could Gravitational Energy take place as the box goes up from the spring?
 
mgerman63016 said:
L is the frictionless ramp of length and yes the speeds will be in m/s.

the energy in this are well Spring, Kinetic and work. Could Gravitational Energy take place as the box goes up from the spring?
Yes, you have to take into account the gain in potential energy. Can you quantify the above changes and thus find the velocity at end of ramp?
 
to find the velocity could I set up an equation like:

W+PEs=KE

I'm calculating now...hopefully it works
 
mgerman63016 said:
I set up an equation like: W+PEs=KE
That doesn't look quite right, but maybe it's not what you meant. The sum of the energies is constant. You start with PE in the spring and finish with gravitational PE and KE at top of ramp.
 
Since there's no Work involved because it is on a frictionless I will use PEs=KE+PEg
 

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