# Ball and a spring#

I have built a game that involves a spring, a smooth slope, and a little ball of $$m =$$0.2 kg. The slope is 24$$^{\circ}$$ above the horizontal. The spring is placed into a small hole such that when it is compressed to the proper starting position, and the ball is placed upon it, the ball will be at the height $$h =$$0 m. The spring has been compressed by 3 cm and has a spring constant of $$k =$$800 N/m.

## Part 1#

When I press a button, the ball is pushed up the slope by the spring. How fast is the ball traveling when it is 0.05 m up the slope?

Please enter in a numeric value in $$m{m/s}$$.

## Part 2#

How fast is the ball traveling when it is 0.1 m up the slope?

Please enter in a numeric value in $$m{m/s}$$.

## Part 3#

What is the maximum DISTANCE the ball reaches from the bottom of the slope?

Please enter in a numeric value in $$m{m}$$.

## Part 4#

Calculate the acceleration of the ball as it goes UP the slope once it is beyond the spring?

You may draw a free body diagram in order to help you write the final acceleration vector in terms of $$\hat\imath$$ (pointing down-slope) and $$\hat\jmath$$ (pointing perpendicular to the slope). Enter answer as a symbolic expression (sin(30) instead of 0.86602).

For

Use

$$\hat\imath$$

i_hat

$$\hat\jmath$$

j_hat

$$g$$

g