Expressing speed with variables

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SUMMARY

The discussion centers on calculating the speed of a ball launched from a ramp attached to a spring mechanism. The initial speed of the ball when leaving the ramp is derived using the formula sqrt((ks^2)-2(mgy))/m. The subsequent challenge involves determining the speed of the ball upon impact with the floor, requiring an understanding of gravitational potential energy and kinetic energy principles. Participants emphasize the importance of theoretical understanding alongside calculations to solve the problem effectively.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Knowledge of spring mechanics, specifically spring constant (k)
  • Familiarity with gravitational potential energy (mgy)
  • Basic principles of energy conservation in physics
NEXT STEPS
  • Research energy conservation principles in mechanics
  • Learn about projectile motion and its equations
  • Study the relationship between potential energy and kinetic energy
  • Explore advanced spring dynamics and their applications
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone involved in mechanics or engineering who seeks to deepen their understanding of energy transformations and motion dynamics in spring systems.

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Homework Statement


A child's toy consists of a block that attaches to a table with a suction cup, a spring connected to that block, a ball, and a launching ramp. The spring has a spring constant k, the ball has a massm , and the ramp rises a height y above the table, the surface of which is a height H above the floor.

Initially, the spring rests at its equilibrium length. The spring then is compressed a distance s, where the ball is held at rest. The ball is then released, launching it up the ramp. When the ball leaves the launching ramp its velocity vector makes an angle with respect to the horizontal.

Throughout this problem, ignore friction and air resistance.


Homework Equations



The first problem told me to calculate the speed of the ball when it leaves the launching ramp.

I got sqrt((ks^2)-2(mgy))/m
This was correct but on the next problem it is asking me with what speed will the ball hit the floor? All of this is in terms of k,s,m,g,y,or H

I have no idea where to start. My teacher does this to us every week without teaching us a thing
 
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Well, you know m, g, and h right? That should give you a bit to get started on. You shouldn't have to concern yourself with the speed at which it comes off of the inclined plane. You might want to look at more of the theory behind the problem that just the calculations.

hope this helps somewhat
 

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