Ball on a spring launched vertically: checking speed and height

[joe426]

Homework Statement

Homework Equations

Since energy is conserved, ME_inital = ME_final

The Attempt at a Solution

1/2 mv_i² + mgy_i + 1/2kx_i² = 1/2 mv_f² + mgy_f + 1/2kx_f²

After finding what equals 0, I am left with:
1/2kx_i² = 1/2mv_f² + mgy_f
v=5.97m/s

I found y_f by: mgy_f = 1/2kx_i²
y_f = 3.63m


Just checking to see if these answers are correct. THank you for the help!

 

[haruspex]

After finding what equals 0, I am left with:
1/2kx_i² = 1/2mv_f² + mgy_f
v=5.97m/s

I get a different result. Please post more details of your calculation.

 

[joe426]

I get a different result. Please post more details of your calculation.

First I found y_f, which is the answer to part b.
Since energy is being conserved, I came up with PE_f = KE_i. This seems weird because usually there is no potential energy at the final position but it was the only thing I could come up with.

mgy_f = 1/2kx_i²
y= (1/2kx_i²) / g
y=3.63m

Then,

1/2kx_i² = 1/2mv_f² + mgy_f

sqrt((kx_i² - mgy_f) / m) = v
v = 5.97m/s

 

[haruspex]

mgy_f = 1/2kx_i²
...
1/2kx_i² = 1/2mv_f² + mgy_f

Compare those two equations. Shouldn't you get v_f=0? ...

sqrt((kx_i² - mgy_f) / m) = v

.. but you didn't because you dropped a factor of 2.
For what point of the trajectory do you think you should be finding the velocity in part (a)? What is the value of y at that point.

 

[joe426]

Compare those two equations. Shouldn't you get v_f=0? ...

.. but you didn't because you dropped a factor of 2.
For what point of the trajectory do you think you should be finding the velocity in part (a)? What is the value of y at that point.

oh ok. i understand. the fastest the ball will be going is right after its released from the spring, not at its highest position in the air.

So its,
1/2mv_i² + 1/2kx_i² = mgy_f
v_i = sqrt( 2gy_f - kx_i² )

But now I'm stuck not knowing what it's final position is.

 

[joe426]

Using yfinal = 3.63m. I got the velocity to be 7m/s

 

[joe426]

Using yfinal = 3.63m. I got the velocity to be 7m/s

I am wrong. The inal position is .15m because that's how far the spring is compressed an that's how far the ball moves before its released from the spring

V= 8.3m/s for part a
Y= 3.6m for part b


Thanks for the help!