Spring and conservation of energy

[cap.r]

Homework Statement

a spring is pulled back .2 meters and a ball is fired. the ball travels 5 meters before stopping 1.5 meters bellow it's firing position which was on a table. there is a picture that I have drawn and attached in a pdf. I have also listed all the givens except the mass. i forgot to do that one. the mass is given and is 1kg.

Homework Equations

conservation of energy.
1/2kx^2 = 1/mv^2

The Attempt at a Solution

also attached in the pdf. i figured it would be easier since there is a picture and lots of equations.

only allowed to use conservation of energy and momentum. also straight line motion stuff. no calc.

 

[Doc Al]

Looks OK to me. You started out with: 1/2kx² + mgh = 1/2mv², which is true but not helpful. You then switched to 1/2kx² = 1/2mv_x², which is better.

 

[cap.r]

but the big assumption i made was that tx=ty here. the ball travels on the surface of the table and then falls off... so only then does it start traveling in the y direction. so wouldn't the ty timer start ticking when this happens? which is long after the tx timer has started... or do both timers start when the projectile starts and the y direction just breaks into two problems with different accelerations?

 

[Doc Al]

I think I see what you're asking. When you compute the speed using V_x = Δx/t_y, the Δx should be measured from the table edge (where the ball leaves the table), not the starting point back at the spring. And t_y is the time it takes to fall, also measured from the moment the ball leaves the table.